{ "paper_id": "Y18-1019", "header": { "generated_with": "S2ORC 1.0.0", "date_generated": "2023-01-19T13:36:30.491028Z" }, "title": "FCA Retrieval: A Multi-operator Algorithm for Information Retrieval from Binary Concept Lattice", "authors": [ { "first": "Fethi", "middle": [], "last": "Fkih", "suffix": "", "affiliation": {}, "email": "fethi.fkih@gmail.com" }, { "first": "Mohamed", "middle": [ "Nazih" ], "last": "Omri", "suffix": "", "affiliation": {}, "email": "mohamednazih.omri@fsm.rnu.tn" } ], "year": "", "venue": null, "identifiers": {}, "abstract": "The use of a concept lattice for the visual representation of knowledge has become very common in the data mining field. Indeed, the theory of Formal Concept Analysis (FCA) gives the possibility of organizing and making reasoning on the knowledge stored in the lattice. In this context, we propose FCA Retrieval a fast and efficient algorithm for information retrieval from a binary concept lattice. This algorithm can respond to queries containing several types of logical operators (conjunction, disjunction and negation). The experimental study proves the good performance of our algorithm.", "pdf_parse": { "paper_id": "Y18-1019", "_pdf_hash": "", "abstract": [ { "text": "The use of a concept lattice for the visual representation of knowledge has become very common in the data mining field. Indeed, the theory of Formal Concept Analysis (FCA) gives the possibility of organizing and making reasoning on the knowledge stored in the lattice. In this context, we propose FCA Retrieval a fast and efficient algorithm for information retrieval from a binary concept lattice. This algorithm can respond to queries containing several types of logical operators (conjunction, disjunction and negation). The experimental study proves the good performance of our algorithm.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Abstract", "sec_num": null } ], "body_text": [ { "text": "With the evolution of documents quantity in databases, it has become very difficult to extract the information corresponding to the exact needs of the user in a reasonable time without the design of an effective strategy. Indeed, this strategy must be based, first, on the right representation of the information found in the documents or in the query and, secondly, on the development of an efficient and fast algorithms for information retrieval (Fkih and Omri, 2012) .", "cite_spans": [ { "start": 448, "end": 469, "text": "(Fkih and Omri, 2012)", "ref_id": "BIBREF9" } ], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1" }, { "text": "In this context, concept lattices are considered as very powerful tools for the visual presentation of knowledge (Poelmans et al., 2013) . Also, Formal Concept Analysis (FCA) is considered a flexible and practical theoretical framework for binary relations management. The relation between a document and the information that presents it is a binary relation (the information presents the document or not). Therefore, a concept lattice can easily model the document/term relation and can be considered as an semantic index (Fkih and Omri, 2016) .", "cite_spans": [ { "start": 113, "end": 136, "text": "(Poelmans et al., 2013)", "ref_id": "BIBREF14" }, { "start": 523, "end": 544, "text": "(Fkih and Omri, 2016)", "ref_id": "BIBREF10" } ], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1" }, { "text": "In this paper, we propose an efficient algorithm (FCA Retrieval) for the retrieval of information in a concept lattice. This algorithm uses the theory of formal concept analysis (FCA) to respond to a user query and retrieve the information in a reasonable time. The main advantage of this algorithm is that it can handle multiple logical operators queries (i.e. conjunctive, disjunctive and negation operators).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1" }, { "text": "The remainder of this paper is structured as follows. In section 2,we provide an overview on the works that use the concept lattice for documents indexing. Section 3 presents the basic notions of the Formal Concept Analysis (FCA) theory. In section 4, we introduce our algorithm, FCA Retrieval, for information retrieval in a concept lattice. Section 5 is reserved for an experimental comparative study between the proposed model and other models in the literature.