$\ell_p$-Norm Multiple Kernel One-Class Fisher Null-Space

The paper addresses the multiple kernel learning (MKL) problem for one-class classification (OCC). For this purpose, based on the Fisher null-space one-class classification method, we present a multiple kernel learning algorithm where a general $\ell_p$-norm constraint ($p\geq1$) on kernel weights is considered. The proposed approach is then extended to learn several related one-class MKL problems jointly by constraining them to share common kernel weights. We pose the one-class MKL task as a min-max saddle point Lagrangian optimisation problem and propose an efficient alternating optimisation method to solve it. An extensive assessment of the proposed method on ten data sets from different application domains in one-class classification confirms its merits against the baseline and several other one-class multiple kernel learning methods.