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<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Sp r ead i n g A c t i v at i o n A p p r o ac h t o Tag -aw ar e Rec o m m en d er s : Mo d el i n g Si m i l ar i t y o n Mu l t i d i m en s i o n al Net w o r k s</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Alexander Troussov</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>University of Pittsburgh and</string-name>
          <email>dap89@pitt.edu</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Peter Brusilovsky</string-name>
          <email>peterb@mail.sis.pitt.edu</email>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>CNGL at Trinity College Dublin</institution>
          ,
          <addr-line>135 North Bellefield Ave., Pittsburgh, PA 15260, USA, +1 (412) 624 9403</addr-line>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>IBM</institution>
          ,
          <addr-line>Ireland, IBM Software Lab, Bld. 6, Mulhuddart, Dublin 15, Ireland, +353-1-815 1906</addr-line>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>University of Pittsburgh</institution>
          ,
          <addr-line>135 North Bellefield Ave., Pittsburgh, PA 15260, USA, +1 (412) 624 9404</addr-line>
        </aff>
      </contrib-group>
      <abstract>
        <p>Social tagging systems present a new challenge to the researchers working on recommender systems. The presence of tags, which uncover the reasons of user interests to tagged items, opens a way to increase the quality of recommendations. Yet, there is no common agreement of how the power of tags can be harnessed for recommendation. In this paper we argue for the use of spreading activation approach for building tag-aware recommender systems and suggest a specific version of this approach adapted to the multidimensional nature of social tagging networks. We introduce the asymmetric measure of relevancy (proximity) of two nodes on a multidimensional network as a cumulative strength of (weighted) multiple connections between two nodes, which includes paths and graph-structures connecting the nodes. This metric is also applicable to measure relevancy of two sub-graphs. Spreading activation methods (SAM), which usually employ breadth first search, are an efficient way to define and compute such measure taking into account not only links constituent a path, but the properties of nodes in the path such as node's types and outdegree. We apply this notion of relevancy to measure similarity of collaborative tagging systems users and present the results of numerical simulation showing that spreading activation methods allow us to discriminate between diverse graph-structures connecting users via resources and tags. We show that the results of simulation are stable w.r.t. the variation of parameters of spreading activation algorithm used in our experiment.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>Categories and Subject Descriptors</title>
      <sec id="sec-1-1">
        <title>H.3.4 [Information Storage and Retrieval]: Systems and</title>
        <p>Software – information networks; H.3.5 [Information Storage
and Retrieval]: Online Information Services – data sharing.</p>
      </sec>
    </sec>
    <sec id="sec-2">
      <title>1. INTRODUCTION</title>
      <p>
        Social tagging systems introduced new challenges to the
wellestablished area of recommender systems. While the majority of
content based, collaborative, and hybrid recommender approaches
were created for a bi-modal world of items and users (connected
by rating incidents), social tagging systems present a more
complicated world of users, items, and tags (connected by tagging
incidents, also known as tagging instances). While some early
works attempted to treat the problem of recommendation in social
tagging systems in an “old way”, basically ignoring the tags, the
majority of researchers in this new area argued that tags are vital
for successful recommendation in this new domain and called for
tag-aware recommenders. They argued that on one hand, tags can
compensate the loss of ratings (which are not available in most
social tagging systems), while on the other hand, tags can make
recommendation more precise because they provide not only the
information of what items are of interest to a user, but also why
they are of interest [
        <xref ref-type="bibr" rid="ref14 ref21 ref27 ref8">8,14,20,26</xref>
        ].
      </p>
      <p>
        Despite the common agreement that tags should be used as a
successful recommender component of a social tagging system,
there is no agreement on how it should be done. As a result, a
multitude of approaches emerged just over the last three years.
Roughly, these approaches can be classified as an extension of
either content-based or collaborative filtering approaches. The
former group emphasizes connections between items and tags
treating tags as an alternative (or additional) way to describe items
and establish a profile of user interests [
        <xref ref-type="bibr" rid="ref15 ref9">9, 15</xref>
        ]. The latter group
emphasizes connections between users and tags to establish a
better similarity between users in a social tagging system [
        <xref ref-type="bibr" rid="ref26 ref27">25, 26</xref>
        ].
We argue than inherently networked nature of social tagging
systems calls for some alternative recommender approaches,
which are not just simple extension of either content-based or
collaborative technologies. A successful recommender approach
for this new context should fully employ the complex network
structure of a typical social tagging system and use all kinds of
links: user-tag, item-tag, user-item. We think that the most
promising in this context is the spreading activation approach.
