=Paper= {{Paper |id=Vol-1151/paper4 |storemode=property |title=From Changes to Dynamics: Dynamics Analysis of Linked Open Data Sources |pdfUrl=https://ceur-ws.org/Vol-1151/paper4.pdf |volume=Vol-1151 |dblpUrl=https://dblp.org/rec/conf/esws/DividinoGSG14 }} ==From Changes to Dynamics: Dynamics Analysis of Linked Open Data Sources== https://ceur-ws.org/Vol-1151/paper4.pdf
    From Changes to Dynamics: Dynamics Analysis of
             Linked Open Data Sources

       Renata Dividino1 , Thomas Gottron1 , Ansgar Scherp2 , and Gerd Gröner3
                     1
                      WeST – Institute for Web Science and Technologies
                           University of Koblenz-Landau, Germany
                 {dividino,scherp,gottron}@uni-koblenz.de
       2
         Kiel University and Leibniz Information Center for Economics, Kiel, Germany
                     {ansgar}@informatik.uni-mannheim.de
                      3
                        Paluno – University of Duisburg-Essen, Germany
                        {gerd.groener}@paluno.uni-due.de



       Abstract The Linked Open Data (LOD) cloud changes frequently. Recent ap-
       proaches focus mainly on quantifying the changes that occur in the LOD cloud
       by comparing two snapshots of a linked dataset captured at two different points in
       time. These change metrics are able to measure absolute changes between these
       two snapshots. However, they cannot determine the dynamics of a dataset over a
       period of time, i.e., the intensity of how the data evolved in this period. In this
       paper, we present a general framework to analyze the dynamics of linked datasets
       within a given time interval. We propose a function to measure the dynamics
       of a LOD dataset, which is defined as the aggregation of absolute, infinitesimal
       changes, provided by change metrics. Our method can be parametrized to in-
       corporate and make use of existing change metrics. Furthermore, our framework
       enables the use of different decay functions within the dynamics computation for
       different weights on changes depending on when they occurred in the observed
       time interval. We apply our framework to conduct an investigation on the dynam-
       ics of selected LOD datasets. We apply our analysis on a large-scale LOD dataset
       that is obtained from the LOD cloud by weekly crawls over more than a year. Fi-
       nally, we discuss the benefits and potential applications of our dynamics function
       in a real world scenario.


1   Introduction

The Linked Open Data (LOD) cloud is a global information space to structurally re-
present and connect data. The LOD principles provide a flexible publishing paradigm
to integrate and interlink any kind of data from arbitrary datasets, published by various
data providers. From the time the Linked Open Data principles have been created until
now, the LOD cloud has grown significantly and is a place of continuous changes.
    Knowledge about these changes and especially about the change behavior of a
dataset over time, i.e., the dynamics of a dataset, is important for many purposes and
applications involving Linked Data such as data caching [18], indexing of distributed
data sources [13], searching in large graph databases [9], optimizing the execution of
queries [14] and recommending appropriate vocabularies to Linked Data engineers [16].
2

For example, as the data changes, caches and indexes that rely on this data need to be
updated since they do no longer reflect the current state of the data anymore. Umbrich
et al. [18] proposed a hybrid query execution engine that takes into account the knowl-
edge if a dataset is rather static or dynamic in order to automatically decide whether
data is retrieved from caches or from the LOD cloud. Caches are created only for data
from static datasets. Therefore, knowledge about the level of dynamics for different
data sources is vital to make best use of the resources available for computing caches or
performing index updates (e. g., network bandwidth for crawling, computation time).
     In related work, changes of LOD sources are analyzed w.r.t. their sets of triples,
sets of links, sets of entities, or schema signatures. For example, given two snapshots
of a dataset captured at two different points in time, the change analysis at the triple
level includes which triples from the previous snapshot have been preserved in the later
snapshot, which triples have been deleted, or which ones have been added. For instance,
in [6] snapshots of a dataset were analyzed with respect to their set of domain entities,
i.e. it was verified if the set of entities described in the datasets has changed. In [7], the
authors measure changes with respect to usage of the schema information of a dataset.
Käfer et al. [12] quantify changes w.r.t the set of triples, set of links, schema signature.
While these kinds of analyses are capable to quantify changes of a dataset captured at
two different points in time, they do not really grasp the dynamics of a dataset.
     The dynamics of a dataset involves a notion of how “fluid” a dataset is, i. e., how
it behaves and evolves over a certain period of time. In the context of this paper, we
understand a period of time to be a continuous time interval beginning at an initial point
in time up to a final one. Therefore, the dynamics of a dataset involves the analysis of its
development over more than two points in time. Due to this time-dependence a measure
for dynamics should capture the frequency, degree and regularity of the changes of the
data. To the best of our knowledge, there is no established method for measuring the
dynamics of LOD datasets.
     To fill this gap, we present a formal notion of dynamics for LOD datasets. First,
we define dynamics as an aggregation of changes, built on top of contemporary change
metrics. Then we extend this notion to incorporate the use of different decay functions
for stressing or weakening periods within a time interval. Finally, we analyze the dy-
namics of different LOD datasets obtained via weekly crawls from the period between
May, 2012 and November, 2013. We compute the dynamics of these datasets and com-
pare their change behavior over time. The notion of dynamics has benefits and potential
impact in different real world scenarios, which we discuss before concluding the paper.


2   Motivating Scenario

Let us introduce a toy example to illustrate the differences between change and dynam-
ics analysis on LOD datasets. In this example, we describe three snapshots of a dataset
captured at three distinct points in time t1 , t2 , and t3 . We are using the FOAF vocabulary
for describing persons working at the University of Koblenz-Landau, the University of
Kiel, and the University of Duisburg, all of them located in Germany. In addition, we de-
scribe relations between persons and their associations to different projects. Besides the
FOAF vocabulary, we use domain-specific LOD vocabularies under the domain of uni-
                                                                                             3




                        Table 1. Scenario: Example dataset at time t1 .


@prefix                    uni-koblenz:         .
@prefix                    uni-duis:            .
@prefix                    rdf:                 .
@prefix                    foaf:                .
uni-duis:GerdGroener       rdf:type            foaf:Person .
uni-duis:GerdGroener       foaf:knows          uni-koblenz:RenataDividino .
uni-koblenz:RenataDividino foaf:name           "Renata Dividino".
uni-koblenz:RenataDividino foaf:knows          uni-duis:GerdGroener .
uni-koblenz:ThomasGottron uni-koblenz:worksFor uni-koblenz:Robust .
uni-koblenz:ThomasGottron foaf:knows           uni-koblenz:RenataDividino.


