Kernel Path for ν-Support Vector Classification.

Area of Science:

• Machine Learning
• Computational Statistics
• Pattern Recognition

Background:

• Kernel method performance is critically dependent on kernel parameter selection.
• Existing kernel path algorithms are limited to simple Support Vector Machines (SVMs), lacking applicability to more complex models like ν-support vector classification (ν-SVC).
• ν-SVC offers advantages in controlling support vectors and margin errors via a regularization parameter ν.

Purpose of the Study:

• To develop a kernel path algorithm for ν-SVC that accurately traces solutions with respect to the kernel parameter.
• To address the challenge of finding the global optimal kernel parameter for ν-SVC.
• To extend existing error path algorithms to nonlinear kernel solution paths.

Main Methods:

• An equivalent formulation of ν-SVC with two equality constraints was developed to facilitate solution tracing.
• A novel kernel path algorithm for ν-SVC (KPνSVC) was proposed based on this formulation.
• The classical error path algorithm was extended to create a kernel error path (KEP) algorithm for global optimal parameter selection.

Main Results:

• The KPνSVC algorithm successfully traces ν-SVC solutions concerning the kernel parameter.
• The KEP algorithm demonstrates effectiveness in finding the global optimal kernel parameter by minimizing cross-validation error.
• Both KPνSVC and KEP algorithms were analyzed for finite convergence and computational complexity.
• Extensive experiments on benchmark datasets validated the effectiveness of KPνSVC and the advantage of KEP for optimal kernel parameter selection.

Conclusions:

• The proposed KPνSVC algorithm provides an effective method for tracing ν-SVC solutions across kernel parameters.
• The KEP algorithm offers a robust approach to guarantee the selection of the globally optimal kernel parameter.
• These algorithms advance the capabilities of kernel methods, particularly for ν-SVC, by addressing parameter optimization challenges.