Rokia Missaoui

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.

A partition-based approach towards constructing Galois (concept) lattices

Galois lattices and formal concept analysis of binary relations have proved useful in the resolution of many problems of theoretical or practical interest. Recent studies of practical applications in data mining and software engineering have put the emphasis on the need for both efficient and flexible algorithms to construct the lattice. Our paper presents a novel approach for lattice construction based on the apposition of binary relation fragments. We extend the existing theory to a complete characterization of the global Galois (concept) lattice as a substructure of the direct product of the lattices related to fragments. The structural properties underlie a procedure for extracting the global lattice from the direct product, which is the basis for a full-scale lattice construction algorithm implementing a divide-and-conquer strategy. The paper provides a complexity analysis of the algorithm together with some results about its practical performance and describes a class of binary relations for which the algorithm outperforms the most efficient lattice-constructing methods.

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.

Building Concept (Galois) Lattices from Parts: Generalizing the Incremental Methods

Formal concept analysis is increasingly used as a data mining technique, whence the need of efficient algorithms for handling large sets of volatile data. Recently, we designed a general framework for constructing concept (Galois) lattices from fragmented and/or evolving data based on a lattice assembly operation. In this paper, the framework is adapted to the maintenance of concept lattices upon the insertion of a set of objects into the context, a problem which generalizes the insertion of individual objects considered by the existing incremental methods. The paper provides a set of structural results for the case of single object insertions which underlie a new incremental algorithm. Our method is shown to improve a key flaw of the major incremental technique.

Enhanced mining of association rules from data cubes

On-line analytical processing (OLAP) provides tools to explore and navigate into data cubes in order to extract interesting information. Nevertheless, OLAP is not capable of explaining relationships that could exist in a data cube. Association rules are one kind of data mining techniques which finds associations among data. In this paper, we propose a framework for mining inter-dimensional association rules from data cubes according to a sum-based aggregate measure more general than simple frequencies provided by the traditional COUNT measure. Our mining process is guided by a meta-rule context driven by analysis objectives and exploits aggregate measures to revisit the definition of support and confidence. We also evaluate the interestingness of mined association rules according to Lift and Loevinger criteria and propose an efficient algorithm for mining inter-dimensional association rules directly from a multidimensional data.