=Paper=
{{Paper
|id=None
|storemode=property
|title=Semantic Querying of Data Guided by Formal Concept Analysis
|pdfUrl=https://ceur-ws.org/Vol-939/paper4.pdf
|volume=Vol-939
|dblpUrl=https://dblp.org/rec/conf/ecai/CodocedoLN12
}}
==Semantic Querying of Data Guided by Formal Concept Analysis==
https://ceur-ws.org/Vol-939/paper4.pdf
Semantic querying of data guided by Formal Concept
Analysis
Vı́ctor Codocedo1, Ioanna Lykourentzou1,2⋆ , and Amedeo Napoli1
1
LORIA - CNRS - INRIA - Univesité de Lorraine, BP 239, 54506 Vandœuvre-les-Nancy.
victor.codocedo@loria.fr, amedeo.napoli@loria.fr,
2
Centre de Recherche Public Henri Tudor - 29, avenue John F. Kennedy L-1855
Luxembourg-Kirchberg, Luxembourg
ioanna.lykourentzou@tudor.lu
Abstract. In this paper we present a novel approach to handle querying over a
concept lattice of documents and annotations. We focus on the problem of “non-
matching documents”, which are those that, despite being semantically relevant
to the user query, do not contain the query’s elements and hence cannot be re-
trieved by typical string matching approaches. In order to find these documents,
we modify the initial user query using the concept lattice as a guide. We achieve
this by identifying in the lattice a formal concept that represents the user query
and then by finding potentially relevant concepts, identified as such through the
proposed notion of cousin concepts. Finally, we use a concept semantic similar-
ity metric to order and present retrieved documents. The main contribution of
this paper is the introduction of the notion of cousin concepts of a given formal
concept followed by a discussion on how this notion is useful for lattice-based
information indexing and retrieval.
1 Introduction
As the amount of information grows, the ability to retrieve documents relevant to the
needs of the user increasingly becomes more important. Several applications have been
proposed, regarding this task, in the field of Information Retrieval (IR). However, as
the information becomes more complex (not only text, but also multimedia documents)
and specific (domain-oriented), the capacity to organize it becomes as important as the
capacity to retrieve it.
Formal Concept Analysis (FCA) is a robust and widely used framework to organize
objects based on their relations through their attributes in a concept lattice [6]. Con-
cept lattices have been used in the past to support Information Retrieval tasks and they
have been found to have better or comparable performance in relation to traditional
approaches, such as Hierarchical Clustering and Best-Match Ranking. We argue that
this performance can be further enhanced considering features as concept and semantic
similarities and lattice navigation techniques.
⋆
The work of Ioanna Lykourentzou in the present project is supported by the National Research
Fund, Luxembourg, and cofunded under the Marie Curie Actions of the European Commission
(FP7-COFUND).
In this work, we present an approach to retrieve documents from a document-term
concept lattice, considering that concepts can be close with respect to their position
within the lattice and semantically similar to one another. We use both of these notions
to find which are the most relevant documents for a given user query.
The rest of this paper is organized as follows: Section 2 presents the related re-
search literature. Section 3 briefly introduces FCA and presents our proposed approach
for navigating the lattice using the notion of cousin concepts, as well as for ranking
the selected concepts with respect to their semantic similarity. Section 4 presents and
discusses the experimental results and finally section 5 presents the conclusions of our
work.
2 Related Work
2.1 Concept lattice-based Information Retrieval
Formal concept analysis is a data representation, organization and management tech-
nique with applications in many fields of information science, ranging from knowledge
representation and discovery to logic and AI [15]. In the last decade researchers have
also focused on examining the potential of FCA addressing problems in the field of In-
formation Retrieval [14]. Under this light, the term Concept lattice-based Information
Retrieval is used to describe the problem of retrieving information relevant to a given
user query, when the document collection that contains the information is organized
within a concept lattice. Some of the IR tasks that FCA and concept lattices have so far
been applied on, include query refinement and expansion, integration of query and nav-
igation and support of faceted search ([4, 2]). Among the most representative works in
the field are the works of Carpineto and Romano, who introduce the method of Concept
lattice-based ranking (CLR) [1].
