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Open AccessArticle

Null Models for Formal Contexts

by Maximilian Felde 1,2,*,‡, Tom Hanika 1,2,‡ and Gerd Stumme 1,2,‡
1
Knowledge & Data Engineering Group, University of Kassel, 34121 Kassel, Germany
2
Interdisciplinary Research Center for Information System Design, University of Kassel, 34121 Kassel, Germany
*
Author to whom correspondence should be addressed.
This paper is an extended version of our paper published in the proceedings of the 24th International Conferences on Conceptual Structures, Marburg, Germany, 1–4 July 2019.
These authors contributed equally to this work.
Information 2020, 11(3), 135; https://doi.org/10.3390/info11030135
Received: 30 January 2020 / Revised: 21 February 2020 / Accepted: 25 February 2020 / Published: 28 February 2020
(This article belongs to the Special Issue Conceptual Structures 2019)
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. View Full-Text
Keywords: formal concept analysis; Dirichlet distribution; random context; null models formal concept analysis; Dirichlet distribution; random context; null models
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Felde, M.; Hanika, T.; Stumme, G. Null Models for Formal Contexts. Information 2020, 11, 135.

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