On the convergence of the decomposition method for support vector machines

Area of Science:

• Machine Learning
• Optimization Algorithms
• Computational Mathematics

Background:

• Decomposition methods are key for solving Support Vector Machines (SVM).
• Previous research established general convergence but had limitations in practical implementations.
• The convergence of practical SVM decomposition algorithms, especially with varying working set sizes, remained incompletely understood.

Purpose of the Study:

• To rigorously prove the asymptotic convergence of the decomposition algorithm used in SVM(light) and similar implementations.
• To extend the understanding of convergence properties beyond the restricted working set sizes previously analyzed.
• To investigate the applicability of these convergence proofs to other Support Vector Machine formulations.

Main Methods:

• Mathematical analysis of the decomposition algorithm's iterative steps.
• Focus on algorithms where the working set size can be any even number.
• Theoretical examination of convergence properties under practical implementation constraints.

Main Results:

• The asymptotic convergence of the SVM(light) decomposition algorithm is mathematically proven.
• The proof accommodates working sets of any even size, a significant improvement over prior work.
• The study provides a theoretical foundation for the reliable performance of widely used SVM software.

Conclusions:

• The convergence of practical SVM decomposition algorithms is now better understood.
• This work validates the theoretical underpinnings of popular SVM implementations.
• The findings pave the way for further theoretical analysis and potential improvements in SVM algorithms.