Experimental Study of Concise Representations of Concepts and Dependencies

TL;DR

This paper investigates concise attribute representations in formal concept analysis, analyzing their statistical properties and proposing measures to evaluate dataset complexity.

Contribution

It introduces new statistical analyses of attribute sets and proposes measures for dataset complexity in formal concept analysis.

Findings

Empirical distributions of attribute sets are characterized.

Proposed measures effectively analyze real-world and synthetic datasets.

Insights into dataset complexity from an FCA perspective.

Abstract

In this paper we are interested in studying concise representations of concepts and dependencies, i.e., implications and association rules. Such representations are based on equivalence classes and their elements, i.e., minimal generators, minimum generators including keys and passkeys, proper premises, and pseudo-intents. All these sets of attributes are significant and well studied from the computational point of view, while their statistical properties remain to be studied. This is the purpose of this paper to study these singular attribute sets and in parallel to study how to evaluate the complexity of a dataset from an FCA point of view. In the paper we analyze the empirical distributions and the sizes of these particular attribute sets. In addition we propose several measures of data complexity, such as distributivity, linearity, size of concepts, size of minimum generators, for the analysis of real-world and synthetic datasets.