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1" }, { "text": "The use of concept lattices for information retrieval began with the introduction of the Formal Concept Analysis (FCA) theory by (Wille, 1982) in the 1980s. Information retrieval is considered a direct application of the concept lattice due to the high correspondence between the theoretical foundations of this approach and those of information retrieval (Godin et al., 1995) . Indeed, if we replace objects by documents and attributes by terms, the formal context becomes a simple inverted file (index) used for documents indexing.", "cite_spans": [ { "start": 129, "end": 142, "text": "(Wille, 1982)", "ref_id": "BIBREF17" }, { "start": 356, "end": 376, "text": "(Godin et al., 1995)", "ref_id": "BIBREF11" } ], "ref_spans": [], "eq_spans": [], "section": "Related Works", "sec_num": "2" }, { "text": "There are several approaches for information retrieval based on concept lattice, we cite: information retrieval systems for medical documentation (Cole and Eklund, 1996; Cole and Eklund, 1999) , software documentation (Linding, 1995; Priss, 2000) and Bioinformatic Databases (Smal-Tabbone et al., 2005) . We can classify FCA-based models into three main families: CLR (Concept Lattice-based Ranking) methods, refinement and organization methods and classification-based reasoning methods.", "cite_spans": [ { "start": 146, "end": 169, "text": "(Cole and Eklund, 1996;", "ref_id": "BIBREF3" }, { "start": 170, "end": 192, "text": "Cole and Eklund, 1999)", "ref_id": "BIBREF4" }, { "start": 218, "end": 233, "text": "(Linding, 1995;", "ref_id": "BIBREF13" }, { "start": 234, "end": 246, "text": "Priss, 2000)", "ref_id": "BIBREF15" }, { "start": 275, "end": 302, "text": "(Smal-Tabbone et al., 2005)", "ref_id": "BIBREF16" } ], "ref_spans": [], "eq_spans": [], "section": "Related Works", "sec_num": "2" }, { "text": "Approaches belonging to the CLR family are based essentially on the idea of considering the query as a new entry for the formal context. In this case, the search for documents satisfying the query turns into a problem of reconstruction of the lattice. These retrieval algorithms use incremental construction techniques to insure the insertion of the new entry in context. These incremental construction techniques are more efficient, from the point of view of complexity and efficiency, than those which reconstruct, from scratch, the lattice. In the literature there are several models belonging to the CLR family, such as: BR-Explorer (Messai et al., 2006) , BMR (current best-match ranking) and HCR (model and hierarchical clustering-based ranking) (Carpineto and Romano, 2000a) .", "cite_spans": [ { "start": 625, "end": 658, "text": "BR-Explorer (Messai et al., 2006)", "ref_id": null }, { "start": 752, "end": 781, "text": "(Carpineto and Romano, 2000a)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Concept Lattice-based Ranking methods", "sec_num": "2.1" }, { "text": "These approaches use a search engine to respond to a user query and exploit the links of documents as well as summaries and titles provided by the engine. Their primary role is to provide the user the ability to refine his query by browsing the concept lattice and exploring neighbouring concepts. For instance, we cite systems CREDO (Carpineto and Romano, 2004) , FooCA (Koester, 2006) and Search-Sleuth (Dau et al., 2008; Ducrou, 2007) .", "cite_spans": [ { "start": 334, "end": 362, "text": "(Carpineto and Romano, 2004)", "ref_id": "BIBREF2" }, { "start": 371, "end": 386, "text": "(Koester, 2006)", "ref_id": "BIBREF12" }, { "start": 405, "end": 423, "text": "(Dau et al., 2008;", "ref_id": "BIBREF5" }, { "start": 424, "end": 437, "text": "Ducrou, 2007)", "ref_id": "BIBREF8" } ], "ref_spans": [], "eq_spans": [], "section": "Refinement and organization methods", "sec_num": "2.2" }, { "text": "This approach uses the concept lattice as an index of a documentary database and applies navigation algorithms to the lattice to respond to a query. The main aim of this type of method is to maximize the lattice navigation. In this case, the lattice is seen as a semantic index for information retrieval since it is the result of a clustering operation. Among systems belonging to this family, we cite CLAIR (Codocedo et al., 2014) . This system is based on the insertion of a query in a classification-based reasoning.", "cite_spans": [ { "start": 408, "end": 431, "text": "(Codocedo et al., 2014)", "ref_id": "BIBREF2" } ], "ref_spans": [], "eq_spans": [], "section": "Classification-based reasoning methods", "sec_num": "2.3" }, { "text": "Definition 1 (Formal context) A formal context is a triplet F = (D, T, I) where:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Basic notions of Formal Concept Analysis", "sec_num": "3" }, { "text": "\u2022 D : set of documents.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Basic notions of Formal Concept Analysis", "sec_num": "3" }, { "text": "\u2022 T : terms set.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Basic notions of Formal Concept Analysis", "sec_num": "3" }, { "text": "\u2022 I : binary relation between D and T verifying that I \u2286 D \u00d7 T I is called the incidence relation of F . Let d \u2208 D and t \u2208 T , the relation (d, t) \u2208 I means that the document d contains the term t (we also say that the term t is satisfied by the document d).