                        Table 2. Scenario: Example dataset at time t2 .

@prefix                    uni-koblenz:         .
@prefix                    uni-duis:            .
@prefix                    uni-kiel:            .
@prefix                    rdf:                 .
@prefix                    foaf:                .
uni-duis:GerdGroener       rdf:type            foaf:Person .
uni-duis:GerdGroener       foaf:knows          uni-koblenz:RenataDividino .
uni-duis:GerdGroener       foaf:knows          uni-kiel:AnsgarScherp.
uni-kiel:AnsgarScherp      rdf:type            foaf:Person .
uni-kiel:AnsgarScherp      foaf:name           "Ansgar Scherp" .
uni-koblenz:RenataDividino foaf:name           "Renata Dividino".
uni-koblenz:RenataDividino foaf:knows          uni-duis:GerdGroener .
uni-koblenz:RenataDividino foaf:knows          uni-koblenz:ThomasGottron.
uni-koblenz:ThomasGottron foaf:mbox            mailto:Gottron@uni-koblenz.de.
uni-koblenz:ThomasGottron foaf:knows           uni-koblenz:RenataDividino.
uni-koblenz:ThomasGottron foaf:knows           uni-kiel:AnsgarScherp.
uni-koblenz:ThomasGottron uni-koblenz:worksFor uni-koblenz:Robust .


                        Table 3. Scenario: Example dataset at time t3 .

@prefix                    uni-koblenz:         .
@prefix                    uni-duis:            .
@prefix                    rdf:                 .
@prefix                    foaf:                .
uni-duis:GerdGroener       rdf:type            foaf:Person .
uni-duis:GerdGroener       foaf:knows          uni-koblenz:RenataDividino .
uni-koblenz:ThomasGottron foaf:knows           uni-koblenz:RenataDividino.
uni-koblenz:ThomasGottron uni-koblenz:worksFor uni-koblenz:Robust .
uni-koblenz:RenataDividino foaf:name           "Renata Dividino".
uni-koblenz:RenataDividino foaf:knows          uni-duis:GerdGroener .
4

koblenz.de, uni-kiel.de and uni-duis.de for modeling persons and projects. For instance,
there are entities like uni-koblenz:ThomasGottron and uni-koblenz:RenataDividino that
are connected via a foaf:knows property. Table 1 summarizes the RDF triples published
in the first snapshot of the dataset at time t1 .
    At time t2 , the same data is visited again. Table 2 shows the RDF triples of this new
snapshot. We can directly observe changes in the triples between these two snapshots.
In the second snapshot, we observe six new RDF triples (see highlighted triples in
Table 2). Table 3 summarizes the RDF triples of the third and last snapshot at time t3 .
This snapshot contains the same set of triples as the first one.
    Existing metrics proposed in the literature are able to quantify changes for every
pair of snapshots of a dataset. For the sake of simplicity, we apply a very simple metric
in this example, which only counts the additions, deletions and changes between the set
of triples from the first and the second snapshot. In this case, there are six new triples
over the total of all triples. The same amount of changes is observed when comparing
the second and third snapshot. However, since the first and the third snapshot contain
the same set of triples, we cannot observe any changes under the considered metric. The
direct comparison of the first and third snapshot of the dataset ignores the changes in
the second snapshot.
    In this paper, we argue that the consideration of the changes in the second snapshot
is of great importance to the analysis of the dataset dynamics in the time period ranging
from t1 to the t3 . Otherwise, when ignoring this evolution the true dynamic character of
the dataset is neglected. In the following sections, we systematically introduce metrics
of changes and present a formalization of how to incorporate them into our notion of
dataset dynamics.


3   LOD Change Analysis

In the literature, many change metrics have been proposed for analyzing RDF data
of LOD [12,7,6,8]. These metrics essentially quantify the changes that occurred in a
dataset by comparing two snapshots of this dataset. Our goal is to re-use such metrics
and to incorporate them as parameter in our framework for measuring dynamics of a
LOD dataset (introduced in the subsequent Sec. 4).
    We will denote a change metric as a function ∆. Basically, such a ∆-function is
a metric that quantifies changes between two datasets, i.e., it is a function that deter-
mines the difference (or distance) between two datasets. Without loss of generality, in
this paper, we restrict ∆-metrics to determine the difference between two RDF datasets.
For instance, changes between two datasets can be measured by the number of differ-
ences between the set of triples of these datasets (such as additions and deletions of
RDF triples). Please note that our framework for measuring the datasets dynamics can
be parametrized to make use of any existing change metrics that satisfies the formal
requirements listed below.

Definition 1. Let S be the set of all possible RDF datasets. A change metric is a func-
tion ∆ : S × S → R that maps two RDF datasets to a real number and satisfies the
following conditions (for X1 , X2 and X3 being RDF datasets).
                                                                                            5

  (i) positivity: ∆(X1 , X2 ) ≥ 0
 (ii) symmetry: ∆(X1 , X2 ) = ∆(X2 , X1 )
(iii) identity of indiscernibles: ∆(X1 , X1 ) = 0 and
(iv) triangle inequality: ∆(X1 , X3 ) ≤ ∆(X1 , X2 ) + ∆(X2 , X3 )

Example 1 (Jaccard distance as change metric). The Jaccard Distance ∆Jaccard between
two RDF sets satisfies the requirements of Definition 1. Let X1 and X2 be the two RDF
datasets presented in Table 1 and Table 2, then the Jaccard distance between the set of
triples of X1 and X2 evaluates to:

                                                     |X1 ∩ X2 |
                             ∆Jaccard (X1 , X2 ) =1 −
                                                     |X1 ∪ X2 |
                                                                                          (1)
                                                =1 − (13/19)
                                                =0.32


4      LOD Dynamics Analysis

In this section, we introduce a formal specification of dynamics and the dynamics func-
tion for LOD datasets.


