DC Algorithm for Extended Robust Support Vector Machine

作者：Fujiwara Shuhei^*; Takeda Akiko; Kanamori Takafumi

来源：Neural Computation, 2017, 29(5): 1406-1438.

DOI：10.1162/NECO_a_00958

Nonconvex variants of support vector machines (SVMs) have been developed for various purposes. For example, robust SVMs attain robustness to outliers by using a nonconvex loss function, while extended nu-SVM (E nu-SVM) extends the range of the hyperparameter by introducing a nonconvex constraint. Here, we consider an extended robust support vector machine (ER-SVM), a robust variant of E nu-SVM. ER-SVM combines two types of nonconvexity from robust SVMs and E nu-SVM. Because of the two nonconvexities, the existing algorithm we proposed needs to be divided into two parts depending on whether the hyperparameter value is in the extended range or not. The algorithm also heuristically solves the nonconvex problem in the extended range.
In this letter, we propose a new, efficient algorithm for ER-SVM. The algorithm deals with two types of nonconvexity while never entailing more computations than either E nu-SVM or robust SVM, and it finds a critical point of ER-SVM. Furthermore, we show that ER-SVM includes the existing robust SVMs as special cases. Numerical experiments confirm the effectiveness of integrating the two nonconvexities.

• 出版日期2017-5
• 单位RIKEN