Fast generalized ramp loss support vector machine for pattern classification

Huajun Wang

doi:10.1016/j.patcog.2023.109987

Fast generalized ramp loss support vector machine for pattern classification

2024-02-01

11

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AI

王华军 (Huajun Wang) *

邵

邵元海 (Yuan‐Hai Shao)

DOI：10.1016/j.patcog.2023.109987

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Support vector machine (SVM) is widely recognized as an effective classification tool and has demonstrated superior performance in diverse applications. However, for large-scale pattern classification problems, it may require much memory and incur prohibitive computational costs. Motivated by this, we propose a new SVM model with novel generalized ramp loss (LR-SVM). The first-order optimality conditions for the non-convex and non-smooth LR-SVM are developed by the newly developed P-stationary point, based on which, the LR support vectors and working set of LR-SVM are defined, interestingly, which shows that all of the LR support vectors are on the two support hyperplanes under mild conditions. A fast proximal alternating direction method of multipliers with working set (LR-ADMM) is developed to handle LR-SVM and LR-ADMM has been demonstrated to achieve global convergence while maintaining a significantly low computational complexity. Numerical comparisons with nine leading solvers show that LR-ADMM demonstrates outstanding performance, particularly when applied to large-scale pattern classification problems with fewer support vectors, higher prediction accuracy and shorter computational time.

Keywords:

Generalized ramp loss

LR-SVM

LR proximal operator

Working set

LR support vectors

LR-ADMM

Fast generalized ramp loss support vector machine for pattern classification

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