4.1     Dynamics Function

The dynamics function aims at quantifying the evolution of a dataset over a specific
period of time and takes into consideration the changes occurring in this period.
     For the sake of simplicity, we model time as a real value. We are looking for a
function Θ : S × R → R, which assigns each dynamic RDF dataset X consisting of a
concrete set of triples X ∈ S at any point in time t a value which models the quantity
of evolution it has undergone1 . Θ is a monotone, non-negative function. This implies
that there cannot be negative evolution. To measure the dynamics as the amount of
evolution a dataset exhibited in a given time interval [t1 , t2 ], it is sufficient to compute
Θ(X , t2 ) − Θ(X , t1 ) ≥ 0. For ease of notation, we will in the following abbreviate Xt
for the dataset X at time t and Θ(X , t) by Θ(Xt ).
     While it is difficult to define the function Θ directly to provide meaningful values,
we will define it indirectly. To this end, we assume that the change rate of a dataset Xt
at time t is given by a function c(Xt ). Then, we define the difference for two values
of the function Θ to be obtained by accumulating the dataset change rate function over
a time interval. This means, we integrate the change rate function of a dataset over a
given period of time. More formally, the dynamics of a dataset is given by:
                                                    Z t2
                             Θ(Xt2 ) − Θ(Xt1 ) =           c(Xt )dt.                      (2)
                                                      t1

 1
     This quantity of evolution is an abstract value but can serve for relative comparisons of
     datasets.
6




    Figure 1. The dynamics of a dataset is obtained by integration over its change rate over time.


    The idea of integrating over a change rate function is depicted in Fig. 1 where the
area under the curve c(Xt ) corresponds to a quantification of a dataset evolution and
thus the dynamics of the dataset.
    However, also the function c is not explicitly known, and cannot be used for the
computation, i.e., it is not possible to determine the change rate of a dataset for a given
point in time. Thus, our idea is to use an approximation for c(Xt ) based on discrete
points in time and the changes between the datasets at these times.
    So, we can effectively assume X = {Xt1 , . . . , Xtn } to be a set snapshots of the
RDF dataset X at points in time ti , for i = 1, . . . n. For any two snapshots of a dataset,
we can measure changes using a ∆-metric, such as the ones presented in Sec. 3. Our
assumption is that for small time intervals (ideally intervals tending towards zero) the
change between datasets is a good enough approximation of the change rate. This cor-
responds to the idea that:

                         ∆(Xti , Xti−1 ) ti−1 →ti        d
                                         −−−−−→ c(Xti ) = Θ(Xti )                               (3)
                           ti − ti−1                     dt
    Therefore, instead of using the change rate function c, we can use its approximation,
namely the ∆-metric of (ideally) small time intervals of each pair Xti and Xti−1 ∈
X . This corresponds to approximating the change rate function using a step function
as depicted in Fig. 2. Computing the integral given in Eq. 2 over this approximated
function corresponds to:
                                              n
                                              X
                                        t
                                 Θ(X )tn1 ≈         ∆(Xti , Xti−1 ).                            (4)
                                              i=2

    In the following example, we illustrate the computation of the dynamics of the
dataset presented in our motivation scenario.

Example 2 (Computing dynamics based on a Jaccard distance change metric). Let
X = {Xt1 , Xt2 , Xt3 } be a dataset, Xt1 , Xt2 , and Xt3 be the snapshots at three dis-
tinct points in time presented in Table 1, Table 2, and Table 3, respectively. Then the
                                                                                             7




Figure 2. Dataset dynamics defined as aggregation of absolute, infinitesimal ∆-metrics changes.


Jaccard distance between the set of triples from Xt1 and Xt2 , and from Xt2 and Xt3
are given as follows:

                 ∆Jaccard (Xt2 , Xt1 ) = 0.32,     ∆Jaccard (Xt3 , Xt2 ) = 0.32            (5)
      Then the dynamics of X is:
                                n
                                X
                          t
                   Θ(X )tn1 =         ∆Jaccard (Xti , Xti−1 )
                                i=2
                                                                                           (6)
                              =∆Jaccard (Xt2 , Xt1 ) + ∆Jaccard (Xt3 , Xt2 )
                              =0.64

4.2    Decay Function
So far, we proposed a general framework in which we can compute the dynamics or
evolution of any RDF dataset over a period of time and which incorporates any change
metric ∆ that follows the requirements given in Sec. 3. Applications such as caching
and index maintenance benefit from the analysis of the change history of datasets, since
update strategies can incorporate the evolution of a dataset in their computation, instead
of only the quantification of changes w.r.t. the last two snapshots.
    However, for such applications changes tend to be less or more important as time
passes, e.g., if a dataset used to change much but does not anymore, its index update
strategy may need to be adapted (e.g., it should be less aggressive than it used to be).
Therefore, it may be important that changes that took place a longer time ago are weak-
ened and that recent ones are strengthened, or the other way around, i.e., changes should
be stressed or weakened relative to how long ago they have happened. For this purpose,
the dynamics function should be flexible to incorporate such requirements.
    Accordingly, we extend the dynamics function with a decay function f (t). Fig 3
illustrates the influence of the decay function when combined with the dynamics func-
tion. In the upper left side of the figure, the dynamics function is shown. In the lower left
8




          Figure 3. Dynamics function with decay to strengthen the recent changes.



side the decay function (in this example, the exponential decay function) is presented.
In the right side, the combination of both is depicted. Please note, that in this example
we want to weaken older changes and strengthen the recent ones.
     Based on these considerations, we introduce the following modifications to the def-
inition of dynamics: Let X be a dynamic RDF dataset and c(Xt ) be a function which
measures the change rate of a dataset at time t, and f (t) be a decay function. Then the
decayed dynamics function of X is defined as:
                                                       Z t2
                  Θdecay (Xt2 ) − Θdecay (Xt1 ) =             f (t) · c(Xt )dt.           (7)
                                                         t1

    Consequently, the discretization is given by:
                                           n
                                           X
                                    t
                        Θdecay (X )tn1 ≈         f (ti )∆(Xti , Xti−1 ).                  (8)
                                           i=2


Example 3 (Dynamics involving a decay function). We continue our Example 2 where
we compute the Jaccard distances ∆Jaccard (Xt2 , Xt1 ) and ∆Jaccard (Xt3 , Xt2 ). We want
to compute the dynamics of X using the dynamics with a decay function. In this ex-
ample, we chose the exponential decay function f (ti ) = e−λ·(tn −ti ) to be our example
decay function. For sake of simplicity, we set the parameter λ to 1. Then Θdecay (X ) is:
            n
            X
               f (ti )∆Jaccard (Xti , Xti−1 )
           i=2

