Non positive SVM
Gaëlle Loosli and Stéphane Canu
In: Optimization in Machine Learning, 16 Dec 2011, Sierra Nevada, Spain.
Learning SVM with non positive kernels is is a problem that has been addressed in the last years but it is not really solved : indeed, either the kernel is corrected (as a pre-treatment or via a modiﬁed learning scheme), either it is used with some well chosen parameters that lead to almost positive-deﬁnite kernels. In this work, we aim at solving the actual problem induced by non positive kernels, i.e. solving the stabilization system in the Krein space associated with the non-positive kernel.
We ﬁrst describe this stabilization system, then we expose a simple algorithm based on the eigen-decomposition of the kernel matrix. While providing satisfying solutions, the proposed algorithm shows limitations in terms of memory storage and computational effort. The direct resolution is still an open question.