Raoul Medina

A Unified Hierarchy for Functional Dependencies, Conditional Functional Dependencies and Association Rules

Conditional Functional Dependencies (CFDs) are Functional Dependencies (FDs) that hold on a fragment relation of the original relation. In this paper, we show the hierarchy between FDs, CFDs and Association Rules (ARs): FDs are the union of CFDs while CFDs are the union of ARs. We also show the link between Approximate Functional Dependencies (AFDs) and approximate ARs. In this paper, we show that all those dependencies are indeed structurally the same and can be unified into a single hierarchy of dependencies. A benefit of this hierarchy is that existing algorithms which discover ARs could be adapted to discover any kind of dependencies and, moreover, generate a reduced set of dependencies. We also establish the link between the problem of finding equivalent pattern tableaux of a CFD and the problem of finding keys of a relation.

Uncovering and reducing hidden combinatorics in guigues-duquenne bases

Mannila and Raiha [5] have shown that minimum implicational bases can have an exponential number of implications. Aim of our paper is to understand how and why this combinatorial explosion arises and to propose mechanisms which reduce it.

Representing lattices using many-valued relations

This paper provides a representation theorem of lattices using many-valued relations. We show that any many-valued relation can be associated to a unique lattice which is a meet-sublattice of a product of chains. Conversely, to any lattice we can associate a many-valued relation such that its associated lattice is isomorphic to the initial one. Thereby, we obtain a representation theorem of lattices using many-valued relations. Moreover, since several many-valued relations might have the same associated lattice, we give a characterization of the minimal many-valued relation that can be associated to a lattice. We then sketch a polynomial time algorithm which computes such a minimal relation from either a lattice or an arbitrary relation. This representation presents several advantages: it is smaller than the usual binary representation; all known reconstruction algorithms working on binary relation can be used without loss of efficiency; it can be used by existing data mining processes.

Conditional functional dependencies: an FCA point of view

Conditional Functional Dependencies (CFDs) are Functional Dependencies (FDs) that hold on a fragment relation of the original relation. In [17], the hierarchy between CFDs, association rules and some other dependencies have been shown. This paper exhibits the relation between CFDs and FCA. Given a many-valued relation we define a labeled lattice which gives a synthetic representation of the hierarchy of dependencies. Moreover, a formal concept in the nominal scaling of the relation is an instance of a closed set in the labeled lattice. Pure CFDs correspond to edges in this labeled lattice. We exhibit a monotone function on CFDs allowing search and pruning strategies. We also show that transitive edges induce redundant CFDs.

Interactive association rules discovery

An interactive discovery method for finding association rules is presented. It consists in a user-guided search using reduction operators on a rule. Rules are generated on-demand according to the navigation made by the user. Main interest of this approach is that, at each step, the user has only a linear number of new rules to analyze and that all computations are done in polynomial time. Several reduction operators are presented. We also show that the search space can be reduced when clone items are present.

About the enumeration algorithms of closed sets

This paper presents a review of enumeration technics used for the generation of closed sets. A link is made between classical enumeration algorithms of objects in graphs and algorithms for the enumeration of closed sets. A unified framework, the transition graph, is presented. It allows to better explain the behavior of the enumeration algorithms and to compare them independently of the data structures they use.

Formal Concept Analysis

Communicative Rationality, Logic, and Mathematics.- Actionability and Formal Concepts: A Data Mining Perspective.- Acquiring Generalized Domain-Range Restrictions.- A Finite Basis for the Set of -Implications Holding in a Finite Model.- Lexico-Logical Acquisition of OWL DL Axioms.- From Concepts to Concept Lattice: A Border Algorithm for Making Covers Explicit.- A Formal Context for Symmetric Dependencies.- The Number of Plane Diagrams of a Lattice.- Spectral Lattices of -Formal Contexts.- About Keys of Formal Context and Conformal Hypergraph.- An Algebraization of Linear Continuum Structures.- On the Complexity of Computing Generators of Closed Sets.- Generating Positive and Negative Exact Rules Using Formal Concept Analysis: Problems and Solutions.- On the Merge of Factor Canonical Bases.- Lattices of Rough Set Abstractions as P-Products.- Scale Coarsening as Feature Selection.- Formal Concept Analysis for the Identification of Combinatorial Biomarkers in Breast Cancer.- Handling Spatial Relations in Logical Concept Analysis to Explore Geographical Data.- Analysis of Social Communities with Iceberg and Stability-Based Concept Lattices.- Formal Concept Analysis Enhances Fault Localization in Software.- Refactorings of Design Defects Using Relational Concept Analysis.- Contingency Structures and Concept Analysis.- Comparison of Dual Orderings in Time II.

Twin Vertices in Hypergraphs

Twin vertices in graphs correspond to vertices sharing the same neighborhood. We propose an extension to hypergraphs of the concept of twin vertices. For this we give two characterizations of twin vertices in hypergraphs, a first one in term of clone vertices (the concept of clone has been introduced in [16]) and a second one in term of committees (introduced in [6]). Finally we give an algorithm to aknowledge a set as committee and two algorithms to compute clone-twin vertices classes ans committee-twin vertices classes.