Estimating the Major Cluster by Mean-Shift with Updating Kernel

Abstract

The mean-shift method is a convenient mode-seeking method. Using a principle of the sample mean over an analysis window, or kernel, in a data space where samples are distributed with bias toward the densest direction of sample from the kernel center, the mean-shift method is an attempt to seek the densest point of samples, or the sample mode, iteratively. A smaller kernel leads to convergence to a local mode that appears because of statistical fluctuation. A larger kernel leads to estimation of a biased mode affected by other clusters, abnormal values, or outliers if they exist other than in the major cluster. Therefore, optimal selection of the kernel size, which is designated as the bandwidth in many reports of the literature, represents an important problem. As described herein, assuming that the major cluster follows a Gaussian probability density distribution, and, assuming that the outliers do not affect the sample mode of the major cluster, and, by adopting a Gaussian kernel, we propose a new mean-shift by which both the mean vector and covariance matrix of the major cluster are estimated in each iteration. Subsequently, the kernel size and shape are updated adaptively. Numerical experiments indicate that the mean vector, covariance matrix, and the number of samples of the major cluster can be estimated stably. Because the kernel shape can be adjusted not only to an isotropic shape but also to an anisotropic shape according to the sample distribution, the proposed method has higher estimation precision than the general mean-shift.