Explainable Rule-Based Clustering based on Cyclic Probabilistic Causal Models

Discovering and visualizing data clusters is an important AI/ML and visual knowledge discovery task. This paper proposes a new data clustering approach inspired by the concept of causal models used in cognitive science. This approach is based on the causal relations between features, instead of similarity of features in traditional clustering approaches. The concept of the center of the cluster is formalized in accordance with prototype theory of concepts explored in the cognitive science in terms of a correlational structure of perceived attributes. Traditionally in AI and cognitive science, causal models are described using Bayesian networks. However, Bayesian networks do not support cycles. This paper proposes a novel mathematical apparatus probabilistic generalization of formal concepts-for describing causal models via cyclical causal relations (fixpoints of causal relations) that form a clusters and generate a clusters prototypes. This approach is illustrated with a case study.