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Basic notions of Formal Concept Analysis", "sec_num": "3" }, { "text": "Definition 2 (Derivation operator) Also called sufficiency operator as in (Dubois et al., 2007) , derivation operators are considered as the basis of the formal analysis. Given X \u2286 D and Y \u2286 T , we denote by X \u2206 (equation 1) the set of terms satisfied by the set of documents X and Y \u2206 (equation 2) the set of documents satisfying the set of terms Y .", "cite_spans": [ { "start": 74, "end": 95, "text": "(Dubois et al., 2007)", "ref_id": "BIBREF7" } ], "ref_spans": [], "eq_spans": [], "section": "Basic notions of Formal Concept Analysis", "sec_num": "3" }, { "text": "X \u2206 = {y \u2208 T | X \u2286 I(y)}", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Basic notions of Formal Concept Analysis", "sec_num": "3" }, { "text": "(1)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Basic notions of Formal Concept Analysis", "sec_num": "3" }, { "text": "Y \u2206 = {x \u2208 D | Y \u2286 I(x)} (2)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Basic notions of Formal Concept Analysis", "sec_num": "3" }, { "text": "Intuitively, X \u2206 is the set of attributes common to all the objects of X and Y \u2206 is the set of the objects that share all the attributes of Y .", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Basic notions of Formal Concept Analysis", "sec_num": "3" }, { "text": "Definition 3 (Formal concept) A formal concept is a pair X, Y such that X \u2206 = Y and Y \u2206 = X. X and Y are called respectively the extent and the intent of the concept X, Y . An order relation, denoted , is defined on the set of all concepts. We have the following equivalence (equation 3):", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Basic notions of Formal Concept Analysis", "sec_num": "3" }, { "text": "Definition 4 (Lattice Concept) The set of concepts ordered by forms a complete lattice denoted B(D, T, I). We say that B(D, T, I) is the lattice associated with the formal context F = (D, T, I). We denote:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Basic notions of Formal Concept Analysis", "sec_num": "3" }, { "text": "\u2022 \u03c4 : the most general concept belonging to B(D, T, I), also called the top element.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Basic notions of Formal Concept Analysis", "sec_num": "3" }, { "text": "\u2022 \u03b2: the most specific concept belonging to B(D, T, I), also called the bottom element.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Basic notions of Formal Concept Analysis", "sec_num": "3" }, { "text": "Our approach is based mainly on the use of the specification/generalization relation that exists between the lattice concepts (see figure 1 ). Indeed, a concept lattice is the result of a clustering operation which groups the documents sharing the same terms in common concepts. The lattice top (\u03c4 ) is considered as the most general concept in the lattice; it groups in its extent all the documents of the collection. The intent of \u03c4 contains common terms between all documents if they exist, the empty set otherwise. If we move to the lower hierarchy level, we find the maximum subsets of documents that share the same terms. In fact, the more we descend in the lattice more we add terms to the intent of each concept, i.e., we specify the documents. The most specific concept is the bottom of the lattice (\u03b2), it contains all the terms in its intent and contains the documents that share all the terms in its extent (the empty set, if there are no documents). For a given query Q, containing a variety of logical operators, our algorithm treats each operator type alone. That is, it separates the conjunction operators from those of disjunction or negation. As it presents the algorithm 1, it begins with the disjunctive part of the query and then processes the disjunctive part. For the negation operator, the algorithm 2 calls algorithm 1 to treat the conjunction and disjunction operators then it applies the negation to the returned result.", "cite_spans": [], "ref_spans": [ { "start": 131, "end": 139, "text": "figure 1", "ref_id": "FIGREF0" } ], "eq_spans": [], "section": "Proposed algorithms", "sec_num": "4" }, { "text": "For conjunction operators, the idea is to find (in the lattice) the most general concept (C conj g ) containing in its intent all the conjunctive terms of the query, by starting the search with the most specific concept ", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conjunctive operators of the query", "sec_num": "4.1" }, { "text": "= Intent C conj g , Extent C conj g", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conjunctive operators of the query", "sec_num": "4.1" }, { "text": "the most general concept in the lattice such that:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conjunctive operators of the query", "sec_num": "4.1" }, { "text": "T Q conj \u2286 Intent C conj g", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conjunctive operators of the query", "sec_num": "4.1" }, { "text": "then, we say that: the documents set Extent C conj g satisfy the conjunctive part of the Query Q.