DC Algorithm for Extended Robust Support Vector Machine.

Area of Science:

• Machine Learning
• Optimization
• Support Vector Machines

Background:

• Nonconvex variants of Support Vector Machines (SVMs) are used for specific applications, such as robust SVMs for outlier handling and extended [Formula: see text]-SVM (E[Formula: see text]-SVM) for hyperparameter range extension.
• The extended robust support vector machine (ER-SVM) integrates nonconvexities from both robust SVMs and E[Formula: see text]-SVM, presenting algorithmic challenges due to its dual nonconvex nature.

Purpose of the Study:

• To propose a novel and efficient algorithm for solving the ER-SVM problem.
• To address the computational complexities arising from the two distinct nonconvexities in ER-SVM.
• To demonstrate that ER-SVM encompasses existing robust SVMs as specific instances.

Main Methods:

• Development of a new algorithm designed to efficiently handle the dual nonconvexities inherent in ER-SVM.
• The proposed algorithm ensures computational costs do not exceed those of E[Formula: see text]-SVM or robust SVM.
• The algorithm is proven to find a critical point for the ER-SVM optimization problem.

Main Results:

• The new algorithm effectively manages the two types of nonconvexity in ER-SVM without increasing computational load.
• ER-SVM is shown to generalize existing robust SVM methods.
• Numerical experiments validate the efficacy of combining the two nonconvexities.

Conclusions:

• The developed algorithm provides an efficient solution for ER-SVM, unifying two nonconvex approaches.
• ER-SVM offers a more generalized framework for robust classification, including previous robust SVMs.
• The integration of dual nonconvexities is computationally effective and practically beneficial.