Conceptual Visualization and Navigation Methods for Polyadic Formal Concept Analysis

Vortrag von Diana Troancă

Veranstaltungsort: APB 3027
Beginn: 15. Juni 2016 um 14:50
Ende: 15. Juni 2016 um 15:50
Forschungsgruppe: Computational Logic
Event series: KBS Seminar
iCal

Formal concept analysis (FCA) is the core of Conceptual Knowledge Processing, being closely related to a deeper understanding of existing facts and relationships, while at the same time trying to find explanations for their existence. Polyadic formal concept analysis is an extension of classical FCA that instead of binary relations uses an n-ary incidence relation to define formal concepts, i.e. data clusters in which all elements are interrelated. In this thesis, we introduce new methods of visualization, navigation and exploration based on polyadic formal concept analysis for n-adic datasets with n = 3. In the first part, we introduce a triadic approach to study the Web usage behavior of an e-learning platform. We analyze temporal aspects of the users' behavior and visualize the results in a circular layout using the Circos tool. In the subsequent chapter, we define methods to reduce the size of a triadic dataset without altering its underlying structure. For this purpose, we extend the notions of clarification and reduction from the dyadic to the triadic setting and show that these processes have an influence solely on the efficiency and not on the results of any further analysis. Next, we introduce a navigation paradigm based on a reachability relation among formal concepts. This relation gives rise to so-called reachability clusters containing mutually reachable concepts. We discuss theoretical aspects about the properties of the formal concepts arising from the defined reachability relation and describe the framework of the proposed navigation paradigm. Subsequently, we consider the problem of satisfiability of membership constraints in order to determine if a formal concept exists whose components include and exclude certain elements. We analyze the computational complexity of this problem for particular cases as well as for the general n-adic problem and present an answer set programming encoding for the membership constraint satisfaction problem. Next, we propose a navigation paradigm based on membership constraints and implement it for the dyadic, triadic and tetradic case using different strategies, one based on the proposed ASP encoding and one using an exhaustive search in the whole concept set, precomputed with an external FCA tool. We evaluate and compare the implementations and discuss the limitations and the possibility of generalizations of each approach. In the final part of the thesis, we describe the achievements of our research as well as possible directions for future work.