# ℓp Slack Norm Support Vector Data Description

arXiv: https://arxiv.org/abs/2203.08932 · HTML: https://mlsanity.com/paper/2203.08932/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 54 references that are in the map.
- First posted on arXiv 16 Mar 2022.

## Builds on (most cited first, 5 of 5)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Latent Space Autoregression for Novelty Detection](https://mlsanity.com/paper/1807.01653/) (2018)
- [One-Class Classification: Taxonomy of Study and Review of Techniques](https://mlsanity.com/paper/1312.0049/) (2013)
- [One-Class Classification: A Survey](https://mlsanity.com/paper/2101.03064/) (2021)
- [Robust One-Class Kernel Spectral Regression](https://mlsanity.com/paper/1902.02208/) (2019)

## Abstract (arXiv)

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.