Clustering by Local Skewering

Clustering p-dimensional data by fitting a mixture of K normals has enjoyed renewed interest (for example, see Splus function “mclust”). However, the number of parameters for the model grows rapidly with dimension p. For example, even if all the covariance matrices are assumed to be equal, the number of parameters is (K − 1)+K ∗ p+ p(p+1)/2 for the weights, means and covariance matrix. At ACAS in 2001, Scott introduced the partial mixture component algorithm which fits only one component of the mixture model at a time. This algorithm requires only 1 + p+ p ∗ (p+ 1)/2 parameters for the weight, mean vector, and covariance matrix. In this talk, we introduce a new algorithm which attempts to find the “best” line through individual clusters. This model requires only 2 ∗ p− 1 parameters. That is, the new algorithm is linear rather than quadratic in p. By repeatedly reinitializing the search algorithm, all clusters may be identified. Intuitively, the line found is approximately the largest eigenvector of the local covariance matrix. The GGobi visualization program will be used to illustrate the success of this algorithm on real and simulated data.