Dependency Clustering of Mixed Data with Gaussian Mixture Copulas

Abstract

Heterogeneous data with complex feature dependencies is common in real-world applications. Clustering algorithms for mixed - continuous and discrete valued - features often do not adequately model dependencies and are limited to modeling meta-Gaussian distributions. Copulas, that provide a modular parameterization of joint distributions, can model a variety of dependencies but their use with discrete data remains limited due to challenges in parameter inference. In this paper we use Gaussian mixture copulas, to model complex dependencies beyond those captured by meta-Gaussian distributions, for clustering. We design a new, efficient, semiparametric algorithm to approximately estimate the parameters of the copula that can fit continuous, ordinal and binary data. We analyze the conditions for obtaining consistent estimates and empirically demonstrate performance improvements over state-of-the-art methods of correlation clustering on synthetic and benchmark datasets.