General Dimensional Multiple-Output Support Vector Regressions and Their Multiple Kernel Learning.

Area of Science:

• Machine Learning
• Computational Statistics

Background:

• Support Vector Regression (SVR) is a key methodology for regression and function approximation.
• Existing SVR methods have limitations in handling multiple outputs and general dimensional data.

Purpose of the Study:

• To introduce two novel general dimensional multiple output support vector regressions (MSVRs): SOCPL1 and SOCPL2.
• To analyze the theoretical underpinnings and relationships of the proposed MSVRs with existing literature.
• To extend the proposed MSVRs to multiple kernel learning frameworks.

Main Methods:

• Formulation of SOCPL1 and SOCPL2 in the dual space.
• Investigation of the theoretical relationship between proposed and previous MSVR methods.
• Extension of MSVRs to multiple kernel learning.
• Training of MSVRs using standard convex optimization tools.

Main Results:

• The proposed SOCPL1 and SOCPL2 MSVR methods are introduced.
• Theoretical analysis and comparisons with prior work are presented.
• Successful application and performance evaluation on benchmark problems.

Conclusions:

• The novel SOCPL1 and SOCPL2 MSVRs offer advanced capabilities for multi-output regression.
• The integration with multiple kernel learning enhances their flexibility.
• Experimental results validate the effectiveness of the proposed methods compared to existing approaches.