This approach has been originally developed in the field of
cognitive psychology [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ] to model human brain and later explored
in the context of information retrieval [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ].
      </p>
      <p>
        The power of spreading activation approach was recognized in the
area of recommenders and other personalized systems as well;
however, so far these approaches form just a small minority. The
problem is that the traditional user-item universe does not provide
a sufficiently rich network for spreading activation technology.
Thus most of known recommenders based on spreading activation
were built for context where an additional network can be formed
such as a hypertext network for Web page recommendation [
        <xref ref-type="bibr" rid="ref18">17</xref>
        ]
or a network of entities and concepts in semantically enriched
recommenders [
        <xref ref-type="bibr" rid="ref12 ref19 ref4">4, 12, 18</xref>
        ].
      </p>
      <p>We believe that social tagging systems will provide a new
promising context as well as new challenges for recommenders
based on spreading activation. What we consider as the main
challenge is the multidimensional nature of a typical social
tagging network. Almost all existing applications of spreading
activation for personalization and recommendation operated in
relatively homogeneous kinds of networks with 1-2 kinds of
nodes and one kind of links. In contrast, even a simplified social
tagging network, where each tagging event is represented by a
group of three links (user-tag, item-tag, and user-item) includes
three types of nodes and three types of asymmetric links. This
organization requires some more sophisticated spreading
activation approaches.</p>
      <p>Our paper attempts to address this challenge by introducing the
asymmetric measure of relevancy (proximity) of two nodes on a
multidimensional network as a cumulative strength of (weighted)
multiple connections between two nodes which includes paths and
graph-structures connecting the nodes. This metric is also
applicable to measure relevancy of two sub-graphs. Spreading
activation methods, as breadth first search, is an efficient way to
define and compute such measure taking into account not only
links constituent a path, but the properties of nodes in the path
such as node’s types and outdegree.</p>
      <p>We apply this notion of relevancy to build a tag-aware approach
to measure similarity between users in collaborative tagging
systems. The paper presents the results of a numerical simulation
showing that spreading activation algorithms allow discriminating
the degree of connectivity of users between certain
graphstructures connecting users via resources and tags. We
demonstrate that the results of the simulation are stable w.r.t. the
variation of parameters of the spreading activation algorithm used
in our experiment.</p>
      <p>The rest of the paper is organized as follows. In section 2 we first
provide a short overview of related work focusing on the use of
spreading activation methods (SAM) to propagating and
redistributing relevancy. We also theorize about desired properties
of relevancy propagation on multidimensional network models of
Web. 2.0 data needed to create efficient and scalable
recommender systems.</p>
      <p>In section 3 we render a formal model of folksonomies (tripartite
hypergraph) as a multidimensional network with four types of
nodes corresponding to users, resources, tags and instances of
tagging. In section 4 we present the results of numerical
simulation. Finally, section 5 describes the conclusions and future
work</p>
    </sec>
    <sec id="sec-3">
      <title>2. RELATED WORK</title>
    </sec>
    <sec id="sec-4">
      <title>2.1 Overview of Relevancy Propagation Using</title>
    </sec>
    <sec id="sec-5">
      <title>Spreading Activation Methods</title>
      <p>
        In neurophysiology interactions between neurons are modeled by
way of activation which propagates from one neuron to another
via connections called synapses to transmit information using
chemical signals. The first spreading activation models were used
in cognitive psychology to model these processes of memory
retrieval [
        <xref ref-type="bibr" rid="ref3 ref5">5, 3</xref>
        ]. This framework was later exploited in Artificial
Intelligence as a processing framework for semantic networks and
ontologies, and applied to Information Retrieval [
        <xref ref-type="bibr" rid="ref2 ref20 ref7">2, 7, 19</xref>
        ] as the
result of direct transfer of information retrieval ideas from
cognitive sciences to AI. In other domain, [
        <xref ref-type="bibr" rid="ref28">27</xref>
        ] created spreading
activation models for trust propagation on the Web.
      </p>
      <p>
        In [
        <xref ref-type="bibr" rid="ref22">21</xref>
        ] and [
        <xref ref-type="bibr" rid="ref24">23</xref>
        ] authors work with the notion of the relevancy of
ontological concepts to a free text. They propagate relevancy of
the concepts explicitly mentioned in a document to other
ontological concepts using a spreading activation algorithm. Their
algorithm works in such a way, that after short number of iteration
the topical foci of a cohesive coherent text become the most
activated concepts (even if they were not explicitly mentioned in
the text).
