Extremal eigenvalue problems with indefinite kernels

EXTREMAL EIGENVALUE PROBLEMS FOR THE LAPLACIANSteven

Support vector machines with indefinite kernels

Training support vector machines (SVM) with indefinite kernels has recently attracted attention in the machine learning community. This is partly due to the fact that many similarity functions that arise in practice are not symmetric positive semidefinite, i.e. the Mercer condition is not satisfied, or the Mercer condition is difficult to verify. Previous work on training SVM with indefinite ke...

Support Vector Machine Classification with Indefinite Kernels

We propose a method for support vector machine classification using indefinite kernels. Instead of directly minimizing or stabilizing a nonconvex loss function, our algorithm simultaneously computes support vectors and a proxy kernel matrix used in forming the loss. This can be interpreted as a penalized kernel learning problem where indefinite kernel matrices are treated as a noisy observation...

Learning SVM Classifiers with Indefinite Kernels

Recently, training support vector machines with indefinite kernels has attracted great attention in the machine learning community. In this paper, we tackle this problem by formulating a joint optimization model over SVM classifications and kernel principal component analysis. We first reformulate the kernel principal component analysis as a general kernel transformation framework, and then inc...

Analysis of SVM with Indefinite Kernels

The recent introduction of indefinite SVM by Luss and d’Aspremont [15] has effectively demonstrated SVM classification with a non-positive semi-definite kernel (indefinite kernel). This paper studies the properties of the objective function introduced there. In particular, we show that the objective function is continuously differentiable and its gradient can be explicitly computed. Indeed, we ...