Kernel tapering: A simple and effective approach to sparse kernels for image processing

Kernel methods have been regarded as an effective approach in image processing. However, when calculating the similarity induced by kernels, existing kernel methods usually incorporate irrelevant features (e.g., the background features of an object in a image), which are then inherited to kernel learning methods and thus lead to suboptimal performance. To attack this problem, we introduce a framework of kernel tapering, which is a simple and effective approach to reduce the effects of irrelevant features while keeping the positive semi-definiteness of kernel matrices. In theory, it can be demonstrated that the tapered kernels asymptotically approximate the original kernel functions. In practical image applications where noises or irrelevant features are widely observed, we have further shown that the introduced kernel tapering framework can greatly enhance the performance of their original kernel partners for kernel k-means and kernel nonnegative matrix factorization.