Metric-Constrained Kernel Union of Subspaces

Abstract

This paper addresses the problem of learning a collection of nonlinear manifolds. Inspired by kernel methods, it puts forth a generalization of the kernel subspace model, termed the Metric-Constrained Kernel Union-of-Subspaces (MC-KUoS) model. It then develops an iterative method for learning of an MC-KUoS whose solution is based on the data representation capability of the manifolds and distances between subspaces in the kernel (feature) space. The proposed method (when using Gaussian and polynomial kernels) outperforms existing competitive state-of-the-art methods for real-world image denoising, which shows the benefits of the MC-KUoS model and the proposed denoising approach.