The CLR method consists of three main steps: i) construction of the formal context
of documents-terms and building of the corresponding concept lattice ii) insertion in the
lattice of a new concept that represents the user query, using a subset of the attributes
of the formal context and iii) retrieval and ranking of the relevant concepts using a
nearest-neighbour approach, which depends on their topological path distance, within
the lattice, from the original concept. The topological path metric used is called distance
”ring”, and it measures the radius of distance between two concepts, using as distance
metric the length of the shortest path between them. The ring metric provides a partially
ordered retrieval output, according to which all the documents that are equally distant
from the original concept, i.e. belong to the same distance ring, are given the same
ranking score.
Carpineto and Romano, also compare the CLR method with two other Informa-
tion retrieval methods, namely Hierarchical Clustering-based Ranking (HCR)[7] and
Best-match ranking (BMR). CLR is found to produce better results compared to HCR.
Compared to BMR, it produces worst results when compared on the retrieval over the
total document collection and better results, when only the first documents of the re-
trieval result are considered. However, CLR was better over both BMR, HCR when
considering the retrieval of non-matching documents, (i.e. documents that do not match
the user query but share common terms with documents that do match the user query)
The main advantage of the CLR method is that, in contrast to other statistical similar-
ity measures that calculate the distance between two document representations using
only the characteristics of those representations, the lattice allows to also incorporate
the similarity that two document representations have in regards to the context, i.e. the
whole document of collections, in which they are found.
The limitations of the traditional CLR method include firstly, the need to build the
whole lattice before retrieving the related concepts. This issue determines the complex-
ity and computational time required to address the problem, and it may result in non-
realistic solutions for large document collections, like for instance the TREC dataset
([4]). Another issue, identified by the authors is that perhaps CLR should be combined
with BMR, since they perform well in different types of documents (non-matching and
matching respectively). Another set of limitations, more related to the present work,
refers to the ranking method used and specifically to the fact that the retrieval and rank-
ing of the related concepts is made taking into account only their topological relation
with the original user query concept. Specifically, due to the use of topological distance
rings as a metric of concept similarity, the CLR method does not distinguish between
generalization and particularization, when moving from the concept of the original user
query to other concepts. This limitation is critical, as it may lead to a loss of the se-
mantic similarity between the retrieved and the original concept and it is explained in
more detail in the section 3 when introducing our proposed method for concept-based
information indexing and ranking.
To address these limitations, in this paper we propose a novel approach, which seeks
to ensure semantic similarity with the original user query, both through the way that
the lattice is traversed and through the way that the concepts are ranked. In particular,
we introduce a new topological-based concept characteristic, called cousin concepts,
to navigate the lattice and retrieve candidate related concepts. In parallel, for ranking
the retrieved concepts we do not rely only on structural concept similarity features,
but instead we use a metric that allows the weighting of both structural and semantic
similarity aspects [5].
3 Methodology
In order to present our approach, first we present a brief description to Formal Concept
Analysis (FCA). The basics of FCA are introduced in [6], but we recall some notions
useful for its understanding in the following.
Data is encoded in a formal context K = (G, M, I), i.e. a binary table where G
is a set of objects, M a set of attributes, and I ⊆ G × M an incidence relation. Two
derivation operators, both denoted by ′ , formalize the sharing of attributes for objects,
and, in a dual way, the sharing of objects for attributes:
′
: ℘(G) −→ ℘(M ) with A′ = {m ∈ M | ∀g ∈ A, gIm}
′
: ℘(M ) −→ ℘(G) with B ′ = {g ∈ G | ∀m ∈ B, gIm},
where ℘(G) and ℘(M ) respectively denote the powersets of G and M . The two
derivation operators ′ form a Galois connection between ℘(G) and ℘(M ). The maximal
sets of objects which are related to the maximal sets of attributes correspond to closed
sets of the composition of both operators ′ , denoted ′′ , for ℘(G) and ℘(M ) respectively.
