Robust Kernel Sparse Subspace Clustering

Abstract

Kernel methods are widely used in pattern recognition, including subspace clustering (SC). They transform nonlinear problems in the input data space into linear ones in a high-dimensional feature space. This transformation, achieved through the kernel trick, makes computationally tractable nonlinear algorithms possible. However, kernelizing linear algorithms through the kernel trick is infeasible in case of gross sparse corruptions that are modeled by the ℓ<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf>-norm of the error term. To address this, we propose, for the first time, a robust kernel sparse SC (RKSSC) algorithm for data with gross sparse corruptions. We validated the proposed approach on two well-known datasets, using the linear robust SSC algorithm and nonlinear (kernel-based) SSC algorithm as baseline models. According to the Wilcoxon test, the RKSSC's algorithm clustering performance is statistically significantly better than baselines.