Composing Tree Graphical Models with Persistent Homology Features for Clustering Mixed-Type Data

Clustering data with both continuous and discrete attributes is a challenging task. Existing methods often lack a principled probabilistic formulation. In this paper, we propose a clustering method based on a tree-structured graphical model to describe the generation process of mixed-type data. Our tree-structured model factorizes into a product of pairwise interactions, and thus localizes the interaction between feature variables of different types. To provide a robust clustering method based on the tree-model, we adopt a topographical view and compute peaks of the density function and their attractive basins for clustering. Furthermore, we leverage the theory from topology data analysis to adaptively merge trivial peaks into large ones in order to achieve meaningful clusterings. Our method outperforms state-of-the-art methods on mixed-type data.