         =e−λ·(t3 −t2 ) · ∆Jaccard (Xt2 , Xt1 ) + e−λ·(t3 −t3 ) · ∆Jaccard (Xt3 , Xt2 )   (9)
         =0.38 · 0.25 + 1 · 0.25
         =0.345
                                                                                             9

                3000
                2500
                2000
                1500
                1000
                  500
                    0
                        2012-05-06
                        2012-06-03
                        2012-07-01
                        2012-07-29
                        2012-08-26
                        2012-09-23
                        2012-10-21
                        2012-11-18
                        2012-12-16
                        2013-01-13
                        2013-02-24
                        2013-03-24
                        2013-04-22
                        2013-05-19
                        2013-06-16
                        2013-07-14
                        2013-08-11
                        2013-09-08
                        2013-10-06
                        2013-11-03
                        Figure 4. Total number of LOD sources per snapshot


5      Experiments

In this section, we apply our dynamics function to real world LOD data sources. By
comparing the evolution of well-known LOD sources to the figures provided by our
dynamics function, we illustrate how the proposed function works and relate its results
to temporal change patterns. The main goal of the experiments is to show that our ap-
proach of quantifying dynamics of LOD sources reflects the broad intuition of historic
change events analysis.
    For this purpose, we work with data from the Dynamic Linked Data Observatory
(DyLDO) [12]. The DyLDO dataset has been created to monitor a fixed set of Linked
Data documents (and their neighborhood) on a weekly basis. For sake of consistency,
we use only the kernel seeds of LOD documents2 . Our test dataset is composed of
84 snapshots corresponding to a period of more than one year (from May, 2012 until
November, 2013). Furthermore, the DyLDO dataset contains (parts of) various well
known and large LOD sources, e.g., dbpedia.com, musicbrainz.com, and bbc.co.uk. We
will analyze each of these sources separately by splitting up the DyLDO dataset. For
more detailed information about the DyLDO dataset, we refer the reader to [12].


5.1     Analysis of DyLDO Sources

Each snapshot of the DyLDO dataset consists of a set of RDF triples retrieved from
different LOD sources. As presented in Fig. 4, the number of LOD sources crawled
during this period ranged from 1,287 (Sep. 08, 2013) to 2,980 (Dec. 02, 2012). Given
the heterogeneity of the dataset, we expect a wide range of different dynamics behavior,
i.e., some of them evolved a lot during this period, others less. Table 4 shows 13 LOD
sources from the DyLDO dataset which we selected for our analyses. These sources
vary a lot in size, e. g., dbpedia.org is a very large source with more than 4 millions
triples per snapshot, and the oreilly.com source is a very small one with around 10.000
 2
     The DyLDO crawler uses a deterministic mechanism for labeling blank-nodes such that, for a
     given document, the labels of blank nodes are consistent.
10


  # Dataset              Description                      Avg. # triples Θ(X ) Θdecay (X )
                                                           per snapshot
  1 dbpedia.org         DBpedia Project                  4,080,910 55.71            23.42
  2 neuinfo.org         Neuroscience Information         2,065,028 13.62             5.23
  3 linkedct.org        LinkedCT Databrowser             1,782,886 51.75            25.03
  4 dbtropes.org        TVTropes.org wrapper             1,729,455 66.96            28.99
  5 dbtune.org          DBTune Server                    1,427,361 20.90             8.33
  6 identi.ca           Open Source social platform      1,341,045 58.45            18.48
  7 opera.com           Opera Browser                    1,297,630 68.03            30.15
  8 ontologycentral.com Ontology Central                 1.146,171 62.63            25.49
  9 bnf.fr              Bibliotheque nationale de France 1,181,134 25.06            10.87
  10 berkeleybop.org    Berkeley Bioinformatics Projects   903,318 12.82             5.78
  11 uriburner.com      Virtuoso LD Middleware             202,529 29.34            13.67
  12 iu.edu             Indiana University                 112,517 53.23            22.43
  13 oreilly.com        O’Reilly Media                      17,188 79.35            33.84
                      Table 4. LOD sources from the DyDLO dataset




