Cooperative Information Retrieval enhanced. by Formal Concept Analysis

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1 Cooperative Information Retrieval enhanced by Formal Concept Analysis IBTISSEM NAFKHA 1, ALI JAOUA 2 1 Department of Computer Science University of Tunis Campus Universitaire, Le Belvédère, 1060 Tunis. TUNISIA 2 Department of Computer Science University of Qatar Faculty of Science, Doha. QATAR Abstract: - Along with the growth of the World Wide Web, information retrieval systems gain importance since they are often the only way to find the few documents actually relevant to a specific question in the vast quantities of text available. Moreover, with the advent of the Web along with the unprecedented amount of information available in electronic format and its distributed structure, Formal Concept Analysis (FCA) is more useful and practical than ever, because this technology addresses important limitations of the systems that currently support users in their quest for information. Over the last few years, the range of functionality has been expanded to include new tasks such as data reduction and collaborative (or cooperative) information retrieval. In fact, due to the huge quantity of available information and its distributed structure, it is necessary to abstract it and eliminate the redundancy data. In this context, a method for data reduction based on the formal concept analysis is proposed in [16,17]. At the same time, new IR domains have been investigated including different types of information ( messages, web documents,..). Thus, there is nowadays a much better awareness of the strengths and limitations of this technique for organising and searching distributed information. We are interested by searching in distributed information. Key-Words: - Information Retrieval - Formal concept Analysis Cooperation Data reduction Conceptual Information retrieval. 1 Introduction As The quick increase of the accessible data quantity, under electronic form, is changing our world. In fact, the development of the Web allows the users the access, the division and the disclosure of the news of an easier manner and in big quantities. Consequently, this quantity of information does not stop increasing. The nature of this information can be various: literal, picture, video, etc. The classical technologies of data treatment prove themselves insufficient for their exploitation. In fact, the catalogs and the research engines in line (Google, Lycos, etc.) allow carrying out queries by keyword and to refine them to the assistance of Boolean operators. Nevertheless, the task more difficult comes back to the user that must search in this mass of information to select the documents that will be for him the pertinent. The obtained results researches from these engines present limits. In fact, the rediscovered documents can be redundant or incomplete. The arrival of the «World Wide Web» and the big internet usage open again perspectives, such as the integration of the cooperation for diffusion and the information division. The information systems evolve while becoming more and more complexes and equally the quantity

2 of information treated is more and more voluminous. Leaving simple data management systems describing the documents «paper», they became accesses systems to the «electronic» documents stocked in different documents collections. The multiplication of the documents as well as the interconnection of the waiters of documents induced the introduction of the cooperation concept between a systems set. The documents collections multiply themselves and the waiters of documents cooperate. Besides, the development of the web, example the more known collections of divided documents, constitutes equally a non negligible factor of the growth of the volume of available information. Thus, it is more and more difficult for each of knowledge where and how to attain quickly to information more pertinent. The meta-engines are presentation techniques of the results coming from several tools. They operate while questioning for every query that is submitted for them different research tools in order to furnish the more exhaustive answer. For their functioning, some index contained information in different research engines, of others questions them in a manner dynamic simultaneously. The problem is not simple for research every tool has its characteristics. Of more, they generate, on the other hand, too much noise (non pertinent answers), and they do not take advantage of the characteristics furnished by every tool. The treatment of the results coming from different research tools is very variable. Certain meta-engines limit the number of obtained answers of each different questioned tool (the 10 to 20 first answers furnished by each tool). This should allow obtaining the answers more pertinent. Of other meta-engine