Feasibility and finite convergence analysis for accurate on-line ν-support vector machine

Area of Science:

• Machine Learning
• Computational Statistics

Background:

• The ν-support vector machine (ν-SVM) offers control over support vectors and margin errors.
• The accurate on-line ν-SVM algorithm (AONSVM) was proposed for efficient ν-SVM training.
• Prior demonstrations of AONSVM's convergence lacked theoretical grounding.

Purpose of the Study:

• To provide theoretical justification for the feasibility and finite convergence of the AONSVM algorithm.
• To address the lack of theoretical analysis for AONSVM, differentiating it from classical methods.

Main Methods:

• Mathematical analysis under two key assumptions.
• Feasibility analysis of critical matrices and update rules within AONSVM.
• Investigation of the role of the variable ζ in weight adjustment.

Main Results:

• Proved the existence of inverses for key matrices in AONSVM.
• Established the reliability of update rules for these matrices.
• Demonstrated efficient weight adjustment via the variable ζ.
• Showed that samples do not oscillate between vector sets during updates.
• Provided direct proofs for the feasibility and finite convergence of accurate on-line C-SVM learning.

Conclusions:

• The AONSVM algorithm is theoretically proven to be feasible and finitely convergent.
• These findings validate the practical performance observed in prior experimental analyses.
• The theoretical framework established also supports the convergence of accurate on-line C-SVM learning.