      </p>
      <p>
        In [
        <xref ref-type="bibr" rid="ref23">22</xref>
        ] authors summarize their experience in creating
graphbased related item recommender for activity centric environment
on a Nepomuk Social Semantic Desktop [
        <xref ref-type="bibr" rid="ref25">24</xref>
        ]: relevancy of a
“pile” of nodes representing resources and concepts is propagated
to other nodes. Authors in [
        <xref ref-type="bibr" rid="ref23">22</xref>
        ] conclude that as a graph-mining
technique, spreading activation combines fuzzy clustering and soft
inferencing, and therefore might be suitable for relevancy
propagation. Propagation should lead to discovery of new nodes
which have short length paths to many (if not all) nodes from the
initial set. In other words, newly discovered nodes should
minimize the “distance” to the initial set of nodes, i.e., nodes
which might be considered as potential centroids of strong
clusters induced by the initial conditions. Since partitioning of the
nodes according to these clusters is not needed, processing of
polycentric queries [
        <xref ref-type="bibr" rid="ref23">22</xref>
        ] for related item recommendation could be
done using soft clustering methods. On the other hand, relevancy
propagates through links. an alternative view on the related item
recommendation is that newly discovered nodes must be
connected to the initial conditions by particular types of directed
links. Therefore, propagation of relevancy might be interpreted as
fuzzy inference.
      </p>
      <p>
        In [
        <xref ref-type="bibr" rid="ref24">23</xref>
        ], the authors go further in analyzing SAM as a very general
class of iterative algorithms for relevancy propagation, local
search, relationship/association search, and computing of dynamic
local ranking. Authors indicate that the same iterative algorithms
were used long before in numerical simulation in physics,
mechanics, chemistry, and engineering sciences. Hence, the
algorithm is quite polymorphic: “Using the same iterative
algorithm, with one set of parameters one can emulate heat
transfer; with another set of parameters the same algorithm will
show us the behavior of oscillating strings”.
      </p>
    </sec>
    <sec id="sec-6">
      <title>2.2 Spreading Activation in Recommender</title>
    </sec>
    <sec id="sec-7">
      <title>Systems</title>
      <p>
        Spreading activation approach as a technology for
recommendation in various kinds of networks belongs to a
broader group, which is typically referred to as graph-based
approaches for recommendation. In addition to several recent
papers mentioned in the introduction, which explicitly use
spreading activation to build recommender systems, we can a few
other examples of using various graph-based approaches. In [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ],
the authors presented a theoretic approach where users are
modeled as nodes in a directed graph and the directed links
represent how representative is a user of another user's behavior.
In [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ], the authors use spreading activation to deal with the
sparsity problem in collaborative filtering. They try to tackle the
problem finding transitive relationships by comparing three
different methods on a bipartite graph which represented
consumer-product interactions. Other interesting approach was the
one presented in [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ], where the authors propose a constrained
spreading activation algorithm having good results compared with
a traditional memory-based approach over a small subset of the
Movie Lens data set. These approaches show the potential of
spreading activation to be used on recommender systems, but they
don't take into account the nature of multidimensional networks,
such as folksonomies derived from collaborative tagging systems,
where different types of nodes, links and relationships can have a
strong influence in the design of the algorithms.
      </p>
    </sec>
    <sec id="sec-8">
      <title>2.3 Propagating Relevancy on</title>
    </sec>
    <sec id="sec-9">
      <title>Multidimensional Web 2.0 Networks</title>
      <p>We focus on the applications of SAM to measure similarity
between the users of collaborative tagging systems modeled as
multidimensional networks. Indeed, we treat graph-based
“similarity” of users as a particular case of “relevancy” of nodes
on multidimensional networks. In this subsection we provide
consideration on which properties of a generic class of spreading
activation algorithms are suitable methods for modeling relevancy
propagation.</p>
      <p>
        The general inspiration behind using graph-based methods to
model relevancy (energy, trust, risk, etc.) propagation on networks
is probably the same in many domains: the relevancy is treated as
a kind of energy which might be “injected” into some nodes, and
propagated through links to other nodes: “… the closer node x to
the injection source s, and the more paths leading from s to x, the
higher the amount of energy flowing into x in general” [
        <xref ref-type="bibr" rid="ref28">27</xref>
        ].