do not synthesize the results and they post them in independent windows such as the metaengine All4One. Certain meta-engines, after to have recovered the different results, merge them with elimination of duplications or the classes by relevance such as the meta-engine Profusion. The answer times of the engines used researches being able to be very variable, certain meta-engines use an expiration value or time out such as the meta-engine Debriefing. For others, the user has a total check on the length of the research. Our work is very interested in to furnish means that pull the best possible party of the cooperative oriented approach system in the information research while benefiting from the provisions furnish by the formal concept analysis. Indeed, several works [4,5,6,7,8,10,13,14,15,18,19,20] were very interested in the exploitation of the formal concept analysis as research tool and of navigation. These works use the terminologies of the formal concept analysis such as the usage of thesaurus in the research process and of navigation [4,5,6,8,10,13,14,15] or in the expansion of queries [7,9]. Nevertheless, they always treat an alone information collection. The put problem is enough complicated and important for that we could treat it on the different types of information. Thus, we particularly were very interested in the specific problems of the information research in of multiples documents collections. So, this paper is organized as follows. In section 2, we introduce some basic definitions on formal concept analysis. Then in section 3, we present the data reduction. The section 4 is devoted to the presentation of several methods for searching in distributed information. In section 5, we present the complexity of those methods. The section 6 is devoted for the evaluation prototype. 2 Mathematical Foundations Among the mathematical theories found recently with important applications in computer science, lattice theory has a specific place for data organization, information engineering, data mining and for reasoning. It may be considered as the mathematical tool that unifies data and knowledge or information retrieval [1,2,3,4,5,6,7,8,9,10,13,14,15,18,19,20]. In this section, we define formal context, formal concept, Galois connection and the lattice of concepts associated to the formal context. 2.1 Formal Context Definition 1: A formal context is a triple k = <O,P,R>, where O is a finite set of elements called objects, P a finite set of elements called properties and R is a binary relation defined between O and P. The notations (g,m), or R(g,m)=1, means that "formal object g verifies property m in relation R" [12]. Example 1: Let O be a set of some animals and P be a set of the properties such as: a= needs water, b= lives in water, c= lives on land, d= can move around. Let O= {Leech, Bream, Frog, Dog} and P={a, b, c, d}. The following context may be defined by the table 1. a b c d 1 Leech Bream Frog Dog Table 1. An example of a formal context.

3 2.2 Galois Connection Definition 2: Let A Ο and B P two finite sets, R a relation on O x P. For both sets A and B, operators f(a) and h (B) are defined as: f (A) = {m g, g A (g,m) R} h (B) = {g m, m B (g,m) R} Operator f defines the properties shared by all elements of A. Operator h defines objects sharing the same properties included in set B. Operators f and h define a Galois Connection between sets O and P [12]. (x)=closure(a)={x} A, where x A. Example 2: Let R be the following relation, in the table, with 5 objects {O1,O2,O3,O4,O5} and three attributes {A,B,C}. A B C O O O O O Table 2. Example of a relation R Proposition 1: Operators f and h define a Galois connection between O and P, such that if A 1, A 2 are subsets of O, and B 1, B 2 are two subsets of P, then f and h verify the following properties [12]: A 1 A 2 f (A 1 ) f (A 2 ) (1) B 1 B 2 h (B 1 ) h (B 2 ) (2) A 1 h o f (A 1 ) and B 1 f o h (B 1 ) (3) A h (B) B f (A) (4) f = f o h o f and h = h o f o h (5) 2.3 Formal Concept Definition 3: A formal concept of the context <O,P,R> is a pair (A,B), where A Ο, B P, such f (A) = B and h (B) = A. Sets A and B are called respectively the domain (extent) and range (intent) of the formal concept [3,12]. 