triples per snapshot. Overall they constitute the data sources contributing most volume
to the DyLDO data set, on average ca. 80% of the triples. In the following, we look into
more detail in each of these data sources.
    From the 84 snapshots available in the dataset, we took each pair of subsequent
snapshots and computed their Jaccard distance (see Sec. 3). This means, we compute
the distance between the sets of triples of each pair, i.e., the more changes are detected
(the deletion or addition of triples), the more distant these snapshots are.
    Figures 5(a) to 5(m) show the Jaccard distance for all pairs for the 13 chosen
DyLDO sources. Recall that the dynamics of a dataset can be approximated by the area
under the change rate’s curve. Both sources iu.edu (in Fig. 5(a)) and oreilly.com (in
Fig. 5(d)) show constantly high change rates over the considered period. Less constant
but with equally high change rates are the sources dbtropes.org (in Fig. 5(i)), dbpe-
dia.org (in Fig. 5(c)) and ontologycentral.com (in Fig. 5(j)). Different is the change be-
havior of the sources bnf.fr (in Fig. 5(k)), berkeleybop.org (in Fig. 5(l)) and uriburner.com
(in Fig. 5(m)), where we observe a low change rate over time, but with regular peaks.
For the sources dbtune.org (in Fig. 5(f)) and neuinfo.org (in Fig. 5(g)), we observe only
very few peaks. In particular, the behavior of the sources linkedct.org (in Fig. 5(h)),
opera.com (in Fig. 5(e)) and identi.ca (in Fig. 5(b)) is interesting. Linkedct.org has in
the earlier period a decreasing change rate, which later turns into increase. Opera.com
has peaks in the earlier period, however it shows intensive and constant change rates
at the later weeks. Finally, the identi.ca has high change rates in the first weeks, but no
changes are observed at the later weeks.
    Based on the Jaccard curves presented in Figures 5(a) to 5(m), we now compute
the dynamics for each of these sources. As decay function, we employed again f (ti ) =
e−λ·(tn −ti ) and set the decay parameter λ to 0.025 since we would like to consider
older changes of almost half a year ago still with a weight of approximately 0.5. Table 4
shows the dynamics without decay function (Θ(X )) and the dynamics when making
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                                                                                                                                                                                                                                                                         2012-05-06
                                                                                                                                                                                                                                                                                                                                                                                                                                               2012-06-03                                                                          2012-05-27
                                                                                                                                                                                                                                                                         2012-06-03                                                                     2012-06-03
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   2012-06-17
                                                                                                                                                                                                                                                                                                                                                        2012-07-01                                                                             2012-07-01
                                                                                                                                                                                                                                                                         2012-07-01                                                                                                                                                                                                                                                2012-07-08
                                                                                                                                                                                                                                                                                                                                                        2012-07-29                                                                             2012-07-29                                                                          2012-07-29
                                                                                                                                                                                                                                                                         2012-07-29
                                                                                                                                                                                                                                                                                                                                                        2012-08-26                                                                             2012-08-26                                                                          2012-08-19
                                                                                                                                                                                                                                                                         2012-08-26                                                                                                                                                                                                                                                2012-09-09
                                                                                                                                                                                                                                                                                                                                                        2012-09-23                                                                             2012-09-23
                                                                                                                                                                                                                                                                         2012-09-23                                                                                                                                                                                                                                                2012-09-30
                                                                                                                                                                                                                                                                                                                                                        2012-10-21                                                                             2012-10-21                                                                          2012-10-21
                                                                                                                                                                                                                                                                         2012-10-21
                                                                                                                                                                                                                                                                                                                                                        2012-11-18                                                                             2012-11-18                                                                          2012-11-11
                                                                                                                                                                                                                                                                         2012-11-18                                                                                                                                                                                                                                                2012-12-02
                                                                                                                                                                                                                                                                         2012-12-16                                                                     2012-12-16                                                                             2012-12-16
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   2012-12-23
                                                                                                                                                                                                                                                                         2013-01-13                                                                     2013-01-13                                                                             2013-01-13                                                                          2013-01-13
                                                                                                                                                                                                                                                                                                                                                        2013-02-24                                                                             2013-02-24                                                                          2013-02-19
                                                                                                                                                                                                                                                                         2013-02-24                                                                                                                                                                                                                                                2013-03-10
                                                                                                                                                                                                                                                                         2013-03-24                                                                     2013-03-24                                                                             2013-03-24
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   2013-03-31
                                                                                                                                                                                                                                                                         2013-04-22
                                                                                                                                                                                                                                                                                                                                                        2013-04-22                                                                             2013-04-22                                                                          2013-04-22
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 (a) iu.edu




                                                                                                                                                                                                                                                                                                                                              Seite 1




                                                                                                                                                                                                                                              Seite 1
                                                                                                                                                                                                                                                                                                                                                        2013-05-19                                                                                                                                                                 2013-05-12
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Tabelle1




                                                                                                                                                                                                                                                                                                                                                                                                                                               2013-05-19
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      Tabelle1




                                                                                                                                                                                                                                                                         2013-05-19
                                                                                                                                                                                                                                                                                                                                                        2013-06-16                                                                                                                                                                 2013-06-04
                                                                                                                                                                                                                                                                                                                                                                                                                                               2013-06-16




                                                                         Seite 1
                                                                                                                                                                                                                                                                         2013-06-16




                                                                                                                                                                                                                                                                                                                             Tabelle1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   2013-06-23




                                                                                                                                                                                                                                                                                                                                                                                                                            (d) oreilly.com




                                                                                                                                                                                                                                                                                                                           (g) neuinfo.org
                                                                                                                                                                                                                                                                                                                                                        2013-07-14




                                                                                                Seite 1
                                                                                                                                                                                                                                                                                                                                                                                                                                               2013-07-14                                                                          2013-07-14




                                                                                                                                                                                                                                                                                                                                                                                                                                Tabelle1
                                                                                                                                                                                                                                                                         2013-07-14
                                                                                                                                                                                                                                                                                                                                                        2013-08-11                                                                             2013-08-11                                                                          2013-08-04
                                                                                                                                                                                                                                                                         2013-08-11
                                                                                                                                                                                                                                                                                                                                                        2013-09-08                                                                                                                                                                 2013-08-25
                                                                                                                                                                                                                                                                         2013-09-08                                                                                                                                                            2013-09-08
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   2013-09-15
                                                                                                                                                                                                                                                                                                                                                        2013-10-06




                                                                                                                                                                                                                                              (j) ontologycentral.com
                                                                                                                                                                                                                                                                         2013-10-06                                                                                                                                                            2013-10-06                                                                          2013-10-06
                                                                                                                                                                                                                                                                                                                                                        2013-11-03                                                                             2013-11-03                                                                          2013-10-27
                                                                                                                                                                                                                                                                         2013-11-03
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   2013-11-17




                                                                                                                                                                                                          0
                                                                                                                                                                                                              0,2
                                                                                                                                                                                                                    0,4
                                                                                                                                                                                                                          0,6
                                                                                                                                                                                                                                  0,8
                                                                                                                                                                                                                                          1
                                                                                                                                                                                                                                                                                      0
                                                                                                                                                                                                                                                                                          0,2
                                                                                                                                                                                                                                                                                                 0,4
                                                                                                                                                                                                                                                                                                        0,6
                                                                                                                                                                                                                                                                                                               0,8
                                                                                                                                                                                                                                                                                                                      1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                0
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    0,2
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          0,4
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                0,6
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      0,8




                                                                                                                                                                                                                                                                                                                                                                         0
                                                                                                                                                                                                                                                                                                                                                                             0,2
                                                                                                                                                                                                                                                                                                                                                                                   0,4
                                                                                                                                                                                                                                                                                                                                                                                         0,6
                                                                                                                                                                                                                                                                                                                                                                                               0,8
                                                                                                                                                                                                                                                                                                                                                                                                      1
                                                                                                                                                                                                                                                                                                                                                                                                                                                            0
                                                                                                                                                                                                                                                                                                                                                                                                                                                                 0,2
                                                                                                                                                                                                                                                                                                                                                                                                                                                                         0,4
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    0,6
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           0,8
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1