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conjunctive operators of the query", "sec_num": "4.1" }, { "text": "The \u03b2 concept must include, in its intent, all the conjunctive terms of the query; otherwise it's said that the lattice can't satisfy the query. If the beta intent contains all the conjunctive terms we pass to the direct parents of the concept (the highest hierarchical level). If one of the concepts don't contain all the conjunctive terms in its intent then it is useless to continue the search in its parents (this will simplify the search space and decrease the complexity of the algorithm). This simplification is justified by the fact that the intent of the parent is included in the intent of his son then if the terms don't exist in the intent of the son, they don't also exist in the intent of the father. Otherwise, if a concept contains all the conjunctive terms and all of its direct parents don't contain them then it's considered as C conj g and the result will be the documents of its extent. The algorithm stops when it finds C conj g or if it finishes the entire lattice.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conjunctive operators of the query", "sec_num": "4.1" }, { "text": "After completing the conjunctive part of the query Q, the algorithm proceeds to the processing of the disjunctive part. Our idea is to look for the most general concept (C disj g ) containing at least one term Algorithm 1: FCA Retrieval(): Generalized algorithm for multiple logical operators query Data: F = (D, T, I), B(D, T, I) Q: multiple logical operators query T Q = {t 1 , t 2 , ..., t n\u22121 , t n } \u03c8 conj : set of concept to explore by conjunctive operators \u03c8 disj : set of concept to explore by disjunctive operators \u03c4 : Lattice Top (most general concept in the lattice) \u03b2: Lattice Bottom (most specific concept in the lattice) Result: Intent Cg = \u2205 then, we say that: the documents set Extent C disj g satisfy the disjunctive part of the Query Q.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Disjunctive operators of the query", "sec_num": "4.2" }, { "text": "R d : set of documents satisfying the query Q) begin 1 R d \u2190\u2212 {\u2205} 2 \u03c8 conj \u2190\u2212 {\u03b2} 3 \u03c8 disj \u2190\u2212 {\u03c4 } for C \u2208 \u03c8 conj do 4 if T Q \u2286 intent(C) then 5 Clean(R d ) 6 R d \u2190\u2212 extent(C) 7 \u03c8 conj \u2190\u2212 \u03c8 conj \u222a F athers(C) 8 \u03c8 conj \u2190\u2212 \u03c8 conj \\ {C} else 9 \u03c8 conj \u2190\u2212 \u03c8 conj \\ {C} 10 delete Ancestors(C) from the lattice end end for C \u2208 \u03c8 disj do 11 if T Q \u2229 intent(C) = {\u2205} then 12 \u03c8 disj \u2190\u2212 \u03c8 disj \u222a Sons(C) 13 \u03c8 disj \u2190\u2212 \u03c8 disj \\ {C} else 14 R d \u2190\u2212 R d \u222a extent(C)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Disjunctive operators of the query", "sec_num": "4.2" }, { "text": "The algorithm 1 explores the intent of \u03c4 , if it finds at least one term of the disjunctive part of the query Q in its intent then it's said that all documents in the collection satisfy the query, otherwise the algorithm passes to its direct sons. If we find a term, at least, in the intent of one of its sons then we take its extent and we ignore all its descendants. The research is continued until all the lattice concepts are checked.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Disjunctive operators of the query", "sec_num": "4.2" }, { "text": "The idea of negation is very simple: first, ignored the negation operator, in this case we can apply the algorithm 1. Then take the complement of the set of returned documents. Algorithm 2 is based on the following proposition:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Negation operators of the query", "sec_num": "4.3" }, { "text": "Proposition 3 Let Q = \u00acQ , and let D Q the documents set that satisfying to Q , then, we say that: the documents set D Q satisfy the Query Q.