2.4 Concept Lattice Definition 4: From a formal context <O,P,R>, we can extract all possible concepts. In [3,12], we prove that the set of all concepts may be organized as a lattice, when we define the following partial order relation << between two concepts, (A1,B1) << (A2,B2) (A1 A2) and (B2 B1). The concepts (A1,B1) and (A2,B2) are called nodes in the lattice. The information searching using FCA takes as input 2.5 Equivalence between an object and a subset of other objects Definition 5: Let x O be an object, A Ο be a finite set and R a relation on O P. We define closure(x) = g(f(x)) and closure(a) = g(f(a)) [16,17]. Definition 6: Let x O be an object, A Ο be a finite set and R be a relation on O P. We say that an object x is equivalent to the objects A, relatively to a relation R, if and only if, {x} A is a domain of a concept of R, and that the closure O5 is equivalent to {O1,O2,O4}, the reason is that the concept containing O5 is CP={O1,O2,O4,O5} {C} ; and inversely the concept containing {O1,O2,O4} is also CP. 3 Current Search Using FCA can complement the existing search systems to address some of their main limitations. Basically, FCA exploits the similarity between documents in order to offer an automatically support structure (i.e., the document lattice) in which to place the information retrieval process. The document lattice can be used to improve basic individual search strategies [1,2,4,5,6,8,10,13,14,15]. Moreover, query refinement is one of the most natural applications of concept lattices. Its main objective is to recover from the null-output or the information overload problem. The concept lattice may be used to make a transformation between the representation of a query and the representation of each document [7,9]. The query is merged into the document lattice and each document is ranked according to the length of the shortest path linking the query to the document concept. In the other hand, on the set of terms describing the document, there exist hierarchies in the form of thesaurus [4,10,13,14]. a query that will be forwarded to a selected search engine [6,7,8]. The first pages retrieved by the search engine in answer to the query are collected and parsed. At this point, a set of index units that describe each returned document is generated; such indices are next used to build the concept lattice corresponding to the retrieved results. The last step consists of showing the lattice to the user and managing the subsequent interaction between the user and the system. In spite of such limitations such as for larger information collection, generally we get a huge number of references, we are interest to build a FCA-based system for distributed information,

4 which may affect both the efficiency and the effectiveness of the overall system. These limitations can be overcome by using data reduction that will be described in the next section. 4 conceptual Reduction Method The fundamental question for data reduction is the following: How can we reduce data without losing any knowledge? The advantage of reduced data is that it can be used directly as a prototype for making decision, for supervised learning or reasoning [16,17]. The proposed algorithm is based on the elimination of any object that may be replaced by a subset of the equivalent objects [17]. Firstly, we use relational join operator in order to obtain a total relation. Secondly, we apply reduction algorithm on the final table to minimize the number of rows. The major problem is that the treatment of an important size databases needs a considerable storage space and makes the reduction process sultry. Our idea is to propose an algorithm which makes simultaneously the join and the reduction of the tables set in only one reduced database. 5 Search enhanced by FCA In this section we will present some search that may be improved through a FCA for distributed information. 5.1 Cooperative conceptual information retrieval The majority of the proposed approaches based on the formal concept analysis construct a documents lattice. These different approaches handle an alone bases documents from which is constructed the documents lattice. Nevertheless, the data distribution on several bases becomes a solution to several problems met. Indeed, our system handles several divided up databases to which ones apply us the foundations of the formal concept analysis for a conceptual information retrieval [18]. As it is showed in the figure 1, the system C2IRS is composed from two phases: - In the first phase, C2IRS uses the different databases for the research process in order to furnish local results. Every local result is a concept that we stock in an Answer vector. If we have different N databases, we obtain thus to the maximum N concepts in the Answer vector. - In the second phase, we are very interested in the final answer formulation composite of two steps. First, we apply algorithm Merge1 that we propose on the Answer vector [18]. Next, we apply algorithm Merge2 on the modified vector in the objective to obtain the final answer. Cooperative IRS Conceptual IRS 1 Concept 1 User Query Fig. 1 C2IRS Architecture. Concept N We were very interested in the retrieval information systems based on the concept formal analysis. Indeed, the concept formal analysis is applied in a retrieval information system handling an alone information database. We presented our system integrating the cooperation between several systems for a research of conceptual information. The research process used by our system, that handles a