Powered Gaussian kernel spectral clustering

Spectral clustering is a useful tool for clustering data. It separates data points into different clusters using eigenvectors corresponding to eigenvalues of the similarity matrix from a data set. There are various types of similarity functions to be used for spectral clustering. In this paper, we propose a powered Gaussian kernel function for spectral clustering. We first consider a Gaussian kernel similarity function with a power parameter, and then use a modified correlation comparison algorithm to estimate the power parameter. This parameter can be used for separating points that actually lie on different clusters, but with small distance. We then use the maximum value among all minimum distances between data points to get better clustering results. Using the estimated power parameter and the maximum value among minimum distances is able to improve spectral clustering. Some numerical data, real data sets, and images are used for making comparisons between the powered Gaussian kernel spectral clustering algorithm and some existing methods. The comparison results show the superiority and effectiveness of the proposed method.