  The support vector data description (SVDD) approach serves as a de facto
standard for one-class classification where the learning task entails inferring
the smallest hyper-sphere to enclose target objects while linearly penalising
any errors/slacks via an $\ell_1$-norm penalty term. In this study, we
generalise this modelling formalism to a general $\ell_p$-norm ($p\geq1$) slack
penalty function. By virtue of an $\ell_p$ slack norm, the proposed approach
enables formulating a non-linear cost function with respect to slacks. From a
dual problem perspective, the proposed method introduces a sparsity-inducing
dual norm into the objective function, and thus, possesses a higher capacity to
tune into the inherent sparsity of the problem for enhanced descriptive
capability. A theoretical analysis based on Rademacher complexities
characterises the generalisation performance of the proposed approach in terms
of parameter $p$ while the experimental results on several datasets confirm the
merits of the proposed method compared to other alternatives.
