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Splitting Method for Support Vector Machine in Reproducing Kernel Banach Space with a Lower Semi-continuous Loss Function

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Splitting Method for Support Vector Machine in Reproducing Kernel Banach Space with a Lower Semi-continuous Loss Function
In this paper,the authors employ the splitting method to address support vector machine within a reproducing kernel Banach space framework,where a lower semi-continuous loss function is utilized.They translate support vector machine in reproducing kernel Banach space with such a loss function to a finite-dimensional tensor optimization problem and propose a splitting method based on the alternating direction method of mul-tipliers.Leveraging Kurdyka-Lojasiewicz property of the augmented Lagrangian function,the authors demonstrate that the sequence derived from this splitting method is globally convergent to a stationary point if the loss function is lower semi-continuous and subana-lytic.Through several numerical examples,they illustrate the effectiveness of the proposed splitting algorithm.

Support vector machineLower semi-continuous loss functionRepro-ducing kernel Banach spaceTensor optimization problemSplitting method

Mingyu MO、Yimin WEI、Qi YE

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Academy for Advanced Interdisciplinary Studies,Peking University,Beijing 100871,China

School of Mathematical Science,South China Normal University,Guangzhou 510631,China

School of Mathematical Science,Key Laboratory of Mathematics for Nonlinear Sciences,Fudan Uni-versity,Shanghai 200433,China

Support vector machine Lower semi-continuous loss function Repro-ducing kernel Banach space Tensor optimization problem Splitting method

2024

10.1007/s11401-024-0041-5

数学年刊B辑(英文版)
国家教育部委托复旦大学主办

数学年刊B辑(英文版)

CSTPCD
影响因子：0.129
ISSN：0252-9599
年,卷(期)：2024.45(6)