local databases set, is based on the formal concept analysis. For every database we look for the local concept. We use a cooperative approach to formulate the final answer while basing us on the concepts extract of different local databases. If we merge the local databases in an alone bases on which apply us the conceptual research, we obtain the same result for a same query. The problem that remains put is linked to the magnitude of the treated database volume. In fact, a research in a voluminous database takes more time than a research in a smaller database. Thus, we need to minimize the every database size. This can be assured by the integration of the conceptual data reduction in our retrieval system that will be the object of the next section Cooperative Conceptual Information Retrieval System based on Data Reduction The research in the voluminous databases takes more time than the small databases. This raises consequently a problem to treat. Of more, the treatment of the databases having an important size Final Answer Formulation Final Answer Conceptual IRS N

5 necessitates a considerable storage space. Thus, we need to minimize the every database size. This can be assured by the integration of the conceptual data reduction in our research system. We propose a system for the conceptual cooperative information research based on the conceptual data reduction of the local data C2IRS_DR [19]. To improve upon cooperative conceptual information retrieval system, we propose a system for cooperative conceptual information retrieval basing on data reduction C2IRS_DR. As it is shown in figure 2, our proposed system is composed of two parts: - In the first party, the system that we propose uses a conceptual approach of reduction of the different local databases. Every local database is reduced in the objective to minimize his size and to obtain a local reduced database and an equivalent objects set. - In the second party, we propose a research process. Basing on the local reduced databases set and on the equivalent objects sets, we apply a cooperative approach in order to treat a query. Part 2 User Query Cooperative Conceptual Information Retrieval Final Answer Part 1 DB 1 Conceptual Data Reduction RDB 1 Equivalent objects 1 Fig. 2 Cooperative Conceptual Information retrieval based on data reduction The C2IRS_DR system solicits reduced databases of small size after to have applied the conceptual data reduction on initial databases having an important size. Thus, this system uses a storage space less important that the one used by the research system of cooperative information C2IRS describes in the DB N RDB N Equivalent objects N section 5.1. Of more, the research while using C2IRS_DR takes less than the time than the research while using C2IRS. Nevertheless, the research in several local databases, reduced or non-reduced, necessitates a merger step of the local results. This step has an impact on the answer time. Of more, the reduction of voluminous databases is costly in term times. Our idea is to propose an algorithm allowing reducing a set of local databases in an alone reduced databases on which the research process will be executed. We propose a cooperative data reduction algorithm applied in an information research. We propose a conceptual information retrieval system based on the conceptual cooperative global data reduction CIRS_CDR. Our conceptual cooperative data reduction algorithm is applied on the set of the local databases to have an alone reduced database and an equivalent objects set. We apply the research process conceptual on the reduced basis and we obtain a concept containing the answer to the query that can be enriched while soliciting the equivalent objects set Conceptual information retrieval system based on cooperative conceptual data reduction We propose a conceptual information retrieval system based on the conceptual cooperative global data reduction CIRS_CDR [20]. Our conceptual cooperative data reduction algorithm is applied on the set of the local databases to have an alone reduced database and an equivalent objects set. We apply the conceptual research process on the reduced database and we obtain a concept containing the answer to the query that can be enriched while soliciting the equivalent objects set. We present an approach for information retrieval that is composed of two parts as it is shows in the following figure: - Part 1: From a set of formal contexts representing the databases, we apply the proposed algorithm for cooperative conceptual data reduction in order to obtain the reduced database and the set of equivalent objects. - Part 2: The research is based on this reduced database. To respond to a query that is a set of terms, we apply the Galois connection to retrieve the documents satisfying the query. The final answer can be enriched by the set of equivalent objects.

