Robert Godin

INCREMENTAL CONCEPT FORMATION ALGORITHMS BASED ON GALOIS (CONCEPT) LATTICES

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.

An Incremental Concept Formation Approach for Learning from Databases

Godin, R. and R. Missaoui, An incremental concept formation approach for learning from databases, Theoretical Computer Science 133 (1994) 3533385. This paper describes a concept formation approach to the discovery of new concepts and implication rules from data. This machine learning approach is based on the Galois lattice theory, and starts from a binary relation between a set of objects and a set of properties (descriptors) to build a concept lattice and a set of rules. Each node (concept) of the lattice represents a subset of objects with their common properties. In this paper, some efficient algorithms for generating concepts and rules are presented. The rules are either in conjunctive or disjunctive form. To avoid the repetitive process of constructing the concept lattice and determining the set of implication rules from scratch each time a new object is introduced in the input relation, we propose an algorithm for incrementally updating both the lattice and the set of generated rules. The empirical behavior of the algorithms is also analysed. The implication problem for these rules can be handled based on the well-known theoretical results on functional dependencies in relational databases.

Experimental comparison of navigation in a Galois lattice with conventional information retrieval methods

Abstract 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 other two 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.

Formal Concept Analysis for Knowledge Discovery and Data Mining: The New Challenges

Data mining (DM) is the extraction of regularities from raw data, which are further transformed within the wider process of knowledge discovery in databases (KDD) into non-trivial facts intended to support decision making. Formal concept analysis (FCA) offers an appropriate framework for KDD, whereby our focus here is on its potential for DM support. A variety of mining methods powered by FCA have been published and the figures grow steadily, especially in the association rule mining (ARM) field. However, an analysis of current ARM practices suggests the impact of FCA has not reached its limits, i.e., appropriate FCA-based techniques could successfully apply in a larger set of situations. As a first step in the projected FCA expansion, we discuss the existing ARM methods, provide a set of guidelines for the design of novel ones, and list some open algorithmic issues on the FCA side. As an illustration, we propose two on-line methods computing the minimal generators of a closure system.

Design of class hierarchies based on concept (Galois) lattices

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, several metrics are computed to help evaluating the quality of the hierarchies. Experiments are presented to better assess the applicability of the approach.

Automatic structuring of knowledge bases by conceptual clustering

An important structuring mechanism for knowledge bases is building an inheritance hierarchy of classes based on the content of their knowledge objects. This hierarchy facilitates group-related processing tasks such as answering set queries, discriminating between objects, finding similarities among objects, etc. Building this hierarchy is a difficult task for the knowledge engineer. Conceptual clustering may be used to automate or assist the engineer in the creation of such a classification structure. This article introduces a new conceptual clustering method which addresses the problem of clustering large amounts of structured objects. The conditions under which the method is applicable are discussed. >

Design of a browsing interface for information retrieval

In conventional Boolean retrieval systems, users have difficulty controlling the amount of output obtained from a given query. This paper describes the design of a user interface which permits gradual enlargement or refinement of the users query by browsing through a graph of term and document subsets. This graph is obtained from a lattice automatically generated from the usual document-term relation. The major design features of the proposed interface are the integration of menu, fill-in the blank and direct manipulation modes of interaction within the “fisheye view” [Furnas, 1986] paradigm. A prototype user interface incorporating some of these ideas has been implemented on a microcomputer. The resulting interface is well adapted to various kinds of users and needs. More experienced users with a particular subject in mind can directly specify a query which results into a jump to a particular vertex in the graph. From there, the user can refine his initial query by browsing through the graph from that point on. On the other hand, casual users without any prior knowledge of the contents of the system or users without any particular subject in mind can freely navigate through the graph without ever specifying any query.

Lattice model of browsable data spaces

Abstract This article describes a new approach to database access suitable for browsing. The underlying data model consists of a number of objects, easily described by a variable number of keywords (simple or qualified). Navigation is performed in terms of certain subsets of keywords and objects (called contexts), which are shown to form a lattice. The complexity of the lattice grows linearly with the number of objects (and not exponentially, as would be the case if all possible keyword subsets were used). The method is illustrated by several practical examples.

Learning algorithms using a Galois lattice structure

An incremental algorithm for updating the Galois lattice is proposed where new objects may be dynamically added by modifying the existing lattice. A large experimental application reveals that adding a new object may be done in time proportional to the number of objects on the average. When there is a fixed upper bound on the number of properties related to an object, which is the case in practical applications, the worst case analysis of the algorithm confirms the experimental observations of linear growth with respect to the number of objects. Algorithms for generating rules from the lattice are also given.<<ETX>>

Generating frequent itemsets incrementally: two novel approaches based on Galois lattice theory

Galois (concept) lattice theory has been successfully applied in data mining for the resolution of the association rule problem. In particular, structural results about lattices have been used in the design of efficient procedures for mining the frequent patterns (itemsets) in transaction databases. Since such databases are often dynamic, we propose a detailed study of the incremental aspects in lattice construction to support effective procedures for incremental mining of frequent closed itemsets (FCIs). Based on a set of descriptive results about lattice substructures involved in incremental updates, the paper presents a novel algorithm for lattice construction that explores only limited parts of a lattice for updating. Two new methods for incremental FCI mining are studied: the first inherits its extensive search strategy from a classical lattice method, whereas the second applies the new lattice construction strategy to the itemset mining context. Unlike batch techniques based on FCIs, both methods avoid rebuilding the FCI family from scratch whenever new transactions are added to the database and/or when the minimal support is changed.