Learning Nonparametric Kernel Matrices from Pairwise Constraints

Kernel plays an important role in many machine learning
techniques. Many kernel learning algorithms (e.g., multiple kernel
learning) have to assume parametric forms for the target kernel functions,
which can significantly limit the capability of kernels in fitting diverse
patterns of data. In this paper, we present a framework for non-parametric
kernel learning that learns a kernel matrix from a given set of pairwise
constraints. A graph Laplacian of the observed data is introduced as a
regularizer when optimizing the kernel matrix. An efficient algorithm is
developed to solve the related Semi-Definite Programming (SDP) problem. We
also present an active learning method for the proposed framework for
non-parametric kernel learning. Extensive evaluation on clustering with a
number of UCI datasets shows that the proposed method is more effective
than other state-of-the-art techniques for kernel learning.