Conceptual Coverage Driven by Essential Concepts: A Formal Concept Analysis Approach

Abstract

Formal concept analysis (FCA) is a mathematical theory that is typically used as a knowledge representation method. The approach starts with an input binary relation specifying a set of objects and attributes, finds the natural groupings (formal concepts) described in the data, and then organizes the concepts in a partial order structure or concept (Galois) lattice. Unfortunately, the total number of concepts in this structure tends to grow exponentially as the size of the data increases. Therefore, there are numerous approaches for selecting a subset of concepts to provide full or partial coverage. In this paper, we rely on the battery of mathematical models offered by FCA to introduce a new greedy algorithm, called Concise, to compute minimal and meaningful subsets of concepts. Thanks to its theoretical properties, the Concise algorithm is shown to avoid the sluggishness of its competitors while offering the ability to mine both partial and full conceptual coverage of formal contexts. Furthermore, experiments on massive datasets also underscore the preservation of the quality of the mined formal concepts through interestingness measures agreed upon by the community.