Learning Kernels from Distance Constraints

Abstract

Recently there has been a surge of interest in kernel methods such as support vector machine due to their flexibility and high performance. It is important how to define a kernel for kernel methods. Most of kernels are defined by inner-product of feature vectors in some vector space. In this paper we discuss an approach which constructs a kernel matrix from distances between examples instead of feature vectors. Namely, the input data of our algorithm are the distances among examples, not feature vectors. Dissimilar to most of conventional kernels where kernel functions are explicitly given and the kernel matrices are determined by simple calculations, our algorithm rather builds a kernel matrix by maximizing its entropy subject to distance constraints. The maximization problem is convex, so we can always attain to the optimal solution. Experiments using artificial data show the benefits of our algorithm. In addition, we apply this method to analysis of heterogeneous microarray gene expression data, and report the experimental results.