Transparent Clustering with Cyclic Probabilistic Causal Models

Abstract

In the previous work data clusters where discovered and visualized by causal models, used in cognitive science. Centers of clusters are presented by prototypes of clusters, formed by causal models, in accordance with the prototype theory of concepts, explored in cognitive science. In this work we describe the system of transparent analysis of such clasterization that bring the light to the interconnection between (1) set of objects with there characteristics (2) probabilistic causal relations between objects characteristics (3) causal models—fixpoints of probabilistic causal relations that form prototypes of clusters (4) clusters—set of objects that defined by prototypes. For that purpose we use a novel mathematical apparatus—probabilistic generalization of formal concepts—for discovering causal models via cyclical causal relations (fixpoints of causal relations). This approach is illustrated with a case study.