6 Part 1 DB 1 DB N C T (n,m) = 2nm + n. Space complexity. The system C2IRS uses k matrix with n lines and m columns. So, it uses (k*n*m) memory cells. So, the space complexity of this method is C S = knm. User Query Equivalent objects Cooperative Conceptual Data Reduction Part Conceptual Information Retrieval RDB 6.2 Cooperative conceptual information retrieval information based on Data reduction We suppose that the database has n documents and m keywords and the reduced database has n documents and m keywords. We remind first all steps of this system: - Phase 1: conceptual data reduction applied on several databases. - Phase 2: cooperative conceptual information retrieval applied on the reduced databases. Answer Fig. 3 Architecture of the conceptual information retrieval system based on cooperative conceptual data reduction 6 Complexity Analysis The complexity analysis of a treatment is ensured by calculating: i) The time complexity, which is the number of operations of the treatment, and ii) The space complexity, which is the number of memories cells used by the treatment. We compute the complexity analysis of cooperative conceptual information retrieval system, conceptual information retrieval system based on data reduction and conceptual information retrieval system based on cooperative data reduction. 6.1 Cooperative Conceptual Information Retrieval System We present the complexity of the cooperative conceptual information retrieval system C2IRS. We suppose that the database has n documents and m keywords. We remind first of all the steps of this system: - Phase 1: the search of concepts from different databases. - Phase 2: the formulation of the final answer from the found concepts. Time Complexity. We suppose that each database has n documents and m keywords. The time complexity of the system C2IRS is 2(n*m) + n. So, Time complexity. It is easy to find the complexity C T (n,m) for this system which is equal in: C T (n,m)=c TPhase 1 (n,m)+c TPhase 2 (n,m ). The complexity of phase 1 is O(n*m). The phase 2 realize (2(n *m )+n ) operations [17]. So, the system realizes n*m+[2(n *m )+n ] operations. So, C T (n,m) =nm+2n m +n. Since the size of the reduced database is lesser than that of the initial database (n <<n). So, the complexity of our proposed system is lesser than that of the C2IRS. C T (n,m)=nm+2n m +n <<C T (n,m)=2nm+ n. Space Complexity. Our retrieval system handles a reduced database. So, we can reserve only (k*n *m ) memory cells. So, the space complexity of our system is C S =kn m. We note that our algorithm uses a less number of memory cells that the C2IRS: C S <<C S. This can be explained by the integration of the conceptual data reduction in our proposed system. 6.3 Conceptual information retrieval system based on Cooperative data reduction Time complexity. If we have K databases, each one has n documents and m keywords, we realize N iterations where N = n n. In each loop, we cover the concepts graph G and we do then G operations where G represents the graph cardinality. So, we do G update operations on the graph (adding or modification operation). So, C T O(N* G 2 ). Then, our algorithm have a complexity less then that of the conceptual data reduction considering the

7 cardinality of the graph is too small compared to the number of keywords ( G << M) Space Complexity. Our algorithm treats in each loop one document. So, we can reserve only M memory cases. For the treatment of each line, the algorithm uses a graph that is constructed in incremental manner. This graph necessities 8* G memory cells since for each graph node, we reserve 8 memory cells. So, the space complexity of our algorithm is C S =M+(8* G ). We note that our algorithm uses a less number of memory cells that the conceptual data reduction: C S <<C S. This can be to explain by the fact why the conceptual data reduction treats a matrix of N lines and M columns on the other hand our algorithm treats only one line. 7 Evaluation prototype The experimentations is done on two test collections MED and CRAN. The CRAN collection (Cranfield collection) includes a textual corpus that has a size greater than 1.6Mo. This collection contains 1400 documents and 4612 different and it is tested on 225 queries. The MED collection MED includes a textual corpus that has a size 1.1Mo. It contains 1033 scientific articles extracted from databases in the medicine domain and 5831 terms different and it is tested on 30 queries. The experimentations realised on the CRAN and MED test collections show that the cooperative conceptual reduction applied on the fragmented collection and the conceptual reduction applied on the initial database generates the same reduced database. The trump of the cooperative conceptual reduction is to reduce a set of databases set in order to obtain a reduced database while generating a concepts graph. So, the research process can be executed either on the reduced database or on the obtained graph. Executing the different queries of the two test collections, we obtain the same answers that the other presented systems. Later, CIRS_RCD has the same recall and precision graph that the systems CIRS, C2IRS and C2IRS_DR (see figure 4 and figure 5). This shows that our proposed approaches assure the non-loss information. In fact, our research approaches integrated the data reduction generates the reduced database and the equivalent objects set. The research in the reduced databases can be enriched by the consultation of equivalent objects. The experimentations show that the treatment of 30 queries of the MED collection with the reduced databases also as the equivalents objects set offers the same result that with the initial MED database or that fragmented on portions. 