Projection method for support vector machines with indefinite kernels

In this paper, we tackle with indefinite kernels by introducing projection matrix to formulate a positive semidefinite kernel. The projection matrix has a nice property of sharing the same set of eigenvectors with the original kernel. The proposed model can be regarded as a generalized version of spectrum method (denoising method and flipping method) by varying parameter λ. The problem of selecting optimal λ for optimizing the prediction performance is also considered. Using the Bregman matrix divergence theory, one can realize kernel learning by using unconstrained optimization. And our suggested λ in projection matrix helps to exhibit optimal performance for different values of λ.