Robust Model‐Based Semi‐Supervised Clustering of Incomplete Records

ABSTRACT This paper develops a multivariate ‐mixture model‐based semi‐supervised clustering methodology for datasets with incomplete records. Specifically, we consider the case where not all features are always observed, as well as the case where label information for some of the records is available, where the interest is in grouping all of them. Our modeling allows for constraints on the shape, size, and orientation of the scale matrices in the component mixtures, and develops a fast alternating expected conditional maximization algorithm for parameter estimation in the semi‐supervised framework that crucially includes the setup where not all classes in the dataset necessarily have representation in the labels. The total number of groups is assessed using Bayesian information criterion. Our approach is evaluated on simulated datasets of different clustering complexity as well as amounts and structure in the unobserved parts of the records or labels. The methodology is applied to further characterize fraudulent and legitimate credit card transactions, and also to categorize incidence and severity in heart disease patients. The publicly available R package MixtClust implements our methods.