Effective subset approach for SVMpath singularities

Singularities are frequently encountered in the powerful SVMpath algorithm. This paper proposes an effective subset approach for handling singularities, which is quite distinct from the previous ridge-adding method that can only obtain some approximate solutions. The main novelty of the new approach is to divide the active set into the effective and ineffective subsets. The effective subset plays an important role in guaranteeing the existence of the inverse matrix, so as to obtain a correct search direction even some singularities are encountered; while the ineffective subset is to temporarily absorb any indexes that might cause singularities, and properly release them into the effective subset when it is necessary. Experimental results are performed to verify our theoretical analysis and illustrate the ability of singularity avoidance.