Kernel matrix learning for one-class classification

Abstract

Kernel-based one-class classification is a special type of classification problem, and is widely used as the outlier detection and novelty detection technique. One of the most commonly used method is the support vector dada description (SVDD). However, the performance is mostly affected by which kernel is used. A promising way is to learn the kernel from the data automatically. In this paper, we focus on the problem of choosing the optimal kernel from a kernel convex hull for the given one-class classification task, and propose a new approach. Kernel methods work by nonlinearly mapping the data into an embedding feature space, and then searching the relations among this space, however this mapping is implicitly performed by the kernel function. How to choose a suitable kernel is a difficult problem. In our method, we first transform the data points linearly so that we obtain a new set whose variances equal unity. Then we choose the minimum embedding ball as the criterion to learn the optimal kernel matrix over the kernel convex hull. It leads to the convex quadratically constrained quadratic programming (QCQP). Experiments results on a collection of benchmark data sets demonstrated the effectiveness of the proposed method. © 2008 Springer-Verlag Berlin Heidelberg.