ℓp Slack Norm Support Vector Data Description

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 ℓ1-norm penalty term. In this study, we generalise this modelling formalism to a general ℓp-norm (p≥1) slack penalty function. By virtue of an ℓp 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.