Therefore, spreading activation methods (SAM), which usually
employ breadth-first search), are an efficient way to propagate
relevancy. Since according [
        <xref ref-type="bibr" rid="ref24">23</xref>
        ] SAM is a broad class of
algorithms, the choice of algorithm’s parameters is crucial and can
be done taking into account the nature of the target application.
First of all, Web 2.0 data could be accurately modeled only by
multidimensional networks. For instance, formal model of a
folksonomy as tripartite hypergraph [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ] converted to network
representation, has four types of nodes: users, resources, tags,
instances of tagging. The shortest possible path between two
folksonomy users has the length four (for instance, user1- instance
of tagging1- tag - instance of tagging2 - user2). As compared to
trust propagation in heterogeneous networks, the amount of
relevancy flowing from one node to another should depend not
only on types of links, but on properties on nodes in paths.
Connections via resources might be more important than
connections through tags. In our future work we are going to
exploit what [
        <xref ref-type="bibr" rid="ref24">23</xref>
        ] calls “the importance of nodes”, but one
property of nodes which should significantly affect the
propagation, can be immediately inferred from the local topology
of the network, namely from the number of outcoming links from
a node. Ambiguous and top popular tags might be linked to big
number of tag instances and big number of users. Intuitively,
connections via such tags should provide less (if any) contribution
to the similarity of users as compared to the connections through
less popular tags.
      </p>
      <p>
        In [
        <xref ref-type="bibr" rid="ref28">27</xref>
        ], the authors assume that nodes with the higher shortest
path distance from the injection source should be accorded less
trust in general. This property of trust propagation is probably not
applicable to propagating relevancy to measure similarity of
folksonomies users. Moreover, we suggest that for many
applications on multidimensional networks the length of the
shortest path might have positive correlation with the relevancy,
but is probably much less important and is too coarse-grained
measurement compared to trust propagation.
      </p>
      <p>A final observation on relevancy propagation on multidimensional
networks: we don’t assume that all (or many) aspects of such
propagation can be properly understood in terms of paths. We
assume that there might be structures (like network B on the Fig.
1), which might significantly affect the relevancy propagation.</p>
    </sec>
    <sec id="sec-10">
      <title>3. THE ALGORITHM</title>
      <p>
        The algorithm we used in our experiment in general follows [
        <xref ref-type="bibr" rid="ref24">23</xref>
        ]
and employs iterative steps where activation is propagated
between neighbor nodes. To facilitate comparison of activation
distributions on the same or different networks and to account for
dissipation of activation caused by list purging step in spreading
activation, we introduce the step of normalization (calibration).
A multidimensional network can be modeled as a directed graph,
which is a pair G = (V,E) where
      </p>
      <sec id="sec-10-1">
        <title>V – is the set of vertices vi</title>
      </sec>
      <sec id="sec-10-2">
        <title>E – is the set of arcs ej</title>
        <p>init: E → V, is the mapping that provides initial nodes for arcs
term: E → V, is the mapping that provides terminal nodes for arcs
imp – is importance value of arcs and nodes.
w – “weights”</p>
      </sec>
      <sec id="sec-10-3">
        <title>F(E) – is the “activation” real valued function</title>
      </sec>
      <sec id="sec-10-4">
        <title>The algorithm has the following steps</title>
      </sec>
      <sec id="sec-10-5">
        <title>Initialization</title>
      </sec>
      <sec id="sec-10-6">
        <title>Iterations</title>
        <p>Sets the parameters of the algorithm, network, and initial</p>
      </sec>
      <sec id="sec-10-7">
        <title>F(E) as a list of non-zero valued nodes V n</title>
        <p>a.
b.
c.
