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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.

A common representation of information about relations of objects and attributes in knowledge domains are data-tables. The structure of such information can be analysed using Formal Concept Analysis (FCA). Attribute exploration is a knowledge acquisition method from FCA that reveals dependencies in a set of attributes with help of a domain expert. However, in general no single expert is capable (time-and knowledge-wise) of exploring knowledge domains alone. Therefore it is important to develop methods that allow multiple experts to explore domains together. To this end we build upon results on representation of incomplete knowledge [2, 8-10], adapt the corresponding version of attribute exploration to fit the setting of multiple experts and suggest formalizations for key components like expert knowledge, interaction and collaboration strategy. Furthermore we discuss ways of comparing collaboration strategies and suggest avenues for future research.

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.

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