A division algebraic framework for multidimensional support vector regression.

Area of Science:

• Machine Learning
• Algebraic Methods in Data Science

Background:

• Support Vector Regression (SVR) is a powerful tool for regression tasks.
• Extending SVR to handle multidimensional targets presents significant challenges.
• Existing multidimensional SVR methods have limitations in performance and sensitivity.

Purpose of the Study:

• To propose division algebras as a novel framework for extending SVR to multidimensional targets.
• To introduce epsilon(H)-SVR, a new multitarget SVR method.
• To evaluate the performance of epsilon(H)-SVR against existing methods.

Main Methods:

• Development of epsilon(H)-SVR based on an epsilon-insensitive loss function.
• Formulation of epsilon(H)-SVR in dual form, analogous to standard epsilon-SVR.
• Comparative analysis with least-square SVR (LS-SVR), Clifford SVR (C-SVR), and multidimensional SVR (M-SVR).

Main Results:

• Epsilon(H)-SVR demonstrates significantly improved performance across various metrics.
• The method shows lower mean-squared error compared to C-SVR, LS-SVR, and M-SVR.
• Epsilon(H)-SVR exhibits reduced outlier sensitivity and enhanced support vector sparsity.

Conclusions:

• Division algebras provide an effective basis for extending SVR to multidimensional problems.
• Epsilon(H)-SVR offers a robust and efficient solution for multitarget regression.
• The proposed method shows promise in practical applications such as function approximation, time-series prediction, and channel equalization.