d.</p>
      </sec>
      <sec id="sec-10-8">
        <title>List Expansion.</title>
      </sec>
      <sec id="sec-10-9">
        <title>Recomputation: The value at each node in the list is recomputed based on the values of the function on nodes which have links to the given node and types of connections.</title>
      </sec>
      <sec id="sec-10-10">
        <title>List Purging: We exclude the nodes with the values less than a threshold.</title>
      </sec>
      <sec id="sec-10-11">
        <title>Conditions Check To Break Iterations.</title>
      </sec>
      <sec id="sec-10-12">
        <title>Normalization</title>
      </sec>
      <sec id="sec-10-13">
        <title>Output</title>
        <p>Linear scaling up or down the numerical values of the
activation level of all nodes in the list of activated nodes to
satisfy some conditions of activation conservation
The list of nodes (value of the function after spread of
activation) ranked according F values.</p>
      </sec>
      <sec id="sec-10-14">
        <title>Recomputation step is as follows:</title>
        <p>
</p>
      </sec>
      <sec id="sec-10-15">
        <title>We have the list of nodes Vn.</title>
        <sec id="sec-10-15-1">
          <title>Input/Output Through Links Computation.</title>
          <p>For each node v we compute the input signal to each arc
e, such that init(e)=v. This computation can be based on
the value F(v), the outdegree of a node etc. For instance,
if the node v has n outgoing arcs of the same type, each
arc e might get input signal:</p>
          <p>I (e) = F(init(e)) ∙ (1 / outdegree(v) ^beta )
where beta might be equal to 1. It could be also less
than one, in which case the node v will propagate more
activation to its neighbors than it has. (This might be
fine for some applications).</p>
          <p>When the signal (“activation”) passes through a link e,
the activation usually experiences decay by a factor
w(e):</p>
          <p>O (e) = I(e) ∙ w(e)
</p>
        </sec>
        <sec id="sec-10-15-2">
          <title>Input/Output Of Node Activation</title>
          <p>Before the pulse, the node v has the activation level
F(v).</p>
        </sec>
      </sec>
      <sec id="sec-10-16">
        <title>Through incoming links v get more activation:</title>
        <p>Input(v) = Σ O(e)
for all links e such that init(e) ∈Vn, term(e) = v.</p>
      </sec>
      <sec id="sec-10-17">
        <title>By dissipating the activation through outgoing links, the node v might lose activation: Output(v) = Σ I(e)</title>
        <p>for all links e such that init(e) = v, term(e) ∈Vn
</p>
        <sec id="sec-10-17-1">
          <title>Computation Of New Level Of Activation</title>
          <p>Fnew(v) = F(v) + Input (v)
To apply spreading activation to measure “similarity” of two
nodes on a network, we put the initial activation 1.0 at the first
node, and measure the activation at the second node after certain
number of iterations.</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-11">
      <title>4. EXPERIMENTS</title>
      <p>To apply graph-based mining on web 2.0 data we model the data
by a multidimensional network (where nodes and links are typed,
and links are “weighted”).</p>
      <p>In our experiments we use three networks representing
instantiations of collaborative tagging systems. Each of these
networks has two actors (A1 and A2), two resources (R1 and R2),
and four instances of tagging (I1, I2, I3 and I4). For instance, the
network A on the figure 1 has the instance of tagging I1 with
links to the actor A1, the resource R1, and the tag T; this
subnetwork shows that the actor A1 used the tag T for the resource
R1. Correspondingly, the links from the instance l2 show that the
actor A1 used the tag T for the resource R2. The instances I3 and
I4 show tagging for the user A2. The network A represents the
situation where both actors used the same tag for both resources.
In the implementation of our algorithm, each of these networks is
modeled by a directed graph, where for each link we create two
reciprocal arcs. In each experiment we set initial activation at the
node corresponding to the actor A1 and after several iterations of
the algorithm we compute the “similarity” of actors A1 and A2
using the method described in 3.</p>
      <p>–
–
–
–
–</p>
      <p>
        In [
        <xref ref-type="bibr" rid="ref24">23</xref>
        ], the authors view SAM in terms of graph-mining
algorithms as a technique for soft clustering. The major
parameters of SAM affecting “the scale” of the phenomena to be
discovered are signal decay and number of iterations (larger
number of iterations and low decay are needed to discover
“bigger” clusters). Since Web 2.0 applications are at the focus of
this paper, we run the experiments varying these two parameters.
Our target was to find regions of the parameters which allow us
consistently to capture structures like that on the Fig.1.
In this paper, we use SAM as a link analysis algorithm for local
ranking, in the same way as PageRank algorithm is used for
global ranking [
        <xref ref-type="bibr" rid="ref29">28</xref>
        ]. The major difference between them is that
PageRank iteratively redistributes the relevancy measure which is
initially set to each node of the network, while we use SAM to
iteratively redistribute the relevancy measure (the activation) from
one (or more) nodes sometimes referred to as “seeds”.
Diameter of graphs B, and C is 6, with the number of iterations
less than 6 the activation from a node on a network will not
necessarily reach all the nodes. The limit distribution (distribution
of the activation after a number of iterations big enough),
produced by SAM, in general does not depend on the choice of
the initial seed. This behavior gives us the estimate that local
ranking, which is highly sensitive to sub-graphs with the diameter
6, could be achieved when the activation will be redistributed on
such sub-graphs several times which amounts roughly to 12-48
iterations.