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0, Recall CIRS - C2IRS - C2IRS_DR - CIRS_CDR -IRS_Graph Fig. 4 The Recall and precision graph of the MED fragmented collection for CIRS, CIRS2, C2IRS_DR and CIRS_RCD. 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0, Recall CIRS - C2IRS - C2IRS_DR - CIRS_CDR - IRS_Graph Fig. 5 The recall and precision graph of the CRAN fragmented collection for CIRS, CIRS2, C2IRS_DR and CIRS_RCD. As we are presented already, the research process can be executed either on the reduced database or on the concepts graph. We remark that research the final answer in the graph is simple and faster than research in the reduced database. Moreover, the system permit to accelerate the answer time par rapport aux three first systems as well as for the MED collection MED as for CRAN collection. (see figure 6 and figure 7)

8 Queries CIRS C2IRS C2IRS_DR CIRS_CDR IRS_Graph Fig. 6 Answer time takes by each system CIRS, CIRS2, C2IRS_DR, CIRS_CDR and IRS_Graph for the MED collection. The systems C2IRS_DR and CIRS_CDR treat the MED collection queries in a reasonable answer time in comparison with that of CIRS. This can be explained by the data reduction integration. In fact, the objective of this later is to reduce the size of a database on that is done the research tout en offer an equivalent object set. The answer time of research executed on the CRAN collection with the five retrieval systems: CIRS, C2IRS, C2IRS_DR and CIRS_CDR (research in the reduced database and in the graph) is presented in the figure 7. We consider only the 30 first queries of a total of 250 queries, because the MED collection treats 30 queries Queries CIRS C2IRS C2IRS_DR CIRS_CDR IRS_Graph Fig. 7 Answer time takes by each system CIRS, C2IRS, C2IRS_DR, CIRS_CDR and IRS_Graph for the CRAN collection. 8 Conclusion In this paper, we have presented three conceptual information retrieval systems. The cooperative conceptual information retrieval system combines the results of several information retrieval systems. Each one has its local formal context representing a database on which we apply a conceptual search to obtain a first set of concepts. From this set of concepts, we formulate the final answer by applying a proposed algorithm merging and combining concepts with a suitable way. The volume of the available information is increasing exponentially. So, generally we get a huge number of references. It is necessary to abstract it and eliminate the redundancy data. However, our main idea is to integrate the data reduction in the search process. The information retrieval is based on the data reduction. From a set of formal contexts presenting a databases set, we apply the relational join operator in order to fusion the tables. Basing on the join resulting table, we apply the data reduction algorithm to obtain the reduced table on which the search process is executed. The major problem is that the treatment of an important size databases needs a considerable storage space and makes the reduction and the research process sultry. We are presented an information retrieval based on a cooperative conceptual data reduction. We have developed a fast algorithm that combines the join and the reduction steps for minimizing formal contexts and we have applied it in an information retrieval system. From a set of databases, we obtain a reduced database on which we apply a conceptual research for responding to a query. This application was experimented on many databases and the obtained results are promising. This study has several perspectives for real and fuzzy data. References: [1] Aboud M., Chrisment C., Razouk R., Florence S., Soulé-Dupuy, Query a Hypertext Information Retrieval System by use of Classification, Information Processing and Management, 29(3), (1993) [2] Amati G., Carpineto C., and Romano G., FUB at TREC-10 Web Track: A Probabilistic Framework for Topic Relevance Term Weighting. In Proceedings of the 10 th Text REtrieval Conference (TREC-10), NIST Special Publication , Gaithersburg, MD, USA (2001) [3] Bordat J.P., Calcul pratique du treillis de Galois d'une correspondance, Math. Sci. Hum., 96, (1986) [4] Carpineto C. and Romano G., Using Concept Lattices for Text Retrieval and Mining. In the first International Conference on Formal Concept Analysis, Darmstadt, Germany, (2003).

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