                                                                                                                                                                                             2012-05-06                                                                  2012-05-06                                                                         2012-05-06                                                                                                                                                             2012-05-06
                                                                                                                                                                                                                                                                                                                                                                                                                                              2012-05-06
                                                                                                                                                                                             2012-06-03                                                                  2012-05-27                                                                                                                                                                                                                                                2012-06-03
                                                                                                                                                                                                                                                                         2012-06-17
                                                                                                                                                                                                                                                                                                                                                            2012-06-03                                                                        2012-06-03
                                                                                                                                                                                             2012-07-01                                                                                                                                                                                                                                       2012-07-01                                                                           2012-07-01
                                                                                                                                                                                                                                                                         2012-07-08                                                                         2012-07-01
                                                                                                                                                                                             2012-07-29                                                                  2012-07-29                                                                                                                                                           2012-07-29                                                                           2012-07-29
                                                                                                                                                                                                                                                                                                                                                            2012-07-29
                                                                                                                                                                                             2012-08-26                                                                  2012-08-19                                                                                                                                                                                                                                                2012-08-26
                                                                                                                                                                                                                                                                                                                                                            2012-08-26                                                                        2012-08-26
                                                                                                                                                                                                                                                                         2012-09-09
                                                                                                                                                                                             2012-09-23                                                                                                                                                                                                                                       2012-09-23                                                                           2012-09-23
                                                                                                                                                                                                                                                                         2012-09-30                                                                         2012-09-23
                                                                                                                                                                                             2012-10-21                                                                  2012-10-21                                                                                                                                                           2012-10-21                                                                           2012-10-21
                                                                                                                                                                                                                                                                                                                                                            2012-10-21
                                                                                                                                                                                             2012-11-18                                                                  2012-11-11                                                                                                                                                           2012-11-18                                                                           2012-11-18
                                                                                                                                                                                                                                                                         2012-12-02                                                                         2012-11-18
                                                                                                                                                                                             2012-12-16                                                                                                                                                                                                                                       2012-12-16                                                                           2012-12-16
                                                                                                                                                                                                                                                                         2012-12-23                                                                         2012-12-16
                                                                                                                                                                                             2013-01-13                                                                  2013-01-13                                                                                                                                                           2013-01-13                                                                           2013-01-13
                                                                                                                                                                                                                                                                                                                                                            2013-01-13
                                                                                                                                                                                             2013-02-24                                                                  2013-02-19                                                                                                                                                           2013-02-24                                                                           2013-02-24
                                                                                                                                                                                                                                                                         2013-03-10                                                                         2013-02-24
                                                                                                                                                                                             2013-03-24                                                                                                                                                                                                                                       2013-03-24                                                                           2013-03-24
                                                                                                                                                                                                                                                                         2013-03-31                                                                         2013-03-24
                                                                                                                                                                                             2013-04-22                                                                  2013-04-22                                                                                                                                                           2013-04-22                                                                           2013-04-22
                                                                                                                                                                                                                                                                                                                                                            2013-04-22




                                       Seite 1
                                                                                                                                                                                                                                              (k) bnf.fr




                                                                                      Seite 1
                                                                                                                                                                                                                                                                         2013-05-12




                                                                                                                                                                                                                                                     Tabelle1
                                                                                                                                                                                                                                                                                                                              Tabelle1
                                                                                                                                                                                             2013-05-19                                                                                                                                                                                                                                       2013-05-19                                                                           2013-05-19
                                                                                                                                                                                                                                                                                                                                              Seite 1
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                                                                                                                                                                                                                                                                         2013-06-04                                                                         2013-05-19
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 (b) identi.ca




                                                                                                                                                               Seite 1
                                                                                                                                                                                             2013-06-16                                                                                                                                                                                                                                       2013-06-16                                                                           2013-06-16
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                                                                                                                                                                                                                                                                         2013-06-23                                                                         2013-06-16
                                                                                                                                                                                                                                                                                                                                                                                                                            (e) opera.com




                                                                                                                                                                                                                                Seite 1
                                                                                                                                                                                             2013-07-14                                                                  2013-07-14                                                                                                                                                           2013-07-14                                                                           2013-07-14
                                                                                                                                                                                                                                                                                                                           (h) linkedct.org
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   Tabelle1




                                                                                                                                                                                                                                                                                                                                                            2013-07-14
                                                                                                                                                                                             2013-08-11                                                                  2013-08-04                                                                                                                                                           2013-08-11                                                                           2013-08-11




                                                                                                                                                                         (m) uriburner.com
                                                                                                                                                                                                                                                                         2013-08-25                                                                         2013-08-11
                                                                                                                                                                                             2013-09-08                                                                                                                                                                                                                                       2013-09-08                                                                           2013-09-08
                                                                                                                                                                                                                                                                         2013-09-15                                                                         2013-09-08
                                                                                                                                                                                             2013-10-06                                                                  2013-10-06                                                                                                                                                           2013-10-06                                                                           2013-10-06
                                                                                                                                                                                                                                                                                                                                                            2013-10-06
                                                                                                                                                                                             2013-11-03                                                                  2013-10-27                                                                                                                                                           2013-11-03                                                                           2013-11-03
                                                                                                                                                                                                                                                                         2013-11-17                                                                         2013-11-03
                                                                                                                                                                                                                                                                                                                                                                                                                                                            0
                                                                                                                                                                                                                                                                                                                                                                                                                                                                  0,2
                                                                                                                                                                                                                                                                                                                                                                                                                                                                             0,4
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     0,6
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            0,8
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                0
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    0,2
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          0,4
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                0,6
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      0,8
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            1




                                                                                                                                                                                                                                                                                          0,2
                                                                                                                                                                                                                                                                                                  0,4
                                                                                                                                                                                                                                                                                                         0,6
                                                                                                                                                                                                                                                                                                                 0,8




                                                                                                                                                                                                                                                                                      0
                                                                                                                                                                                                                                                                                                                       1
                                                                                                                                                                                                                                                                                                                                                                         0
                                                                                                                                                                                                                                                                                                                                                                                                      1




                                                                                                                                                                                                                                                                                                                                                                             0,2
                                                                                                                                                                                                                                                                                                                                                                                   0,4
                                                                                                                                                                                                                                                                                                                                                                                         0,6
                                                                                                                                                                                                                                                                                                                                                                                                0,8




