A New Canonical Log-Euclidean Kernel for Symmetric Positive Definite Matrices for EEG Analysis (Oct 2024).

Area of Science:

• Neuroscience
• Machine Learning
• Geometry

Background:

• The analysis of electroencephalography (EEG) data often utilizes the Riemannian manifold of symmetric positive-definite (SPD) matrices.
• The log-euclidean Riemannian metric is frequently chosen for its computational speed.
• Existing kernels in the log-euclidean framework lack canonical grounding in the underlying geometry.

Purpose of the Study:

• Introduce a novel canonical log-euclidean (CLE) kernel.
• Evaluate the CLE kernel's performance against established kernels (affine-invariant, log-euclidean, Gaussian log-euclidean).
• Assess kernel performance in classification and dimensionality reduction tasks using EEG motor-imagery datasets.

Main Methods:

• Derived the CLE kernel using the log-euclidean metric tensor on the SPD manifold.
• Compared CLE kernel with existing kernels on five open-access brain-computer interface datasets.
• Evaluated performance using balanced classification accuracy and AUClogRNX for dimensionality reduction.

Main Results:

• The CLE kernel significantly outperformed existing log-euclidean kernels in classification tasks.
• The CLE kernel demonstrated several times the speed of the affine-invariant kernel across most datasets.
• Analytical solutions and code for the CLE kernel are provided.

Conclusions:

• Adhering to the geometrical structure of SPD matrices significantly enhances classification accuracy.
• The CLE kernel maintains the speed advantages of the log-euclidean framework.
• The CLE kernel is a suitable choice for time-critical applications and addresses a gap in log-euclidean kernel methods.