Kernel principle component analysis in pixels clustering

We propose two new methods in the nonlinear kernel feature space for pixel clustering based on the traditional KMeans and Gaussian mixture model (GMM). Unlike the previous work on the kernel machines, we give out a new perspective on the new developed kernel machines. That is, kernel principle component analysis (KPCA) combined with the KMeans and the GMM are kernel KMeans (KKMeans) and kernel GMM (KGMM), respectively. In this paper, we prove the new perspective on KKMeans and give out a clear statement on the KGMM as well. Based on this new perspectives, we can implement the KKMeans and the KGMM conveniently. At the end of the paper, we utilize these new algorithms on the problem of the colour image segmentation. Based on a series of experimental results on Corel colour images, we find that the KKMeans and KGMM can outperform the traditional KMeans and GMM consistently, respectively.