Null Models for Formal Contexts

Abstract

Null model generation for formal contexts is an important task in the realm of formal concept analysis. These random models are in particular useful for, but not limited to, comparing the performance of algorithms. Nonetheless, a thorough investigation of how to generate null models for formal contexts is absent. Thus we suggest a novel approach using Dirichlet distributions. We recollect and analyze the classical coin-toss model, recapitulate some of its shortcomings and examine its stochastic properties. Building upon this we propose a model which is capable of generating random formal contexts as well as null models for a given input context. Through an experimental evaluation we show that our approach is a significant improvement with respect to the variety of contexts generated. Furthermore, we demonstrate the applicability of our null models with respect to real world datasets.