. 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...

Software reuse is one of the most advertised advantages of object-orientation. Inheritance, in all its forms, plays an important part in achieving greater reuse, at all stages of development. Class hierarchies start taking shape at the analysis level, where classes that share application-significant data and application-meaningful external behavior are grouped under more general classes. At the design level, such hierarchies are augmented with implementation classes, and possibly reorganized to take into account implementation factors such as performance or code reuse [22]. Getting the analysis-level hierarchy "right" is very important for the understandability and traceability of the models and the reusability of the resulting code [22]. In this paper, we propose a formal method that organizes a set of class interfaces into a lattice structure called Galois Lattice [10]. Such a lattice has several advantages including: 1) embodying protocol conformance, 2) supporting an incremental up...

A controlled experiment was conducted comparing information retrieval using a Galois lattice structure with two more conventional retrieval methods: navigating in a manually built hierarchical classification and Boolean querying with index terms. No significant performance difference was found between Boolean querying and the Galois lattice retrieval method for subject searching with the three measures used for the experiment: user searching time, recall and precision. However, hierarchical classification retrieval did show significantly lower recall compared to the two other methods. This experiment suggests that retrieval using a Galois lattice structure may be an attractive alternative since it combines a good performance for subject searching along with browsing potential. 11/12/98 2 1. Introduction Information retrieval is concerned with the representation, storage, organization, and accessing of information items (Salton & McGill, 1983). As opposed to the traditional f...

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...

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

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

An important structuring mechanism for knowledge bases is building an inheritance hierarchy of classes based on the content of their knowledge objects. The hierarchy can be used to handle several query processing tasks more efficiently. Building and maintaining this hierarchy is a difficult task for the knowledge engineer. The notion of knowledge space has been previously proposed to help automate such a task. In this paper an incremental algorithm for building the knowledge space is proposed and tested on a sample knowledge base. The empirical behavior shows that after a point the knowledge space can be updated in close to constant time on the average. The knowledge space structure is presented in the framework of the theory of concept lattices. The presentation suggests that the notion of a complete knowledge lattice might be a worthwhile alternative because of the additional richness of the structure. However, this richness induces a large amount of additional processing and storage...

A tool for generating the interface hierarchy of a set of classes for the Smalltalk-80 library is described. The tool can be useful for analyzing the class library or simply for reuse purposes by providing an alternative view that is closer to the client's perspective than the inheritance hierarchy. The interface of each class to consider is extracted directly from the Smalltalk code. From the extracted interfaces, the interface hierarchy can be generated automatically based on structures from the theory of concept (Galois) lattices. A simple graphical user interface is provided for browsing the resulting hierarchy. 1. Introduction Generating the interface hierarchy of a set of classes is an important tool for understanding and analyzing a class library. Cook 5 generated the interface hierarchy of the Smalltalk-80 Collection classes and used it as a tool to review the design of the library. This helped to identify several problems with the library and to suggest improvements. His an...

Abstract. Formal concept analysis (FCA) is used nowadays in a large number of applications in several different areas. Nevertheless, in some applications the size of a concept lattice may be prohibitively large, thus creating a need for new approaches and algorithms to reduce concept lattices to a manageable size. This paper presents a new method for reducing a concept lattice’s complexity and introduces a new methodology for evaluating reduction methods. The main idea of the proposed approach, junction based on objects similarity (JBOS), is the substitution of groups of “similar ” objects by prototypical ones. As a consequence, the resulting lattice is simplified in its size and structure. The user has control of the degree of simplification by means of parameters specification. Two measures are proposed for the evaluation of the final lattice with respect to the original one, the first related to the consistency of the reduced lattice and the other to the descriptive losses incurred by the reduction. The JBOS approach was applied to two data sets from the UCI machine learning repository. The results show that it is possible to reduce the size of a concept lattice in a controlled way. In particular, it makes possible the use of FCA in a data set (formal context) for which that use was previously impossible.