ℓp-Norm Support Vector Data Description. (December 2022) - Rahimzadeh Arashloo, Shervin
Highlights: The support vector data description method optimises an-norm cost w.r.t. errors We generalise this modelling formalism to an-norm () slack penalty function The proposed method enables formulating a non-linear cost function w.r.t. errors Through a dual-norm, it introduces a controlling mechanism over the relative sparsity Experiments confirm the merits of the proposed method against other alternatives Abstract: 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 the errors/slacks via an ℓ 1 -norm penalty term. In this study, we generalise this modelling formalism to a general ℓ p -norm ( p ≥ 1 ) penalty function on slacks. By virtue of an ℓ p -norm function, in the primal space, the proposed approach enables formulating a non-linear cost for slacks. From a dual problem perspective, the proposed method introduces a dual norm into the objective function, thus, proving a controlling mechanism to tune into the intrinsic sparsity/uniformity of the problem for enhanced descriptive capability. A theoretical analysis based on Rademacher complexities characterises the generalisation performance of the proposed approach while the experimental results on several datasets confirm the merits of the proposed method compared to other alternatives.