                                                                                                                                                                                                                                                                        2012-05-06                                                                          2012-05-06                                                                         2012-05-06                                                                          2012-05-06




the Θdecay of these data sources (see last column of Table 4).
                                                                                                                                                                                                                                                                                                                                                                                                                                               2012-06-03                                                                          2012-05-27
                                                                                                                                                                                                                                                                        2012-06-03                                                                          2012-06-03                                                                                                                                                             2012-06-17
                                                                                                                                                                                                                                                                        2012-07-01                                                                          2012-07-01                                                                         2012-07-01                                                                          2012-07-08
                                                                                                                                                                                                                                                                        2012-07-29                                                                          2012-07-29                                                                         2012-07-29                                                                          2012-07-29
                                                                                                                                                                                                                                                                                                                                                                                                                                               2012-08-26                                                                          2012-08-19
                                                                                                                                                                                                                                                                        2012-08-26                                                                          2012-08-26                                                                                                                                                             2012-09-09
                                                                                                                                                                                                                                                                        2012-09-23                                                                          2012-09-23                                                                         2012-09-23                                                                          2012-09-30
                                                                                                                                                                                                                                                                        2012-10-21                                                                          2012-10-21                                                                         2012-10-21                                                                          2012-10-21
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   2012-11-11




                                                                                                      Figure 5. Jaccard distance plots for the DyLDO sources
                                                                                                                                                                                                                                                                        2012-11-18                                                                          2012-11-18                                                                         2012-11-18
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   2012-12-02
                                                                                                                                                                                                                                                                        2012-12-16                                                                          2012-12-16                                                                         2012-12-16                                                                          2012-12-23
                                                                                                                                                                                                                                                                        2013-01-13                                                                          2013-01-13                                                                         2013-01-13                                                                          2013-01-13
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   2013-02-19
                                                                                                                                                                                                                                                                        2013-02-24                                                                          2013-02-24                                                                         2013-02-24
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   2013-03-10
                                                                                                                                                                                                                                                                        2013-03-24                                                                          2013-03-24                                                                         2013-03-24                                                                          2013-03-31
                                                                                                                                                                                                                                                                        2013-04-22                                                                          2013-04-22                                                                         2013-04-22                                                                          2013-04-22




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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   2013-05-12
                                                                                                                                                                                                                                                                        2013-05-19                                                                          2013-05-19                                                                         2013-05-19
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   2013-06-04
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                                                                                                                                                                                                                                                                        2013-06-16                                                                          2013-06-16                                                                         2013-06-16                                                                          2013-06-23
                                                                                                                                                                                                                                                                                                                                                                                                                            (f) dbtune.org
                                                                                                                                                                                                                                                                                                                                                                                                                 Tabelle1
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 (c) dbpedia.org




                                                                                                                                                                                                                                                                                                                           (i) dbtropes.org




                                                                                                                                                                                                                                                                        2013-07-14                                                                          2013-07-14                                                                         2013-07-14                                                                          2013-07-14
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   2013-08-04
                                                                                                                                                                                                                                                                        2013-08-11                                                                          2013-08-11                                                                         2013-08-11
                                                                                                                                                                                                                                              (l) berkeleybop.org




                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   2013-08-25
                                                                                                                                                                                                                                                                        2013-09-08                                                                          2013-09-08                                                                         2013-09-08                                                                          2013-09-15
                                                                                                                                                                                                                                                                        2013-10-06                                                                          2013-10-06                                                                         2013-10-06                                                                          2013-10-06
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   2013-10-27
                                                                                                                                                                                                                                                                        2013-11-03                                                                          2013-11-03                                                                         2013-11-03                                                                          2013-11-17




tion, the dynamics of the source identi.ca (in Fig. 5(b)) is very low (please note that its
function which strengthens such kind of change behavior. Also due to the decay func-
points in time in the period. Their high dynamic is a consequence of the use of a decay
contain high change rates over the entire period. High change rates occur in the latest
namic. Looking at their Jaccard curve in Fig. 5(h) and Fig. 5(e), we see that they do not
a few lows). Furthermore, the sources opera.com and linkedct.org are also highly dy-
pedia.org, and iu.edu. This reflects their high change rates over the entire period (with
    Highly dynamic are the sources oreilly.com, dbtropes.org, ontologycentral.com, db-
high change rates are the most dynamics one. Therefore, in the following we consider
analysis of the Θ values of each source is straightforward: sources which have mostly
use of a decay function (Θdecay (X )) of the DyLDO sources in its last columns. The
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 11
12

non-decayed dynamics is one of the highest). This data source presents no changes in
the last weeks, and therefore, its dynamics drops off.
    The less dynamic sources presented in Table 4 include the sources bnf.fr, berkeley-
bop.org, uriburner.com, dbtune.org, and neuinfo.org. These sources have a low change
rate over the period studied. However, their degree of dynamics differs. The more peaks
are observed (especially late in the period), the more dynamic they are.


6    Discussion

Which are the advantages of the continuous Θ-function and how to interpret it? The
notion of dynamics on the basis of an integral over a continuous change rate function
has several theoretic and practical reasons:

 1. it allows for a natural incorporation of the continuous decay functions,
 2. it allows to elegantly deal with time intervals of different sizes and,
 3. is flexible to incorporate more sophisticated approximations for the change rate
    function.

   The dynamics functions delivers a real number which can be interpreted as the de-
gree of evolution of a dataset in a period of time.
What kind of change analysis is applied? In the experiments, we use the Jaccard dis-
tance to compute the changes of each snapshot pairs. In this work, we restrict change
analysis to quantify changes on the set of triples (deletions and additions of triples).
Without modifying the framework, it would be also possible to verify changes under
others aspects such as changes on the set of entities, links, and or schema signature. We
do not verify how these changes affect the dataset over time w.r.t. consistency, compre-
hensiveness, expressivity, etc. Instead, we verify if changes are presented. We consider
such approaches orthogonal to ours.
What is the difference between the Θ function and the ∆ metrics in the literature?
Change metrics proposed in the literature [6,7,12] are limited to quantify changes be-
tween two datasets. In our framework, we define dynamics as an aggregation of changes,
built on top of such change metrics.
Which applications can benefit from the Θ function? The dynamics function delivers a
new kind of information to LOD applications, i. e., how much a dataset evolved over a
given period of time. Such information can be used by methods and approaches such as
updating indexes and caches of data sources [8]. For these approaches, it is important
to analyse the historic change events in order to predict the most suitable point in time
to update such indexes and caches. There, dynamics serve as feature in the decision
process to determine which sources need to be updated with highest priority, i.e., the
information of the dataset evolution is used as an input for prediction algorithms. In
a following-up work, we investigate the use of our dynamics metrics in index updates
scenarios. For instance, in our experiments, the maintenance of indexes relying on the
sources dbtropes.org (Fig. 5(i)) and ontologycentral.com (Fig. 5(j)) will certainly need
more updates than the sources berkeleybop.org (Fig. 5(l)) and neuinfo.org (Fig. 5(g)).
                                                                                        13

