SPARSE k-MEANS WITH l(infinity)/l(0) PENALTY FOR HIGH-DIMENSIONAL DATA CLUSTERING

摘要

One of the existing sparse clustering approaches, l(1)-k-means, maximizes the weighted between-cluster sum of squares subject to the l(1) penalty. In this paper, we propose a sparse clustering method based on an l(infinity)/l(0) penalty, which we call l(0)-k-means. We design an efficient iterative algorithm for solving it. To compare the theoretical properties of l(1) and l(0)-k-means, we show that they can be explained explicitly from a thresholding perspective based on different thresholding functions. Moreover, l(1) and l(0)-k-means are proven to have a screening consistent property under Gaussian mixture models. Experiments on synthetic as well as real data justify the outperforming results of l(0) with respect to l(1)-k-means.