Outlier Detection and Clustering by Partial Mixture Modeling

Clustering algorithms based upon nonparametric or semiparametric density estimation are of more theoretical interest than some of the distance-based hierarchical or ad hoc algorithmic procedures. However density estimation is subject to the curse of dimensionality so that care must be exercised. Clustering algorithms are sometimes described as biased since solutions may be highly influenced by initial configurations. Clusters may be associated with modes of a nonparametric density estimator or with components of a (normal) mixture estimator. Mode-finding algorithms are related to but different than gaussian mixture models. In this paper, we describe a hybrid algorithm which finds modes by fitting incomplete mixture models, or partial mixture component models. Problems with bias are reduced since the partial mixture model is fitted many times using carefully chosen random starting guesses. Many of these partial fits offer unique diagnostic information about the structure and features hidden in the data. We describe the algorithms and present some case studies.