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| Splitting Method for Support Vector Machine in Reproducing KernelBanach Space with a Lower Semi-continuous Loss Function |
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Citation： |
Mingyu MO,Yimin WEI,Qi YE.Splitting Method for Support Vector Machine in Reproducing KernelBanach Space with a Lower Semi-continuous Loss Function[J].Chinese Annals of Mathematics B,2024,45(6):823~854 |
| Page view： 865
Net amount： 314 |
Authors： |
Mingyu MO; Yimin WEI;Qi YE |
Foundation： |
the National Natural Science Foundation of China (Nos. 12026602,
12071157, 12271108), the Natural Science Foundation of Guangdong Provience (No. 2024A1515012288),
the Science and Technology Commission of Shanghai Municipality (No. 23JC1400501) and the Ministry
of Science and Technology of China (No. G2023132005L). |
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| Abstract： |
In this paper, the authors employ the splitting method to address support
vector machine within a reproducing kernel Banach space framework, where a lower semicontinuous 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 multipliers. 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 subanalytic. Through several numerical examples, they illustrate the effectiveness of the proposed
splitting algorithm. |
Keywords： |
Support vector machine, Lower semi-continuous loss function, Reproducing kernel Banach space, Tensor optimization problem, Splitting
method |
Classification： |
68Q32, 68T05, 46E22, 68P01 |
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