Which decay function should I use? There are many decay functions proposed in the
literature [19]. The decision which decay function is the best depends on the appli-
cation requirements For instance, for index update scenarios, it may be important to
weight recent changes higher than older ones. For the scenario of accessibility of LOD
documents and network traffic evolution analysis (for instance, restricting to the period
of day (24h) in 30m interval slots), it may be important to strengthen the older changes
instead of the recent ones.
     The use of a decay function within the dynamics function is, however, not manda-
tory. We choose in the experiment to use the decay function f (ti ) = e−λ·(tn −ti ) in
order to weaken the influence of changes that took place longer time ago. The sources
linkedct.org (Fig. 5(h)) and identi.ca (Fig. 5(b)) show similar change rates, but in di-
fferent periods. The source linkedct.org shows intensive changes in the later period,
while the source identi.ca has intensive changes in the earlier period. Due to the decay
function, the source linkedct.org has a higher dynamic degree than the source identi.ca
(25.03 > 18.48). Without the decay function, this correlation would be changed, i.e.,
identi.ca would be more dynamic than linkedct.org (58.45 > 51.75).


7      Related Work

Various related work has investigated the characteristics of the LOD cloud. Some works
conducted structural analysis of the LOD cloud such as [2,10,1] in order to obtain sta-
tistical insights into the characteristics of the data. In addition, there is related work on
analyzing the LOD cloud in order to verify its compliance with established guidelines
and best practices how to model and publish data as Linked Data [11]. Other works
like [14] analyze LOD in order to obtain statistics about, e. g., its distribution in the
network. The goal is to apply these statistics for the purpose of query recommendation.
Although these works provide interesting insights into the characteristics of LOD, they
typically do not consider the dynamics of the cloud, i. e., the way how it changes.
     Among those works that are dedicated on the study of the Linked Data dynamics is
Ding and Finin [6]. The authors have crawled about 300 million triples from different
so-called Semantic Web documents (SWDs) in 2006. The authors have conducted di-
fferent analyses such as extracting the age of the SWDs based on the last-modified time
information contained in the HTTP response header of the SWDs. The data exhibits an
exponential distribution, which indicates that many new SWDs have been added or that
many old ones are actively modified. Overall, their analysis also shows that the volume
of the Semantic Web documents available on the web is growing, an observation which
is well consistent with and well known from other sources like the LOD cloud web
site3 . However, it remains unknown at which point in the time the different snapshots
of the SWDs have been captured, i. e., also the time span starting from the initial to the
final snapshot is unknown.
     Umbrich et al. [17] measure the dynamics of Linked Data and the dynamics of
Linked datasets with HTML documents on the Web. Their change detection uses (i) HTTP
metadata monitoring, (ii) content monitoring and (iii) active notification of datasets.
 3
     http://www.lod-cloud.net/, last accessed: 23 March, 2013
14

These three detection mechanisms are compared by several aspects like costs, relia-
bility, and scalability of the mechanism. The content monitoring applies a syntactic
comparison of the dataset content, i.e., a comparison of RDF triples ignoring inference.
     The Dynamic Linked Data Observatory is a monitoring framework to analyze dy-
namics of Linked Data [12]. Snapshots of the Web of data are regularly collected and
then compared in order to detect and categorize changes. Using these snapshots, the
authors study the availability of documents, the links being added to the documents,
and the schema signature of documents involving predicates and values for rdf:type and
determine their change rate. Motivated by this work, in [7] Dividino et al. analyzed
the changes on the usage of the vocabulary terms. They also make use of the DyLDO
dataset in their experiments. The authors show that the vocabulary terms which appear
in the description of a LOD document changes a lot.
     An analysis of temporal information in Linked Open Data is presented in [15], i. e.,
temporal information available in document headers and in triples. The experiments on
the BTC 2012 dataset show that only 10% of all triples explicitly provide temporal in-
formation. Thus, we have decided to apply our analysis not on this dataset but on the
DyLDO dataset that provides weekly snapshots of a selected set of crawled resources.
The evolution of the Web has been observed in [4] in order to obtain implications of
changes on incremental Web crawlers. Incremental crawlers update local data collec-
tions if they recognize influencing changes. Likewise, the dynamics of the Web pages is
empirically analyzed in [3] with a dedicated focus on the update frequencies of search
engine indices. Estimations for changes of data items and elements are proposed in [5].
Such estimations are used if the history of changes is incomplete, e.g., it is known that a
Web page has changed but it is not known how often it has changed in a certain period.

8    Conclusions
In this paper, we have presented a general and flexible framework for analyzing data
dynamics on the LOD cloud. Different from quantifying changes of datasets, the dy-
namics capture the evolution of a dataset over time. We propose a function to measure
the dynamics of a LOD dataset, which is defined as the aggregation of absolute, in-
finitesimal changes, where such changes may be quantified by the different existing
change metrics in the literature. Furthermore, our method can be parametrized to make
use of different decay functions for stressing or weakening changes as time passes. We
apply our notion of dynamics by analyzing a large-scale LOD dataset that is obtained
from the cloud by weekly crawls over more than a year in order to show the use of our
dynamics function in a real world dataset. In future work, we intend to approximate the
change rate function based on piecewise linear functions, polynomial interpolation and
cubic splines over the observations of changes at discrete points in time. However, the
benefit of such more sophisticated approximations needs to be evaluated in different
real world scenarios. In particularly, we aim to analyze the benefits of the dynamics
function for optimizing methods for updating indexes.

Acknowledgements The research leading to these results has received funding from the
European Community’s Seventh Framework Programme (FP7/2007-2013), REVEAL
(Grant agree number 610928).
                                                                                                15

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