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Common clustering algorithms require multiple scans of all the data toachieve convergence, and this is prohibitive when large databases, with dataarriving in streams, must be processed. Some algorithms to extend the popularK-means method to the analysis of streaming data are present in literaturesince 1998 (Bradley et al. in Scaling clustering algorithms to large databases.In: KDD. p. 9-15, 1998; O'Callaghan et al. in Streaming-data algorithms forhigh-quality clustering. In: Proceedings of IEEE international conference ondata engineering. p. 685, 2001), based on the memorization and recursive updateof a small number of summary statistics, but they either don't take intoaccount the specific variability of the clusters, or assume that the randomvectors which are processed and grouped have uncorrelated components.Unfortunately this is not the case in many practical situations. We herepropose a new algorithm to process data streams, with data having correlatedcomponents and coming from clusters with different covariance matrices. Suchcovariance matrices are estimated via an optimal double shrinkage method, whichprovides positive definite estimates even in presence of a few data points, orof data having components with small variance. This is needed to invert thematrices and compute the Mahalanobis distances that we use for the dataassignment to the clusters. We also estimate the total number of clusters fromthe data.

A clustering algorithm for multivariate data streams with correlated components