A pair (A, B) ∈ ℘(G) × ℘(M ), where A = B ′ and B = A′ , is a formal concept, A
being the extent and B being the intent of the concept. The set CK of all concepts from
K is ordered by extent inclusion, denoted by ≤K , i.e. (A1 , B1 ) ≤K (A2 , B2 ) when
A1 ⊆ A2 (or dually B2 ⊆ B1 ). Then, LK = hCK , ≤K i forms the concept lattice of K.
Typically, a concept lattice to index documents is created from a formal context
Kindex = (G, M, I) where G is a set of documents and M is a set of terms. Thus, the
set I represents document annotations (i.e. gIm indicates that the document g is anno-
tated with the term m). In a nutshell, to retrieve documents given a conjunctive query3
q = {mi }, mi ∈ M (mi in the query are hereafter referred as keywords), the goal is
to find those formal concepts (A, B) where B ∼ q and to retrieve the documents in A.
The usual approach is to insert into the lattice a query concept Cq = ({∅}, q) [11, 10,
1] the intent of which contains all the keywords in the user query. Different techniques
have been proposed to navigate the lattice, however they rely on topological properties
(navigating the super-concepts and sub-concepts if Cq ) of the concept lattice to search
for documents. Although topology-based measures are useful to retrieve related docu-
ments from a query, there are some drawbacks that could be overcome with the use of
semantic similarity.
The first disadvantage with the navigating in the hierarchy of Cq refers to the gen-
eralization of the query. By obtaining the super-concepts of the query concept inserted
in the lattice, a level of granularity already provided by the user is lost. For example,
for a query of the form “complications, arthroscopy”, a query concept Cq = (Aq =
{∅}, Bq = {complications, arthroscopy}) is created within the lattice. Any super-
concept Csup = (Asup , Bsup ) of the query concept has to comply with Bsup ⊂ Bq . In
this case, only three super-concepts can be obtained: Csup1 = (Asup1 , {complications}),
Csup2 = (Asup2 , {arthroscopy}) and Csup3 = (Asup3 , {∅}). However, Asup1 contains
documents about complications in any aspect leading to a decrease in precision. The
same happens with documents in Asup2 containing documents about arthroscopy in
general whether the user had already specified a restriction for them. Csup3 represents
the supremum where Asup3 contains every possible document, this, of course, is the
worst case scenario where the system has no restrictions to retrieve documents.
The second disadvantage is about the specification of the query. By obtaining the
whole set of sub-concepts of the query concept the system assumes restrictions not
provided by the user. While this is the main idea behind query expansion [3] the problem
is that there are no discrimination with the sub-concepts that should be used to retrieve
documents. For example, given the same query used in the last example and the sub-
concepts Csub1 = (Asub1 , {complications, arthroscopy, inf ection}) and Csub2 =
(Asub2 , {complications, arthroscopy, practice}), the system cannot decide whether
the documents in Asub1 or the documents in Asub2 are the most relevant. From a human
perspective, it could be assumed that documents in Asub1 may be of more interest for
the user since an infection is a possible complication in the context of a surgery such as
an arthroscopy and hence they should be retrieved first. On the other side, practice is a
general word which may lead to non-relevant documents.
3
Keywords and the conjunction operator ∧
Regarding these problems we propose a technique to improve information retrieval
based on concept lattices using the idea of “concept similarity” provided by Formica.
We combine this idea with a novel heuristic to navigate the lattice in order to find those
concepts holding relevant documents for a given query.
3.1 Navigating the lattice
Given the formal context Kindex and the query q = mi at the beginning of this section,
a very simplistic approach to retrieve documents relevant to the query is to find those
concepts (Aj , Bj ) where mi ∈ Bj : ∀mi ∈ q defined in [13] as retrieve algorithm.