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Negation operators of the query", "sec_num": "4.3" }, { "text": "Algorithm 2: FCA Retrieval Negative(): an algorithm for negative query Data: F = (D, T, I), B(D, T, I) Q : negative query Table 1 presents a formal context I that models a binary relation between the set of documents D = {d1, d2, d3, d4, d5, d6, d7} and the set of terms T = {t1, t2, t3, t4, t5, t6}. In this case, the formal context is considered as a binary document-term incidence matrix. Practically, if a document contains a term then we put 1, 0 otherwise. Table 1 : An example of a formal context F = (D, T, I) modelling the relation document-term Document-Term t1 t2 t3 t4 t5 t6 d1 1 0 1 0 1 1 d2 1 1 0 0 0 0 d3 0 0 1 1 1 0 d4 0 0 0 0 1 1 d5 0 0 0 1 0 1 d6 1 0 1 0 0 0 d7 0 1 0 1 0 1 Figure 2 shows the Hasse diagram of the concept lattice B(D, T, I) corresponding to the formal context F = (D, T, I). This diagram is drawn by Con-Exp 1 , a free software for building and visualizing lattices.", "cite_spans": [], "ref_spans": [ { "start": 122, "end": 129, "text": "Table 1", "ref_id": null }, { "start": 463, "end": 470, "text": "Table 1", "ref_id": null }, { "start": 692, "end": 700, "text": "Figure 2", "ref_id": "FIGREF2" } ], "eq_spans": [], "section": "Negation operators of the query", "sec_num": "4.3" }, { "text": "T Q = {t 1 , t 2 , ..., t n\u22121 , t n } Q = \u00acQ Result: R N eg d : set of documents satisfying the query Q begin 1 R N eg d \u2190\u2212 F CA Retrieval(Q) 2 Return R N eg d end", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Negation operators of the query", "sec_num": "4.3" }, { "text": "For this example, the corresponding concepts to the top (\u03c4 ) and the bottom (\u03b2) of the lattice B(D, T, I) are:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Demonstrative example", "sec_num": "4.4" }, { "text": "EQUATION", "cite_spans": [], "ref_spans": [], "eq_spans": [ { "start": 0, "end": 8, "text": "EQUATION", "ref_id": "EQREF", "raw_str": "\u03c4 = {d 1 , d 2 , d 3 , d 4 , d 5 , d 6 , d 7 }, {\u2205} (4) \u03b2 = {\u2205}, {t 1 , t 2 , t 3 , t 4 , t 5 , t 6 }", "eq_num": "(5)" } ], "section": "Demonstrative example", "sec_num": "4.4" }, { "text": "In this example, we try to apply our algorithm 1 to the lattice described in the figure 2. This set of docu-1 http://sourceforge.net/projects/conexp/ Figure 3 : There are a one concept contains in its intent the query terms (surrounded by a green circle) ments (noted R d ) To do this, we look for documents that satisfy to the query Q = t 5 \u2227 t 6 \u2228 t 2 .", "cite_spans": [], "ref_spans": [ { "start": 150, "end": 158, "text": "Figure 3", "ref_id": null } ], "eq_spans": [], "section": "Demonstrative example", "sec_num": "4.4" }, { "text": "First, we start with the processing of the conjunctive part of the query, i.e, t 5 \u2227 t 6 . As the algorithm specifies, we begin the exploration of the lattice by the processing of the concept \u03b2 (the most specific concept in the lattice). In this level, we find that \u03b2 contains all query terms, so", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Demonstrative example", "sec_num": "4.4" }, { "text": "R d = {\u2205}.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Demonstrative example", "sec_num": "4.4" }, { "text": "Thereafter,we move on to the exploration of higher level concepts (direct fathers). We find a single concept that its intent contains all the query terms (surrounded by a green circle in the figure 3) , all the fathers of the other concepts (surrounded by a red circle in the figure 4) will be ignored by the algorithm to simplify the search space. The extent of this concept contains a single document d1. Then, we update the set of results", "cite_spans": [], "ref_spans": [ { "start": 191, "end": 200, "text": "figure 3)", "ref_id": null } ], "eq_spans": [], "section": "Demonstrative example", "sec_num": "4.4" }, { "text": "R d = {d1}.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Demonstrative example", "sec_num": "4.4" }, { "text": "Before stopping the processing of the conjunctive part of the query, there is one concept to explore (surrounded by a green circle in the figure 4). We find that the intent of this concept contains all the terms of the query, so we assign its extent to R d . The set of results becomes", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Demonstrative example", "sec_num": "4.4" }, { "text": "R d = {d1, d4}.