Geodesic Multi-Class SVM with Stiefel Manifold Embedding.

Area of Science:

• Machine Learning
• Data Geometry
• Computational Statistics

Background:

• Existing Support Vector Machine (SVM) methods often overlook intrinsic data geometry.
• Neglecting manifold structure can lead to functional degeneration or model collapse with noisy training data.

Purpose of the Study:

• To develop a manifold SVM method that extracts and preserves data manifold structure.
• To enhance robustness against training noise and data contamination.

Main Methods:

• A novel ξ-measure geodesic is devised to capture manifold structure.
• Kullback-Leibler (KL) regularization with steerable sparsity constraint is introduced for noise handling.
• Adaptive loss weights and automatic Stiefel manifold scale learning are employed.

Main Results:

• The proposed method effectively extracts and preserves data manifold structure.
• Robust fitting is achieved even with significantly contaminated training data.
• Improved model flexibility and performance are demonstrated through extensive experiments.

Conclusions:

• The novel manifold SVM method offers superior performance in characterizing intrinsic data geometry.
• The approach provides a robust solution for dealing with noisy and contaminated datasets.
• This work advances SVM capabilities by integrating manifold learning principles.