Actually, it is possible to find a single concept Cq = (Aq , Bq ), where Bq holds the
minimal set of words containing all keywords. Subsequently, Aq contains the maxi-
mal set of documents containing all the keywords. We refer to Cq = (Aq , Bq ) as the
matching concept.
It should be noted here that, for a given query q, the matching concept Cq may not
exist. This is more likely to happen if the number of keywords is high. In a complete
concept lattice (not filtered through any means and constructed using the total amount
of information), such a case would actually mean that there are no documents which
comply with all the restrictions provided in the user’s query. While some strategies
can be implemented to overcome this issue (asking the user to provide a simpler query
or manipulating the query in order to answer) for the scope of this work we do not
elaborate on this and we rather consider the case of an existing matching concept.
Once the matching concept Cq = (Aq , Bq ) is found, all documents in Aq can be
retrieved to the user. Since the number of documents in Aq may be not sufficient, what
is important, in the following, is how to complete the answer with more documents
using the lattice.
A simple strategy would involve the hierarchy of Cq , however every sub-concept
(Asq , Bsq ) ≤K (Aq , Bq ) will provide no different documents than those in Aq since
Asq ⊂ Aq . Super-concepts of Cq are not useful either because of the problems de-
scribed in the beginning of this section regarding generalization. Hence, in order to
complete the answer with more documents, it is necessary to obtain from the concept
lattice some formal concepts which are neither super- nor sub-concepts of (Aq , Bq ). To
achieve this, we use the notion of cousin concepts defined as follows.
Definition of cousin concepts: Two concepts (A1 , B1 ) and (A2 , B2 ) which are
not comparable for ≤K are said to be cousins iff there exists (A3 , B3 ) 6=⊥ such that
(A3 , B3 ) ≤K (A1 , B1 ) and (A3 , B3 ) ≤K (A2 , B2 ) and dK ((A2 , B2 ), (A3 , B3 )) = 1
(where ⊥ is the bottom concept and dK measures the minimal distance between two
formal concepts in the lattice K). Intuitively, this means that (A1 , B1 ) and (A2 , B2 ) do
not subsume each other and that (A3 , B3 ) can be either the lower bound or be subsumed
by the lower bound (A1 , B1 ) ⊓ (A2 , B2 ) (where (A1 , B1 ) ⊓ (A2 , B2 ) denotes the lower
bound of (A1 , B1 ) and (A2 , B2 ).
The use of cousin concepts allows us to move in the lattice from one concept to an-
other using the relations that the elements in their intents possess and that are expressed
through their common subsumer. In the example on Figure 1, C2 is a cousin concept
of C1 because of concept C3 . The attributes “arthroscopy”, “complication” and “in-
fection” are all related through the intent of concept C3 . In this small example, if C1 is
Fig. 1. Example. Five concepts within a lattice, extents and intents are shown. Arrows indicate
query expansion and modification
the matching concept, moving from it to concept C2 is the same as replacing the word
“complication” with the word “infection” in the query. The extent of concept C2 will
contain documents, some of which are different from those of C1 and therefore they
can be used to complete the answer provided by C1 .
We may also notice that the use of C3 works as a query expansion, adding attributes
to the original user query, while the use of C2 works as a query modification, since its
attributes are a subset of the attributes of C3 .
Using the entire sub-hierarchy of the matching concept (excluding the infimum)
allows us to retrieve several cousin concepts which can be used to complete the answer
far beyond the initial set of documents contained in the matching concept’s extent.
Each cousin concept is a possible query modification obtained from a query expansion,
represented by the sub-concepts of the matching concept.
Although cousin concepts are useful to expand the answer by representing query
modifications, their use may entail the same problem described in the beginning of this
section, as the second disadvantage of structure-based concept retrieval. In the same
example on Figure 1 concepts C2 and C4 are cousin concepts of C1 . However, in this
scenario the system cannot decide which set of documents, between those of C2 and
C4 , should be retrieved first.
