Abstract

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 f 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.