      </p>
      <p>Our underlying common-sense assumption is that connectivity of
A1 and A2 is bigger in the network A than in B and C; and that
the connectivity of A1 and A2 in the network B is bigger than in
the network C. In other words, if we denote the final activation of
the node v in the network configuration X as x(v), we would
expect that sensible local ranking results should satisfy inequality:
The shortest path between the nodes A1 and A2 equals to 4 in the
network A, and to 6 in networks B and C. So the first part of the
inequality is easily achieved with any parameters of the algorithm
(provided that the number of iterations is not less than 3). To
investigate how the algorithm can discriminate between
configurations B and C we introduce the network discrimination
factor as
(2)
(1)
We computed the NDF ranging the number of iterations from 1 to
50, and the decay factor from 0 to 1. Figure 2 shows the results,
where the X axis represents number of iterations, the Y axis the
decay factor, and the Z axis the network discrimination factor.
The results in figure 2 show that we maximize the NDF when
running our spreading activation algorithm with a decay factor
between 0.8 and 0.9, and 24 iterations. Additionally, the plot
shows stable results for our algorithm, which suggests that
selecting values in close ranges will not return unexpected or
random activation values.</p>
      <p>We have shown that on small networks SAM might be used to
measure similarity between users. It is part of our future plans to
show that on big multidimensional networks representing Web 2.0
data activation initiated at one of the nodes could be kept flowing
within strong clusters induced by the initial set of activated nodes
(because of high degree of clustering); and therefore the results
could be generalized to real-world data.</p>
    </sec>
    <sec id="sec-12">
      <title>5. CONCLUSIONS AND FUTURE WORK</title>
      <p>
        Our paper argued for the use of spreading activation as a
recommendation mechanism in multidimensional networks
produced by collaborative tagging systems. We introduced the
new network-based asymmetric measure of relevancy of two
nodes on a multidimensional network and applied it to build a
tagaware approach to measure similarity between users in
collaborative tagging systems. While it is just one of several
possible ways to use spreading activation in collaborative tagging
context, we consider it as the best way to start. As demonstrated
by the stream of recent works, calculating similarity between
users is a component of the recommendation process where the
use of tags can provide a most valuable impact [
        <xref ref-type="bibr" rid="ref26 ref27">25, 26</xref>
        ].
The results of our experiments show that our metrics can be used
to differentiate activation levels on different network
configurations and they also show a stable behavior when input
parameters are changed. These results lead us to pass to the next
step on our research on this bottom-up approach, which is to
prove that our results are repeatable in large scale networks. We
are currently running our experiments on real social network data
that we have collected from the social bookmarking service
CiteUlike.
      </p>
      <p>
        In this paper we presented applications of spreading activation
methods to local ranking on small networks. We didn’t prove yet
that the same “good” properties hold true when the algorithm runs
on massive networks. However, multidimensional networks which
model web 2.0 data and processes usually exhibit small world
phenomena properties, which include small average distance and
clustering effect. According to [
        <xref ref-type="bibr" rid="ref24">23</xref>
        ] spreading activation might be
considered as a method for soft clustering. Intuitive justification
of the use of spreading activation for ranking is the same as for
the PageRank algorithm [
        <xref ref-type="bibr" rid="ref29">28</xref>
        ]: a node can have a high rank if there
are many nodes that point to it, or if there are some nodes that
point to it and have a high rank. On each iteration strongly
activated nodes continue to support the high level of activation of
nodes to which they have outcoming links, while nodes which
have little connection with strongly activated nodes eventually
lose their activation. Therefore, even if constrained spread of
activation from one node might in several iterations reach
significant portion of the network (small average distance), strong
level of activation will be supported mainly in strong clusters
induced by the node.
      </p>
    </sec>
    <sec id="sec-13">
      <title>6. ACKNOWLEDGMENTS</title>
      <p>This material is based upon work supported by the National
Science Foundation under Grant No. 0840597. We also want to
thank Dr. Vincent Wade from the CNGL of the Trinity College
Dublin for his support to work on this collaborative research.
Dr. Alexander Troussov's work was done in collaboration with
CNGL, which is funded under Science Foundation Ireland's CSET
programme: Grant# 07/CE2/I1142.</p>
    </sec>
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