Robust Kernel Sparse Subspace Clustering

Abstract

Kernel methods are applied to many problems in pattern recognition, including subspace clustering (SC). That way, nonlinear problems in the input data space become linear in mapped high-dimensional feature space. Thereby, computationally tractable nonlinear algorithms are enabled through implicit mapping by the virtue of kernel trick. However, kernelization of linear algorithms is possible only if square of the Froebenious norm of the error term is used in related optimization problem. That, however, implies normal distribution of the error. That is not appropriate for non-Gaussian errors such as gross sparse corruptions that are modeled by -norm. Herein, to the best of our knowledge, we propose for the first time robust kernel sparse SC (RKSSC) algorithm for data with gross sparse corruptions. The concept, in principle, can be applied to other SC algorithms to achieve robustness to the presence of such type of corruption. We validated proposed approach on two well-known datasets with linear robust SSC algorithm as a baseline model. According to Wilcoxon test, clustering performance obtained by the RKSSC algorithm is statistically significantly better than corresponding performance obtained by the robust SSC algorithm. MATLAB code of proposed RKSSC algorithm is posted on https://github.com/ikopriva/RKSSC.