Lotfi Lakhal

Discovering Frequent Closed Itemsets for Association Rules

In this paper, we address the problem of finding frequent itemsets in a database. Using the closed itemset lattice framework, we show that this problem can be reduced to the problem of finding frequent closed itemsets. Based on this statement, we can construct efficient data mining algorithms by limiting the search space to the closed itemset lattice rather than the subset lattice. Moreover, we show that the set of all frequent closed itemsets suffices to determine a reduced set of association rules, thus addressing another important data mining problem: limiting the number of rules produced without information loss. We propose a new algorithm, called A-Close, using a closure mechanism to find frequent closed itemsets. We realized experiments to compare our approach to the commonly used frequent itemset search approach. Those experiments showed that our approach is very valuable for dense and/or correlated data that represent an important part of existing databases.

Efficient mining of association rules using closed itemset lattices

Abstract Discovering association rules is one of the most important task in data mining. Many efficient algorithms have been proposed in the literature. The most noticeable are Apriori, Mannilas algorithm, Partition, Sampling and DIC, that are all based on the Apriori mining method: pruning the subset lattice (itemset lattice). In this paper we propose an efficient algorithm, called Close, based on a new mining method: pruning the closed set lattice (closed itemset lattice). This lattice, which is a sub-order of the subset lattice, is closely related to Willes concept lattice in formal concept analysis. Experiments comparing Close to an optimized version of Apriori showed that Close is very efficient for mining dense and/or correlated data such as census style data, and performs reasonably well for market basket style data.

Mining Minimal Non-redundant Association Rules Using Frequent Closed Itemsets

The problem of the relevance and the usefulness of extracted association rules is of primary importance because, in the majority of cases, real-life databases lead to several thousands association rules with high confidence and among which are many redundancies. Using the closure of the Galois connection, we define two new bases for association rules which union is a generating set for all valid association rules with support and confidence. These bases are characterized using frequent closed itemsets and their generators; they consist of the nonredundant exact and approximate association rules having minimal antecedents and maximal consequents, i.e. the most relevant association rules. Algorithms for extracting these bases are presented and results of experiments carried out on real-life databases show that the proposed bases are useful, and that their generation is not time consuming.

Efficient Discovery of Functional Dependencies and Armstrong Relations

In this paper, we propose a new efficient algorithm called Dep-Miner for discovering minimal non-trivial functional dependencies from large databases. Based on theoretical foundations, our approach combines the discovery of functional dependencies along with the construction of real-world Armstrong relations (without additional execution time). These relations are small Armstrong relations taking their values in the initial relation. Discovering both minimal functional dependencies and real-world Armstrong relations facilitate the tasks of database administrators when maintaining and analyzing existing databases. We evaluate Dep-Miner performances by using a new benchmark database. Experimental results show both the efficiency of our approach compared to the best current algorithm (i.e. Tane), and the usefulness of real-world Armstrong relations.

Functional and approximate dependency mining: database and FCA points of view

In this article, we deal with the functional and approximate dependency inference problem by pointing out some relationships between relational database theory and formal concept analysis (FCA). More precisely, the notion of functional dependency in database is compared to the notion of implication in FCA. We propose a framework and several algorithms for mining these dependencies from large database relations. The common data centric step of this framework is the discovery of agree sets, which are closed sets with respect to the closure operator for functional dependency. Two approaches for discovering agree sets from database relations are proposed: the former is a database approach based on SQL queries and the latter is a data mining approach based on partitions. Experiments were performed in order to compare the two proposed methods.

Towards an Object Database Approach for Managing Concept Lattices

The concept lattice is a conceptual model firstly introduced by Wille in formal concept analysis, a theory of concept formation derived from lattice and order theory. Various concept lattice based applications have been reported in several domains such as conceptual clustering, conceptual knowledge representation and acquisition, and information retrieval. In this paper, we propose an object database approach for managing concept lattices in these applications. The goal of our work is two-fold. First, we extend the concept lattice model by basic operations supporting concept analysis. These operations allow to search and discover data directly from the concept lattice. Then, we present an approach for modeling and querying concept lattices within an object database framework.

A framework for understanding existing databases

The authors propose a framework for a broad class of data mining algorithms for understanding existing databases: functional and approximate dependency inference, minimal key inference, example relation generation and normal form tests. We point out that the common data centric step of these algorithms is the discovery of agree sets. A set-oriented approach for discovering agree sets from database relations based on SQL queries is proposed. Experiments have been performed in order to compare the proposed approach with a data mining approach. We also present a novel way to extract approximate functional dependencies having minimal errors from agree sets.

Building Inheritance Graphs in Object Database Design

In this paper, object database schema design is addressed through the problem of designing the inheritance graph. We propose a method, called iO2, for building the inheritance graph of an O2 database schema. The iO2 method is based on the Galois lattice data structure. It encompasses three steps: a (first) construction step, a (second) optimization step, and a (final) generation step. This paper focuses on the two latter steps. The optimization step builds the Galois inheritance graph from the Galois graph (delivered by the construction step) of the finite binary relation associating properties to entity and relationship types. We define a new optimization algorithm which eliminates redundancies from the Galois graph. The generation step yields the O2 inheritance graph from the Galois inheritance graph.

Incremental Inheritance Model for an OODBMS

The semantics of inheritance presented in this paper is based on the incremental modification mechanism that is formalized by the generator associated with class, modification function, and the building inheritance operators. The model is based upon an intuitive explanation of the proper use and purpose of inheritance, and is essentially dedicated to dynamic (i.e. run-time) inheritance of properties, for OODBMS. A simple typing of inheritance is derived by Cooks constraint, that defines the conditions of the validity of generator derivation. We show by using the subtyping relation defined in the 02 OODBMS, the correctness of the proposed model (i.e. the Cooks constraint is respected). And therefore, the integration of our incremental model in O2 is valid.