Matrix-Regularized Multiple Kernel Learning via (r,p) Norms.

Area of Science:

• Machine Learning
• Computational Statistics

Background:

• Model complexity in Support Vector Machine (SVM)-based multiple kernel learning (MKL) is managed via regularization of combined kernel weights.
• Existing generalized ℓp-norm MKL frameworks offer tunable sparsity but neglect base kernel interactions.

Purpose of the Study:

• To extend ℓp-norm MKL to a "2-D" matrix (r,p)-norm framework to incorporate higher-order kernel-pair relationships.
• To develop a novel formulation and efficient optimization strategy for (r,p)-MKL.

Main Methods:

• Introduced a matrix-regularized multiple kernel learning (MKL) technique utilizing (r,p)-norms.
• Developed a new formulation and an efficient optimization strategy for (r,p)-MKL with guaranteed convergence.
• Conducted theoretical analysis and experiments on seven UCI datasets.

Main Results:

• The proposed (r,p)-MKL framework effectively captures kernel-pair interactions, a limitation of previous ℓp-MKL methods.
• Demonstrated the superiority of (r,p)-MKL over ℓp-MKL across various scenarios in experimental evaluations.
• The optimization strategy for (r,p)-MKL ensures convergence.

Conclusions:

• The (r,p)-norm MKL approach offers significant advantages over ℓp-norm MKL by exploiting kernel interactions.
• This method provides a more effective way to control model complexity and improve performance in MKL.
• The developed framework and optimization strategy are robust and efficient for practical applications.