The Galois (or concept) lattice produced from a binary relation has proved useful for many applications. Building the Galois lattice can be considered a conceptual clustering method because 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 update is done in time proportional to the number of instances previously treated. Although the worst case is exponential, when there is a fixed upper bound on the number of features related to an instance, which is usually the case in practical applications, the worst-case analysis of the algorithm also shows linear growth with respect to the number of instances.

Incremental concept formation algorithms based on galois (concept) lattices

http://perso.ens-lyon.fr/eric.thierry/Graphes2007/lattice-generation.pdf

A fast algorithm for building lattices

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 updating algorithm [9]), with applications for class hierarchy maintenance. We first present the basic method and illustrate its use through an example inspired from [3]. Next, we discuss extensions to the method to take into account richer class descriptions in general, and the specifics of OO analysis-level models. Finally, we discuss some of the research directions we are currently pursuing.

Building and maintaining analysis-level class hierarchies using Galois Lattices

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 docu- ment 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 docu- ments 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 http://credo.fub.it.

/pdf/exploiting-the-potential-of-concept-lattices-for-information-w9q1w5peka.pdf

Exploiting the Potential of Concept Lattices for Information Retrieval with CREDO

Describes a general technique for identifying modules in legacy code. The method is based on concept analysis - a branch of lattice theory that can be used to identify similarities among a set of objects based on their attributes. We discuss how concept analysis can identify potential modules using both "positive" and "negative" information. We present an algorithmic framework to construct a lattice of concepts from a program, where each concept represents a potential module. We define the notion of a concept partition, present an algorithm for discovering all concept partitions of a given concept lattice, and prove the algorithm to be correct.

/pdf/identifying-modules-via-concept-analysis-57wyq1x73x.pdf

Eugene Saunders

Papers

Lattice model of browsable data spaces