Convergence of ?-insensive Smooth Support Vector Regression

doi:10.3969/j.issn.1000-3428.2010.15.065

Abstract

Abstract: The ?-insensive Smooth Support Vector Regression(?-SSVR) is solved by a fast iterative algorithm, which improves the performance and efficiency of regression, but the problem of convergence remains still. In the present paper, ?-SSVR’s global convergence for an arbitrary given penalty parameter is proved by the method of set theory, and the upper bound of the convergence is worked out, which provides the smooth support vector machine with a basic theoretical support.

Key words: ?-insensive loss function ?-insensive loss function, regression, support vector machine, smooth, convergence

摘要： ?-不敏感的光滑支持向量回归机采用快速的迭代方法进行求解，使回归性能及效率得到了提高，但并没有考虑该回归机的收敛性。针对该问题，采用集合论等方法，通过相关的理论推导，证明该光滑支持向量回归机对任意给定的惩罚参数都是全局收敛的，并给出它的收敛上界，为该光滑支持向量机提供了基本的理论支持。

关键词: ?-不敏感损失函数, 回归, 支持向量机, 光滑, 收敛

CLC Number:

TP18

CHEN Yong, XU Jian-Min. Convergence of ?-insensive Smooth Support Vector Regression[J]. Computer Engineering, 2010, 36(15): 185-187,190.

陈勇, 徐建敏. ε-不敏感的光滑支持向量回归机的收敛性[J]. 计算机工程, 2010, 36(15): 185-187,190.

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References

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