A closed-form unsupervised geometry-aware dimensionality reduction method in the Riemannian Manifold of SPD matrices

Area of Science:

• Computational geometry
• Machine learning
• Neuroscience

Background:

• Riemannian geometry offers robust multidimensional data classification, particularly in electroencephalography-based brain-computer interfaces.
• Embedding high-dimensional data onto lower-dimensional manifolds is essential for computational efficiency and preserving accuracy.
• Existing geometry-aware methods aim to maintain data structure during dimensionality reduction.

Purpose of the Study:

• To develop a closed-form, unsupervised method for dimensionality reduction of data on the manifold of symmetric positive-definite matrices.
• To assess the effectiveness of geometry-aware dimensionality reduction in preserving classification accuracy.

Main Methods:

• A novel closed-form solution for unsupervised, geometry-aware dimensionality reduction was derived.
• The method was applied to data from three brain-computer interface databases.

Main Results:

• The proposed method achieved substantial dimensionality reduction.
• Classification accuracy was maintained despite significant reduction in data dimensions.
• The approach respects the underlying geometry of the data.

Conclusions:

• The developed unsupervised, geometry-aware dimensionality reduction technique is effective for brain-computer interface data.
• This method offers a computationally efficient way to handle high-dimensional data without sacrificing performance.