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A fast learning algorithm for One-Class Slab Support Vector Machines

Bagesh Kumar, Ayush Sinha, Sourin Chakrabarti, O. P. Vyas

TL;DR

The paper tackles the high computational cost of training one-class classifiers in open-set contexts by developing a fast SMO-based algorithm for One-Class Slab SVMs (OCSSVM). It reformulates the OCSSVM training into reduced two-variable subproblems using gamma variables, derives efficient update rules, and employs a KKT-driven working-set heuristic to select variable pairs. Empirical results on toy data demonstrate favorable training times and competitive classification metrics, highlighting improved scalability over general quadratic programming solvers. The approach promises practical impact for large-scale open-set recognition and anomaly detection by enabling faster model fitting while preserving accuracy, with suggested directions for parallelization and hardware acceleration.

Abstract

One Class Slab Support Vector Machines (OCSSVM) have turned out to be better in terms of accuracy in certain classes of classification problems than the traditional SVMs and One Class SVMs or even other One class classifiers. This paper proposes fast training method for One Class Slab SVMs using an updated Sequential Minimal Optimization (SMO) which divides the multi variable optimization problem to smaller sub problems of size two that can then be solved analytically. The results indicate that this training method scales better to large sets of training data than other Quadratic Programming (QP) solvers.

A fast learning algorithm for One-Class Slab Support Vector Machines

TL;DR

The paper tackles the high computational cost of training one-class classifiers in open-set contexts by developing a fast SMO-based algorithm for One-Class Slab SVMs (OCSSVM). It reformulates the OCSSVM training into reduced two-variable subproblems using gamma variables, derives efficient update rules, and employs a KKT-driven working-set heuristic to select variable pairs. Empirical results on toy data demonstrate favorable training times and competitive classification metrics, highlighting improved scalability over general quadratic programming solvers. The approach promises practical impact for large-scale open-set recognition and anomaly detection by enabling faster model fitting while preserving accuracy, with suggested directions for parallelization and hardware acceleration.

Abstract

One Class Slab Support Vector Machines (OCSSVM) have turned out to be better in terms of accuracy in certain classes of classification problems than the traditional SVMs and One Class SVMs or even other One class classifiers. This paper proposes fast training method for One Class Slab SVMs using an updated Sequential Minimal Optimization (SMO) which divides the multi variable optimization problem to smaller sub problems of size two that can then be solved analytically. The results indicate that this training method scales better to large sets of training data than other Quadratic Programming (QP) solvers.

Paper Structure

This paper contains 7 sections, 26 equations, 2 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. One-Class Slab Support Vector Machines
  3. SMO Algorithm for OCSSVM
  4. Solving reduced optimization problem
  5. Variable pair selection heuristic
  6. Experimentation and Results
  7. Conclusion and Future Scope

Figures (2)

  • Figure 1: The final plot for 1000 data samples of a toy dataset with the data points in blue, the lower and upper hyper-planes in red and green respectively. The horizontal and vertical axes are the x and y axis respectively. The value of constants used were $\nu_1 = 0.5$, $\nu_2 = 0.01$ and $\varepsilon=\frac{2}{3}$.
  • Figure 2: The final plot for 2000 data samples of a toy dataset with the data points in blue, the lower and upper hyper-planes in red and green respectively. The horizontal and vertical axes are the x and y axis respectively. The value of constants used were $\nu_1 = 0.2$, $\nu_2 = 0.08$ and $\varepsilon=\frac{1}{2}$.