Strong Consistency of Reduced K-means Clustering
arXiv:1212.4942
Abstract
Reduced k-means clustering is a method for clustering objects in a low-dimensional subspace. The advantage of this method is that both clustering of objects and low-dimensional subspace reflecting the cluster structure are simultaneously obtained. In this paper, the relationship between conventional k-means clustering and reduced k-means clustering is discussed. Conditions ensuring almost sure convergence of the estimator of reduced k-means clustering as unboundedly increasing sample size have been presented. The results for a more general model considering conventional k-means clustering and reduced k-means clustering are provided in this paper. Moreover, a new criterion and its consistent estimator are proposed to determine the optimal dimension number of a subspace, given the number of clusters.
A revised version of this was accepted in Scandinavian Journal of Statistics. Please refer to the accepted ver