A Robust Distance Measure for Similarity-Based Classification on the SPD Manifold

Area of Science:

• Computer Vision
• Machine Learning
• Manifold Learning

Background:

• Symmetric Positive Definite (SPD) matrices represent data on a Riemannian manifold.
• The non-Euclidean geometry of SPD manifolds complicates traditional machine learning algorithms.
• Similarity-based learning offers a geometry-agnostic approach but often uses holistic representations.

Purpose of the Study:

• To develop a novel SPD distance measure for similarity-based learning.
• To address the limitation of holistic representations in existing SPD manifold models.
• To improve performance in visual recognition tasks by capturing discriminative information within SPD matrices.

Main Methods:

• Proposed a point-to-set transformation to learn multiple lower-dimensional SPD manifolds.
• Introduced a tailored set-to-set distance measure using alpha-beta divergences for these lower-dimensional manifolds.
• Developed a joint learning framework for the point-to-set transformation and set-to-set distance.

Main Results:

• The proposed method effectively learns multiple discriminative SPD manifolds.
• The joint learning approach yields a powerful similarity-based algorithm.
• Demonstrated superior performance over state-of-the-art algorithms in action classification and face recognition.

Conclusions:

• The novel SPD distance measure enhances similarity-based learning on SPD manifolds.
• The point-to-set and set-to-set distance framework captures crucial information within SPD matrices.
• The proposed algorithm offers significant improvements for visual recognition tasks.