Formal Context Generation Using Dirichlet Distributions

Abstract

We suggest an improved way to randomly generate formal contexts based on Dirichlet distributions. For this purpose we investigate the predominant way to generate formal contexts, a coin-tossing model, recapitulate some of its shortcomings and examine its stochastic model. Building up on this we propose our Dirichlet model and develop an algorithm employing this idea. By comparing our generation model to a coin-tossing model we show that our approach is a significant improvement with respect to the variety of contexts generated. Finally, we outline a possible application in null model generation for formal contexts.

Null Models for Formal Contexts

“…In this case we basically draw from the set of categories, i.e., from the possible numbers of attributes. Those are related as corners of the simplex and the probability to land in the corner belonging to the category of |M|−1 attributes is approximately 1 |M| + 1 . Contexts where every object has the same number of attributes are referred to as contexts with fixed row-density in [8].…”

“…We show different distributions of probabilities for three categories drawn from 3-dimensional Dirichlet distributions. The base measure α in each case is the uniform distribution, i.e., ( 1 3 , 1 3 , 1 3 ), the precision parameter β ∈ {30,3, 3 10 } varies. The choice of β = 3 then results in a uniform distribution on the probability simplex.…”

“…This presented work is an extension of the already published conference paper [1]. There we investigated how to randomly generate formal contexts using Dirichlet distributions.…”

Boolean Substructures in Formal Concept Analysis

“…However, despite of the only slight difference, these Boolean subcontexts are responsible for an exponential growth of the concept lattice [3]. Such Boolean subcontexts occur in real-world data as well as in randomly generated formal contexts [5].…”