An Analysis of Transformation on Non-Positive Semidefinite Similarity Matrix for Kernel Machines

Many emerging applications formulate nonpositive semidefinite similarity matrices, and hence cannot fit into the framework of kernel machines. A popular approach to this problem is to transform the spectrum of the similarity matrix so as to generate a positive semidefinite kernel matrix. In this paper, we present an analytical framework to explore four representative transformation methods: denoise, flip, diffusion, and shift. Theoretically, we interpret each transformation and analyze its influence on classification using kernel machines. Moreover, when situations arise where the test data are not available during transformation, we propose an efficient algorithm to address the problem of updating the cross-similarity matrix between test and training data. Extensive experiments have been conducted to evaluate the performance of these methods on several realworld (dis)similarity matrices with semantic meanings.