Unconstrained optimization in projection method for indefinite SVMs

Abstract

Positive semi-definiteness is a critical property in Support Vector Machine (SVM) methods to ensure efficient solutions through convex quadratic programming. In this paper, we introduce a projection matrix on indefinite kernels to formulate a positive semi-definite one. The proposed model can be regarded as a generalized version of the spectrum method (denoising method and flipping method) by varying parameter λ. In particular, our suggested optimal λ under the Bregman matrix divergence theory can be obtained using unconstrained optimization. Experimental results on 4 real world data sets ranging from glycan classification to cancer prediction show that the proposed model can achieve better or competitive performance when compared to the related indefinite kernel methods. This may suggest a new way in motif extractions or cancer predictions.