Maximilian Felde

Maximilian Felde, Gerd Stumme

Attribute exploration is a method from Formal Concept Analysis (FCA) that helps a domain expert discover structural dependencies in knowledge domains which can be represented as formal contexts (cross tables of objects and attributes). In this paper we present an extension of attribute exploration that allows for a group of domain experts and explores their shared views. Each expert has their own view of the domain and the views of multiple experts may contain contradicting information.

Maximilian Felde, Gerd Stumme

Formal Concept Analysis (FCA) provides a method called attribute exploration which helps a domain expert discover structural dependencies in knowledge domains that can be represented by a formal context (a cross table of objects and attributes). Triadic Concept Analysis is an extension of FCA that incorporates the notion of conditions. Many extensions and variants of attribute exploration have been studied but only few attempts at incorporating multiple experts have been made. In this paper we present triadic exploration based on Triadic Concept Analysis to explore conditional attribute implications in a triadic domain. We then adapt this approach to formulate attribute exploration with multiple experts that have different views on a domain.

Maximilian Felde, Gerd Stumme

A well-known knowledge acquisition method in the field of Formal Concept Analysis (FCA) is attribute exploration. It is used to reveal dependencies in a set of attributes with help of a domain expert. In most applications no single expert is capable (time- and knowledge-wise) of exploring the knowledge domain alone. However, there is up to now no theory that models the interaction of multiple experts for the task of attribute exploration with incomplete knowledge. To this end, we to develop a theoretical framework that allows multiple experts to explore domains together. We use a representation of incomplete knowledge as three-valued contexts. We then adapt the corresponding version of attribute exploration to fit the setting of multiple experts. We suggest formalizations for key components like expert knowledge, interaction and collaboration strategy. In particular, we define an order that allows to compare the results of different exploration strategies on the same task with respect to their information completeness. Furthermore we discuss other ways of comparing collaboration strategies and suggest avenues for future research.

Maximilian Felde, Tom Hanika

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.