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Demonstrative example", "sec_num": "4.4" }, { "text": "After having finished processing the conjunctive part of the query, the algorithm begins processing the disjunctive part, i.e., it looks (in our example) for the documents containing the term t2. To do this, our algorithm explores the concept \u03c4 (the most general concept in the lattice). In our example, the algorithm can't find the term t2 in the intent of \u03c4 , so it pursues the search in its direct descendants. The algorithm finds t2 in the intent of a direct descendant of \u03c4 (surrounded by a green circle in the figure 5), then it adds all the documents that are in its extent (in this case, d2 and d7) to the set of results, which becomes:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Demonstrative example", "sec_num": "4.4" }, { "text": "R d = {d1, d4, d2, d7}", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Demonstrative example", "sec_num": "4.4" }, { "text": ". In this stage, the algorithm ignores all the descendants of the concept containing the term t2. In addition, it ignores the neighbours of this concept, because, it's useless to look for t2 in concepts of the same hierarchical level (all concepts surrounded by red circles in figure 6) . Thus, the algorithm stops the processing of the query Q and returns the set of documents R d .", "cite_spans": [], "ref_spans": [ { "start": 277, "end": 286, "text": "figure 6)", "ref_id": "FIGREF5" } ], "eq_spans": [], "section": "Demonstrative example", "sec_num": "4.4" }, { "text": "To simulate the behaviour of our algorithm vis-vis the logical negation operator, we try to process the query Q = \u00acQ. As indicated in algorithm 2, we first call algorithm 1 and then we look for the complement of the returned set, i.e., if R d is the set of documents returned by algorithm 1, then the set of documents returned by algorithm 2 can be defined by: ", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Demonstrative example", "sec_num": "4.4" }, { "text": "R N eg d = R d = {d1, d4, d2, d7} = {d3, d5, d6}.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Demonstrative example", "sec_num": "4.4" }, { "text": "To show that our algorithm is faster and simpler than other algorithms in the literature, we conduct a comparative study between FCA Retrieval, CLR (Carpineto and Romano, 2000b) , BR-Explorer (Messai et al., 2006) and CLAIR (Codocedo et al., 2014) . In order to achieve this, we implement all these algorithms in Java programming language on a Windows 7 platform. To evaluate the performance in execution time, the experimental tests were conducted on a Intel Core i5-6200U machine having a clock frequency of 2.8Ghz and 8GB of main memory.", "cite_spans": [ { "start": 148, "end": 177, "text": "(Carpineto and Romano, 2000b)", "ref_id": "BIBREF1" }, { "start": 180, "end": 213, "text": "BR-Explorer (Messai et al., 2006)", "ref_id": null }, { "start": 218, "end": 247, "text": "CLAIR (Codocedo et al., 2014)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Experimental study", "sec_num": "5" }, { "text": "The different models were evaluated using Connect-4 2 , a standard dataset. This test data is seen as a multi-valued formal context (each attribute can take one of three values of the set {x, o, b}). To make it more compatible with our application, we have transformed this multi-valued formal context to a binary formal context. Indeed, each attribute of the formal context takes 0 if its value is b, 1 otherwise.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Test Data description", "sec_num": "5.1" }, { "text": "In this stage, our goal is to study the behaviour of the different models (taking the execution time as an indicator) if we vary the size of the data set (number of objects). To achieve this, we have prepared 15 formal contexts (extracted from Connect-4) each one contains 42 attributes and a number of instances ranging from 1 to 10000 (see table 5.1). 10000 2564", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Test Data description", "sec_num": "5.1" }, { "text": "Figure 7: Comparative study between our algorithm and other algorithms of the literature.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Test Data description", "sec_num": "5.1" }, { "text": "Each model is tested on the 10 concept lattices using 10 different queries. In practice, we calculate for each model the response time to a given query. Subsequently, we calculate the average time for all queries. Table 5 .2 summarizes the results obtained for all models. Figure 7 shows the variation of the execution speed of each algorithm according to the number of objects in the lattice. The experimental study shows that our algorithm is faster than the other algorithms. In fact,the gap between the performance of our algorithm and other algorithms increases with the number of objects. By way of example, the difference between the execution times of FCA Retreival and CLR can reach 12.22 for a trellis of 10000 objects.", "cite_spans": [], "ref_spans": [ { "start": 214, "end": 221, "text": "Table 5", "ref_id": null }, { "start": 273, "end": 281, "text": "Figure 7", "ref_id": null } ], "eq_spans": [], "section": "Results and discussion", "sec_num": "5.2" }, { "text": "The experimental result can be justified by a theoretical study. Therefore, if we compare the complexity of our algorithm with the complexity of other algorithms, we find that FCA Retrieval is the least complex. The table shows the temporal complexity of each model. The complexity of FCA Retrieval is O(n) (worst case, where n is the number of concepts in the lattice) while the complexity of the others is O(n 2 ) which justifies the superiority of our algorithm in execution time.