The paper studies face spoofing, a.k.a. presentation attack detection (PAD) in the demanding scenarios of unknown attacks. While earlier studies have revealed the benefits of ensemble methods, and in particular, a multiple kernel learning (MKL) approach to the problem, one limitation of such techniques is that they typically treat the entire observation space similarly and ignore any variability and \textit{local} structure inherent to the data. This work studies this aspect of face presentation attack detection with regards to one-class multiple kernel learning to benefit from the intrinsic local structure in bona fide samples to adaptively weight each representation in the composite kernel. More concretely, inspired by the success of the one-class Fisher null formalism, we formulate a convex \textit{localised} multiple kernel learning algorithm by imposing a joint matrix-norm constraint on the collection of local kernel weights and infer locally adaptive weights for zero-shot one-class unseen attack detection. We present a theoretical study of the proposed localised MKL algorithm using Rademacher complexities to characterise its generalisation capability and demonstrate the advantages of the proposed technique over some other options. An assessment of the proposed approach on general object image datasets illustrates its efficacy for abnormality and novelty detection while the results of the experiments on face PAD datasets verify its potential in detecting unknown/unseen face presentation attacks.

The paper addresses the one-class classification (OCC) problem and advocates a one-class multiple kernel learning (MKL) approach for this purpose. To this aim, based on the Fisher null-space one-class classification principle, we present a multiple kernel learning algorithm where an $\ell_p$-norm constraint ($p\geq1$) on kernel weights is considered. We cast the proposed one-class MKL task as a min-max saddle point Lagrangian optimisation problem and propose an efficient method to solve it. An extension of the proposed one-class MKL approach is also considered where several related one-class MKL tasks are learned concurrently by constraining them to share common kernel weights. An extensive assessment of the proposed method on a range of data sets from different application domains confirms its merits against the baseline and several other algorithms.