A Bayesian Predictive Model for Clustering Data of Mixed Discrete and Continuous Type

Advantages of model-based clustering methods over heuristic alternatives have been widely demonstrated in the literature. Most model-based clustering algorithms assume that the data are either discrete or continuous, possibly allowing both types to be present in separate features. In this paper, we introduce a model-based approach for clustering feature vectors of mixed type, allowing each feature to simultaneously take on both categorical and real values. Such data may be encountered, for instance, in chemical and biological analyses, in the analysis of survey data, as well as in image analysis. Our model is formulated within a Bayesian predictive framework, where clustering solutions correspond to random partitions of the data. Using conjugate analysis, the posterior probability for each possible partition can be determined analytically, enabling the utilization of efficient computational search strategies for finding the posterior optimal partition. The derived model is illustrated using several synthetic and real datasets.