. The Galois (or concept) lattice produced from a binary relation has been proved useful for many applications. Building the Galois lattice can be considered as a conceptual clustering method since it results in a concept hierarchy. This article presents incremental algorithms for updating the Galois lattice and corresponding graph, resulting in an incremental concept formation method. Different strategies are considered based on a characterization of the modifications implied by such an update. Results of empirical tests are given in order to compare the performance of the incremental algorithms to three other batch algorithms. Surprisingly, when the total time for incremental generation is used, the simplest and less efficient variant of the incremental algorithms outperforms the batch algorithms in most cases. When only the incremental update time is used, the incremental algorithm outperforms all the batch algorithms. Empirical evidence shows that, on the average, the incremental u...

Abstract. The theory of concept (or Galois) lattices provides a simple and formal approach to conceptual clustering. In this paper we present GALOIS, a system that automates and applies this theory. The algorithm utilized by GALOIS to build a concept lattice is incremental and efficient, each update being done in time at most quadratic in the number of objects in the lattice. Also, the algorithm may incorporate background information into the lattice, and through clustering, extend the scope of the theory. The application we present is concerned with information retrieval via browsing, for which we argue that concept lattices may represent major support structures. We describe a prototype user interface for browsing through the concept lattice of a document-term relation, possibly enriched with a thesaurus of terms. An experimental evaluation of the system performed on a medium-sized bibliographic database shows good retrieval performance and a significant improvement after the introduction of background knowledge.

Formal concept analysis is increasingly used for large contexts that are built by programs. This paper presents an efficient algorithm for concept analysis that computes concepts together with their explicit lattice structure. An experimental evaluation uses randomly generated contexts to compare the running time of the presented algorithm with two other algorithms. Running time increases quadratically with the number of concepts, but with a small quadratic component. At least contexts with sparsely filled context tables cause concept lattices grow quadratically with respect to the size of their base relation. The growth rate is controlled by the density of context tables. Modest growth combined with efficient algorithms lead to fast concept analysis. 1

Building and maintaining the class hierarchy has been recognized as an important but one of the most difficult activities of object-oriented design. Concept (or Galois) lattices and related structures are presented as a framework for dealing with the design and maintenance of class hierarchies. Because the design of class hierarchies is inherently an iterative and incremental process, we designed incremental algorithms that update existing Galois lattices as the result of adding, removing, or modifying class specifications. A prototype tool incorporating this and other algorithms has been developed as part of the IGLOO project, which is a large object-oriented software engineering joint research project involving academic and industrial partners. The tool can generate either the concept lattice or several variant structures incrementally by incorporating new classes one by one. The resulting hierarchies can be interactively explored and refined using a graphical browser. In addition, s...

Abstract not found

The recent advances in Formal Concept Analysis (FCA) together with the major changes faced by modern Information Retrieval (IR) provide new unprecedented challenges and opportunities for FCA-based IR applications. The main advantage of FCA for IR is the possibility of creating a conceptual representation of a given document collection in the form of a document lattice, which may be used both to improve the retrieval of specific items and to drive the mining of the collection’s contents. In this paper, we will examine the best features of FCA for solving IR tasks that could not be easily addressed by conventional systems, as well as the most critical aspects for building FCA-based IR applications. These observations have led to the development of CREDO, a system that allows the user to query Web documents and see retrieval results organized in a browsable concept lattice. This is the second major focus of the paper. We will show that CREDO is especially useful for quickly locating the documents corresponding to the meaning of interest among those retrieved in response to an ambiguous query, or for mining the contents of the documents that reference a given entity. An on-line version of the system is available for testing at

. We present the design of a file system whose organization is based on Concept Analysis "`a la Wille-Ganter". The aim is to combine querying and navigation facilities in one formalism. The file system is supposed to offer a standard interface but the interpretation of common notions like directories is new. The contents of a file system is interpreted as a Formal Context, directories as Formal Concepts, and the sub-directory relation as Formal Concepts inclusion. We present an organization that allows for an efficient implementation of such a Conceptual File System. 1 Introduction: Querying vs. Navigation Information retrieval includes representation, storage, organization, and access to information. Two information retrieval methods are widely adopted and applied. The first method is hierarchical classification, which is frequently found in computer tools: e.g., file systems, bookmarks, or menus. In this model, searches are done by navigating in a classification structure t...

. We propose a generalization of Formal Concept Analysis (FCA) in which sets of attributes are replaced by expressions of an almost arbitrary logic. We prove that all FCA can be reconstructed on this basis. We show that from any logic that is used in place of sets of attributes can be derived a contextualized logic that takes into account the formal context and that is isomorphic to the concept lattice. We then justify the generalization of FCA compared with existing extensions and in the perspective of its application to information systems. 1 Introduction The origin of this work is the search for flexible organisations for managing, updating, querying, or navigating in data. In this context, several roles are played by possibly different people: designer, administrator, and end-user. Hierarchical organisations are not flexible, and updating, querying and navigation are difficult to conciliate (see for instance the view update problem in data-bases). The literature shows that...

Current best-match ranking (BMR) systems perform well but cannot handle word mismatch between a query and a document. The best known alternative ranking method, hierarchical clustering-based ranking (HCR), seems to be more robust than BMR with respect to this problem, but it is hampered by theoretical and practical limitations. We present an approach to document ranking that explicitly addresses the word mismatch problem by exploiting interdocument similarity information in a novel way. Document ranking is seen as a querydocument transformation driven by a conceptual representation of the whole document collection, into which the query is merged. Our approach is based on the theory of concept (or Galois) lattices, which, we argue, provides a powerful, well-founded, and computationallytractable framework to model the space in which documents and query are represented and to compute such a transformation. We compared information retrieval using concept lattice-based ranking (CLR) to BMR and HCR. The results showed that HCR was outperformed by CLR as well as by BMR, and suggested that, of the two best methods, BMR achieved better performance than CLR on the whole document set while CLR compared more favorably when only the first retrieved documents were used for evaluation. We also evaluated the three methods' specific ability to rank documents that did not match the query, in which case the superiority of CLR over BMR and HCR (and that of HCR over BMR) was apparent.

In this paper we present a comprehensive approach to automatic organization and hybrid navigation of text databases. An organizing stage first builds a particular lattice representation of the data, through text indexing followed by lattice clustering of the indexed texts. The lattice representation, then, supports the navigation stage of the system, a visual retrieval interface that combines three main retrieval strategies: browsing, querying, and bounding. Browsing and querying are used to search the retrieval space, bounding is used to restrict it based on the information that users have, or get during their interaction with the system. We show that such a hybrid paradigm permits high flexibility in trading off information exploration and retrieval and, in addition, has good retrieval performance. We compared information retrieval using lattice-based hybrid navigation with conventional Boolean querying. The results of an experiment conducted on two medium-sized bibliographic databases showed that the performance of lattice retrieval was comparable to or better than Boolean retrieval