Regularization path for ν-support vector classification.

Area of Science:

• Machine Learning
• Computational Statistics
• Pattern Recognition

Background:

• v-support vector classification (v-SVC) offers control over support vectors and margin errors via a regularization parameter v.
• Existing v-SVC formulations are complex, lacking effective methods for computing the regularization path.
• Efficient computation of the regularization path is crucial for optimizing v-SVC models.

Purpose of the Study:

• To propose a novel regularization path algorithm for v-SVC.
• To enable efficient computation of the v-SVC solution path with respect to the regularization parameter v.
• To facilitate the selection of the optimal regularization parameter for v-SVC models.

Main Methods:

• Development of a new regularization path algorithm based on a modified v-SVC formulation.
• Theoretical analysis to ensure avoidance of infeasible updating paths.
• Integration with Yang and Ong's approach for global optimal solution of validation functions.

Main Results:

• The proposed algorithm successfully traces the v-SVC solution path in a finite number of steps.
• The algorithm avoids infeasible updating paths under stated assumptions.
• Numerical experiments demonstrate superior efficiency compared to grid search methods for parameter selection.

Conclusions:

• The novel regularization path algorithm provides an effective and efficient method for v-SVC.
• This advancement simplifies the process of finding the optimal regularization parameter v.
• The method enables minimal computation for obtaining global optimal solutions for v-SVC validation functions.