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Results and discussion", "sec_num": "5.2" }, { "text": "In this paper, we have presented a novel algorithm for information retrieval from a binary concept lattice. This algorithm is based on the theory of formal concept analysis and can handle a query containing a variety of logical operators (conjunction, disjunction and negation). The experimental study shows that our model is efficient and provides the most optimal execution time.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conclusion", "sec_num": "6" }, { "text": "As future work, we try to integrate semantic resources into our model to deal with the semantic ambiguity that exists in user queries. ", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Conclusion", "sec_num": "6" }, { "text": "32nd Pacific Asia Conference on Language, Information and Computation Hong Kong, 1-3 December 2018Copyright 2018 by the authors", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "", "sec_num": null }, { "text": "32nd Pacific Asia Conference on Language, Information and Computation Hong Kong, 1-3 December 2018Copyright 2018 by the authors", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "", "sec_num": null }, { "text": "32nd Pacific Asia Conference on Language, Information and Computation Hong Kong, 1-3 December 2018Copyright 2018 by the authors", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "", "sec_num": null } ], "back_matter": [], "bib_entries": { "BIBREF0": { "ref_id": "b0", "title": "by the authors References Claudio Carpineto and Giovanni Romano", "authors": [], "year": 2000, "venue": "Pacific Asia Conference on Language, Information and Computation Hong Kong", "volume": "51", "issue": "", "pages": "587--601", "other_ids": {}, "num": null, "urls": [], "raw_text": "Pacific Asia Conference on Language, Information and Computation Hong Kong, 1-3 December 2018 Copyright 2018 by the authors References Claudio Carpineto and Giovanni Romano. 2000a. 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The proposition 1 defines the characteristics of the concept C conj g . Proposition 1 Let T Q conj The set of conjunctive terms of the query Q, and let C conj g", "uris": null }, "FIGREF1": { "type_str": "figure", "num": null, "text": "end of the disjunctive query, by starting with the most general concept (\u03c4 ). The following proposition 3 describes the characteristics of C disj g Proposition 2 Let T Q disj The set of disjunctive terms of the query Q, and let C disj g lattice such that: T Q conj", "uris": null }, "FIGREF2": { "type_str": "figure", "num": null, "text": "Concept lattice B(D, T, I).", "uris": null }, "FIGREF3": { "type_str": "figure", "num": null, "text": "The processing of the conjunctive part of the query stops when the algorithm processes all the concepts of the lattice.", "uris": null }, "FIGREF4": { "type_str": "figure", "num": null, "text": "The algorithm starts the processing of the disjunctive part of the query.", "uris": null }, "FIGREF5": { "type_str": "figure", "num": null, "text": "If the algorithm finds the term t2 in a concept, then it ignores its descendants and neighbors and stops processing.", "uris": null }, "TABREF0": { "content": "
PACLIC 32
169
32nd Pacific Asia Conference on Language, Information and Computation
Hong Kong, 1-3 December 2018
Copyright 2018 by the authors
", "html": null, "type_str": "table", "num": null, "text": "http://archive.ics.uci.edu/ml/datasets/Connect-4" }, "TABREF1": { "content": "
Connect-4
Data sets Objects number Concepts number
S 11000575
S 22000685
S 330001314
S 440001387
S 550001564
S 660001620
S 770001620
S 880001620
S 990002203
S 10
", "html": null, "type_str": "table", "num": null, "text": "Test Data description" }, "TABREF2": { "content": "
Data setsAverage time (second)
Sets Object count FCA Retrieval BR-Explorer CLAIRCLR
S 110000.6820.7630.6961.340
S 220000.8271.1431.1262.185
S 330001.6403.7283.1014.483
S 440001.7854.2233.6125.404
S 550002.0635.3594.5736.747
S 660002.1835.8185.0587.642
S 770002.1015.9255.2988.306
S 880002.1086.0325.5378.970
S 990002.90110.5308.852 12.532
S 10100003.20814.02711.466 15.433
", "html": null, "type_str": "table", "num": null, "text": "Evolution of the execution time according to the objects number" }, "TABREF3": { "content": "
: Complexity comparison
ModelComplexity
FCA RetrievalO(n)
CLRO(n 2 )
BR-ExplorerO(n 2 )
CLAIRO(n 2 )
", "html": null, "type_str": "table", "num": null, "text": "" } } } }