One-Class Kernel Spectral Regression

Abstract

The paper introduces a new efficient nonlinear one-class classifier formulated as the Rayleigh quotient criterion optimisation. The method, operating in a reproducing kernel Hilbert space, minimises the scatter of target distribution along an optimal projection direction while at the same time keeping projections of positive observations distant from the mean of the negative class. We provide a graph embedding view of the problem which can then be solved efficiently using the spectral regression approach. In this sense, unlike previous similar methods which often require costly eigen-computations of dense matrices, the proposed approach casts the problem under consideration into a regression framework which is computationally more efficient. In particular, it is shown that the dominant complexity of the proposed method is the complexity of computing the kernel matrix. Additional appealing characteristics of the proposed one-class classifier are: 1-the ability to be trained in an incremental fashion (allowing for application in streaming data scenarios while also reducing the computational complexity in a non-streaming operation mode); 2-being unsupervised, but providing the option for refining the solution using negative training examples, when available; And last but not the least, 3-the use of the kernel trick which facilitates a nonlinear mapping of the data into a high-dimensional feature space to seek better solutions.