Very fast EM-based mixture model clustering using multiresolution kd-trees

Clustering is important in many fields including manufacturing, biology, finance, and astronomy. Mixture models are a popular approach due to their statistical foundations. and EM is a very popular method for finding: mixture models. EM, however, requires many accesses of the data, and thus has been dismissed as impractical (e.g. [9]) for data milling of enormous datasets. We present a new algorithm, based on the multiresolution. kd-trees of [5], which dramatically reduces the cost of EM-based clustering, with savings rising linearly with the number of datapoints. Although presented here for maximum likelihood estimation of Gaussian mixture models, it is also applicable to non-Gaussian models (provided class densities are monotonic in Mahalanobis distance?), mixed categorical/numeric clusters, and Bayesian methods such as Autoclass [1].