Learning nonparametric kernel matrices from pairwise constraints

Many kernel learning methods have to assume parametric forms for the target kernel functions, which significantly limits the capability of kernels in fitting diverse patterns. Some kernel learning methods assume the target kernel matrix to be a linear combination of parametric kernel matrices. This assumption again importantly limits the flexibility of the target kernel matrices. The key challenge with nonparametric kernel learning arises from the difficulty in linking the nonparametric kernels to the input patterns. In this paper, we resolve this problem by introducing the graph Laplacian of the observed data as a regularizer when optimizing the kernel matrix with respect to the pairwise constraints. We formulate the problem into Semi-Definite Programs (SDP), and propose an efficient algorithm to solve the SDP problem. The extensive evaluation on clustering with pairwise constraints shows that the proposed nonparametric kernel learning method is more effective than other state-of-the-art kernel learning techniques.