Overlapping area hyperspheres for kernel-based similarity method

Measuring similarity between sets of objects is a key step in a wide areas of machine learning. Popular examples include general classification framework and numerous applications in computer vision. In this paper, we propose a kernel-based similarity method which is inspired from an interesting biological behavior of trees and induced mathematically by formulating it as a quadratic optimization problem in a reproducing kernel Hilbert space (RKHS). The proposed method is compared to the maximum mean discrepancy, a recent and challenging kernel similarity method. We conduct and present several numerical experiments on synthetic data as well as real-word image data. The proposed method yields favorable performances in terms of classification performances in the context of supervised classification tasks on the challenging Caltech101 dataset and other datasets such as USPS and ETH80. Furthermore, the efficiency of the proposed method in the context of image segmentation through unsupervised clustering of superpixels has been also asserted.