Some Notes on Polyadic Concept Analysis

TL;DR

This paper discusses Polyadic Concept Analysis, an extension of Formal Concept Analysis, highlighting its differences, open questions, and presenting initial results to foster further research in this understudied area.

Contribution

It clarifies fundamental differences between FCA and PCA, identifies open research questions, and provides partial results on the size of concept n-lattices.

Findings

Partial results on the maximal size of concept n-lattices

Identification of key differences between FCA and PCA

Discussion of open questions and future research directions

Abstract

Despite the popularity of Formal Concept Analysis (FCA) as a mathematical framework for data analysis, some of its extensions are still considered arcane. Polyadic Concept Analysis (PCA) is one of the most promising yet understudied of these extensions. This formalism offers many interesting open questions but is hindered in its dissemination by complex notations and a lack of agreed-upon basic definitions. In this paper, we discuss in a mostly informal way the fundamental differences between FCA and PCA in the relation between contexts, conceptual structures, and rules. We identify open questions, present partial results on the maximal size of concept n-lattices and suggest new research directions.