Unsupervised non-parametric kernel learning algorithm

A foundational problem in kernel-based learning is how to design suitable kernels. Non-Parametric Kernel Learning (NPKL) is one of the most important kernel learning methods. However, most research on NPKL has tended to focus on the semi-supervised scenario. In this paper, we propose a novel unsupervised non-parametric kernel learning method, which can seamlessly combine the spectral embedding of unlabeled data and manifold Regularized Least-Squares (RLS) to learn non-parametric kernels efficiently. The proposed algorithm enjoys a closed-form solution in each iteration, which can be efficiently computed by the Lanczos sparse eigen-decomposition technique. Meanwhile, it can be extended to supervised kernel learning naturally. Experimental results show that our proposed unsupervised non-parametric kernel learning algorithm is significantly more effective and applicable to enhance the performance of Maximum Margin Clustering (MMC). Especially, it outperforms multiple kernel learning in both unsupervised and supervised settings.