A way to rank cousin concepts is therefore necessary in order to decide which doc-
uments should be retrieved to the user first. In this paper we do so using the measure of
concept similarity proposed by Formica [5].
3.2 Concept ranking through similarity
The ranking of the retrieved cousin concepts is performed using a semantic similarity
metric proposed by Formica[5]. That is, given two formal concepts C1 = (A1 , B1 ) and
C2 = (A2 , B2 ) the similarity between them is defined as:
|A1 ∩ A2 | M(B1 , B2 )
sim(C1 , C2 ) = ∗w+ ∗ (1 − w) (1)
max(|A1 |, |A2 |) max(|B1 |, |B2 |)
where 0 ≤ w ≤ 1 is a weighting parameter and M(B1 , B2 ) is the maximization
of the sum of the information content similarities between each possible pair of terms
created using one term from B1 and another from B2 . Information content similarity
between two terms is measured using their distance in a lexical hierarchy and/or their
co-occurrence in a text corpus. The full explanation of this metric is beyond the scope of
this paper. For further information, the reader is referred to the original work of Formica
[5].
Consider the example of Figure 1: Concepts C2 and C4 are both cousin concepts
of the matching concept C1 , and they have the exact same structural features, i.e. the
cardinalities of the intersections of their extents/intents with the matching concept are
the same, as well as their extent/intent cardinalities. However, when using the semantic
similarity metric defined above with w = 0.5 and Wordnet4 as the external lexical hi-
erarchy, we observe that sim(C1 , C2 ) = 0.7275, while sim(C1 , C4 ) = 0.45, because
the pair (complication, infection) has a higher semantic relation than the pair (compli-
cation, practice). In this way, we may rank and retrieve the documents of concept C2 ,
higher than those of concept C4 . Differentiations in the weight value w allow for dif-
ferentiations in the preference over the structural (from the extents) and semantic (from
the intents) similarities of the compared concepts.
4 Experimental results and discussion
We applied our approach using the MuchMore5 dataset, which contains annotated med-
ical document abstracts (7822 documents, 9485 single or multi-word terms). In order to
answer a given user query we follow a 3-step knowledge discovery process, as follows.
Step 1 - Data preprocessing: Pre-filter the set of documents and terms Since the
creation of a lattice containing the full set of documents/terms would be computation-
ally expensive, we create a reduced lattice for each given user query. To do so, we imple-
ment a simple pre-filtering strategy of iterative expansion similar to the one described
in [4]. Given a conjunctive query q = {ti } we fetch all documents dn that contain all
the keywords in the query. Afterwards, we obtain all the terms tj that these documents
contain. Finally, we fetch all the additional documents dm which contain any of these
terms. At the end we obtain a set of dn + dm documents and ti + tj terms which is used
to create a formal context. For the query qs = {“complication”,“arthroscopy”}, this
process returns a set of 11 initial documents, which in turn leads to an expanded set of
177 terms and 7560 documents.
Unfortunately, this strategy yields more than 95% of the corpus’ documents be-
cause of highly frequent terms. To avoid this, documents with a number of terms below
the average (in the above example, 7 terms) are not included in the expanded set of
documents (3485 documents for the example). It should be noted that the pre-filtering
strategy can be further improved considering weighting techniques such as tf.idf, piv-
oted normalized document length [9] or heuristic approaches specifically focusing on
the reduction of irrelevant concepts in a FCA lattice [4].
4
Wordnet is a widely-used free semantic dictionary organized in a hierarchical manner [12]
5
http://muchmore.dfki.de/
Step 2 - Transformation: Concept lattice creation The creation of the concept lattice
is straightforward since we rely on a fixed framework (Coron Toolkit6 ). For the example
of query qs we obtain 134718 formal concepts without using support pruning.
Step 3 - Data mining & Evaluation: Retrieving documents from the lattice The
retrieval step consists of three sub-steps, described in the following.
