# Newton Method-based Subspace Support Vector Data Description

arXiv: https://arxiv.org/abs/2309.13960 · HTML: https://mlsanity.com/paper/2309.13960/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 28 references that are in the map.
- First posted on arXiv 25 Sep 2023.

## Builds on (most cited first, 13 of 13)

- [Non-convex Optimization for Machine Learning](https://mlsanity.com/paper/1712.07897/) (2017)
- [Second-Order Optimization for Non-Convex Machine Learning: An Empirical Study](https://mlsanity.com/paper/1708.07827/) (2017)
- [Subspace Support Vector Data Description](https://mlsanity.com/paper/1802.03989/) (2018)
- [Multimodal Subspace Support Vector Data Description](https://mlsanity.com/paper/1904.07698/) (2019)
- [An Inertial Newton Algorithm for Deep Learning](https://mlsanity.com/paper/1905.12278/) (2019)
- [Ellipsoidal Subspace Support Vector Data Description](https://mlsanity.com/paper/2003.09504/) (2020)
- [Graph-Embedded Subspace Support Vector Data Description](https://mlsanity.com/paper/2104.14370/) (2021)
- [Quasi-Newton Methods for Machine Learning: Forget the Past, Just Sample](https://mlsanity.com/paper/1901.09997/) (2019)
- [Boosting rare benthic macroinvertebrates taxa identification with one-class classification](https://mlsanity.com/paper/2002.10420/) (2020)
- [Early Myocardial Infarction Detection with One-Class Classification over Multi-view Echocardiography](https://mlsanity.com/paper/2204.07253/) (2022)
- [Gradient Descent based Optimization Algorithms for Deep Learning Models Training](https://mlsanity.com/paper/1903.03614/) (2019)
- [Hyperspectral Image Analysis with Subspace Learning-based One-Class Classification](https://mlsanity.com/paper/2304.09730/) (2023)
- [Quasi-Newton Optimization Methods For Deep Learning Applications](https://mlsanity.com/paper/1909.01994/) (2019)

## Built on by (most cited first, 5 of 5)

- [Trustworthiness of mathbbX Users: A One-Class Classification Approach](https://mlsanity.com/paper/2402.02066/) (2024)
- [Refining Myocardial Infarction Detection: A Novel Multi-Modal Composite Kernel Strategy in One-Class Classification](https://mlsanity.com/paper/2402.06530/) (2024)
- [Anomaly Detection in Smart Power Grids with Graph-Regularized MS-SVDD: a Multimodal Subspace Learning Approach](https://mlsanity.com/paper/2502.15793/) (2025)
- [A Mathematical Optimization Approach to Multisphere Support Vector Data Description](https://mlsanity.com/paper/2507.11106/) (2025)
- [To Vaccinate or not to Vaccinate? Analyzing mathbbX Power over the Pandemic](https://mlsanity.com/paper/2503.02563/) (2025)

## Abstract (arXiv)

In this paper, we present an adaptation of Newton's method for the optimization of Subspace Support Vector Data Description (S-SVDD). The objective of S-SVDD is to map the original data to a subspace optimized for one-class classification, and the iterative optimization process of data mapping and description in S-SVDD relies on gradient descent. However, gradient descent only utilizes first-order information, which may lead to suboptimal results. To address this limitation, we leverage Newton's method to enhance data mapping and data description for an improved optimization of subspace learning-based one-class classification. By incorporating this auxiliary information, Newton's method offers a more efficient strategy for subspace learning in one-class classification as compared to gradient-based optimization. The paper discusses the limitations of gradient descent and the advantages of using Newton's method in subspace learning for one-class classification tasks. We provide both linear and nonlinear formulations of Newton's method-based optimization for S-SVDD. In our experiments, we explored both the minimization and maximization strategies of the objective. The results demonstrate that the proposed optimization strategy outperforms the gradient-based S-SVDD in most cases.