1. Find the matching concept. We search for the matching concept Cq in the lattice
using a level-wise algorithm, starting from the supremum. The matching concept
Cq is the closer concept to the supremum which contains in its intent all the key-
words provided in the query. The existence of the matching concept is predicated in
the assumption of a conjunctive query to pre-filter the dataset and create the formal
context. In the case that there are no documents containing at least all the keywords,
the query is consider unsuccessful and the retrieval process is stopped at step 1. The
documents in the extent of the matching concept are retrieved to the user and they
are hereafter referred to as exact answer.
2. Find the cousin concepts of the matching concept. Cousin concepts are obtained
for the matching concept and for each of its sub-concepts Ci . A list called candidate
answers is created storing the pair (Ci , Cj ) where Ci ≤ Cq and Cj is a cousin
concept of Ci . For qs , the candidate answers list contains 2301 (concept, cousin
concepts) pairs.
3. Rank the cousin concepts. The ranking process is performed using the similar-
ity measure described in section 3.2. Every pair (concept, cousin concept) from
the candidate answers list is compared, or what is the same, each query expansion
is compared to its correspondent query modification. Formica’s concept similarity
was implemented using Wordnet [12] as a lexical hierarchy7, the Brown corpus as
a base to obtain term frequencies and a modified version of the Hungarian algo-
rithm [8] to match terms from both intents8 . The experiments here presented where
performed with a value of w = 0.5.
Table 2 shows the results for two queries executed using the described approach.
For qs = {“arthroscopy”,“complication”} the exact answer retrieved 11 documents of
which 7 are relevant to the user. The close answer, composed of the documents retrieved
from the ranked cousin concepts, contains 100 documents of which 6 are relevant to the
user. Therefore, out of the 21 documents relevant to the user the approach was able to
retrieve 13.
It is of special interest to analyse the characteristics of the obtained results. The
cousin concept with intent joints, surgical aspects, complication, diagnostic has a sim-
ilarity of 0.71 with the concept with intent arthroscopy, surgical aspects, complication,
diagnostic which is a sub-concept of the matching concept created for qs and hence,
does not have additional documents than those already retrieved. What can be appreci-
ated here is that the algorithm works firstly by expanding the original query with related
6
http://coron.loria.fr/site/index.php
7
Wordnet is a dictionary where terms are grouped by synonymia (synset) and ordered in a
hierarchical tree by the hypernym relation.
8
The Hungarian algorithm minimizes the sum of values in the diagonal of a square matrix.
terms (from arthroscopy to surgical aspects9 ) and secondly by modifying the expanded
query with a semantically similar term (from arthroscopy to joints). The above process
is illustrated in Table 1.
Table 1. Query expansion and modification.
matching concept sub-concept cousin concept
query expansion modification
arthroscopy → arthroscopy → arthroscopy → joints
complication complication complication complication
surgical aspects surgical aspects surgical aspects
diagnostic diagnostic diagnostic
The second query in Table 2 is also of interest in the sense that it indicates algorithm
robustness. The word laparoscopic is not present in Wordnet, making it not suitable for
the comparison in the similarity measure. This means that laparoscopic can be replaced
with any other term since the algorithm is not able to measure the difference. However,
since the similarity measure relies also in extent intersection, the algorithm will try to
replace laparoscopic with terms used by documents similar to those in the exact answer.
In that way, the first ranked close answer is correct and its intent is complication, risk,
cholecystectomy. Notice that in this case the algorithm does not conclude that the term
risk is semantically close to the term laparoscopic, but that it is the best term to replace
the latter in the query.
Table 2. Results for two queries.
Exact answer Close Answer Total Answers
Query correct/found correct/found correct/expected
arthroscopy, complication 7/11 6/100 13/21
complication, laparoscopic 3/3 3/100 6/7
cholecystectomy
5 Conclusions
In this paper we present a technique to use a concept lattice for the retrieval of doc-
uments from a given user query. The proposed technique differs from previous ap-
proaches in two main aspects: the lattice navigation algorithm is not restricted to the
9
an arthroscopy is a knee surgery
hierarchy of the query concept and the ranking algorithm is based on the semantic sim-
ilarity, rather than on the structural characteristics of the compared concepts.
In terms of navigation, we introduce the notion of cousin concepts, which represents
query modifications that can be used to retrieve documents different from those directly
related to the query. In terms of ranking, we use external knowledge sources (a lexical
hierarchy and a text corpus) to measure semantic similarity and order the retrieved
cousin concepts by relevance to the initial query.
We illustrate our approach using two examples from a dataset of medical document
abstracts. We also explain certain limitations of the proposed approach, mainly regard-
ing the performance the concept lattice construction and the availability of the terms
of the user query in the dataset. Currently, we are applying this approach on the same
dataset but on a full scale, in order to measure precision and recall, as well as to compare
the proposed technique with other Information Retrieval state-of-the-art techniques.
References
1. Claudio Carpineto and Giovanni Romano. Order-theoretical ranking. Journal of the Ameri-
can Society for Information Sciencies, 51(7):587–601, May 2000.
2. Claudio Carpineto and Giovanni Romano. Using concept lattices for text retrieval and min-
ing. In Formal Concept Analysis, pages 161–179. Springer-Verlag, Berlin, Heidelberg, 2005.
3. Claudio Carpineto and Giovanni Romano. A survey of automatic query expansion in infor-
mation retrieval. ACM Computing Surveys (CSUR), 44(1), January 2012.
4. Claudio Carpineto, Giovanni Romano, and Fondazione Ugo Bordoni. Exploiting the poten-
tial of concept lattices for information retrieval with credo. Journal of Universal Computer
Science, 10:985–1013, 2004.
5. Anna Formica. Concept similarity in formal concept analysis: An information content ap-
proach. Knowledge-Based Systems, 21(1):80 – 87, 2008.
6. Benrhard Ganter and Rudoph Wille. Formal Concept Analysis. Springer, Berlin, 1999.
7. Marti A. Hearst and Jan O. Pedersen. Reexamining the cluster hypothesis: scatter/gather on
retrieval results. In Proceedings of SIGIR 1996, SIGIR ’96, pages 76–84. ACM, 1996.
8. H. W. Kuhn and Bryn Yaw. The hungarian method for the assignment problem. Naval
Research Logistic Quarterly, pages 83–97, 1955.
9. Christopher D. Manning, Prabhakar Raghavan, and Hinrich Schtze. Introduction to Infor-
mation Retrieval. Cambridge University Press, New York, NY, USA, 2008.
10. Nizar Messai, Marie-Dominique Devignes, Amedeo Napoli, and Malika Smaı̈l-Tabbone. Us-
ing domain knowledge to guide lattice-based complex data exploration. In Proceedings of
the 2010 conference on ECAI 2010, pages 847–852. IOS Press, 2010.
11. Nizar Messai, Marie-Dominique Devignes, Amedeo Napoli, and Malika Smal-Tabbone.
Querying a bioinformatic data sources registry with concept lattices. In Proceedings of ICCS
2005, pages 323–336. LNCS 3596, Springer, 2005.
12. George A. Miller. Wordnet: a lexical database for english. Communications of the ACM,
38(11):39–41, November 1995.
13. Ibtissem Nafkha, Samir Elloumi, and Ali Jaoua. Using concept formal analysis for cooper-
ative information retrieval. In Concept Lattices and their Applications 2004, volume 110 of
CEUR Workshop Proceedings. CEUR-WS.org, 2004.
14. Uta Priss. Lattice-based information retrieval. Knowledge Organization, 27:132–142, 2000.
15. Uta Priss. Formal concept analysis in information science. Annual Review of Information
Science and Technology., 40(1):521–543, December 2006.