A Closed-Form Unsupervised Geometry-Aware Dimensionality Reduction Method in the Riemannian Manifold of SPD Matrices

Marco Congedo 1, * Pedro Rodrigues 1 Florent Bouchard 1 Alexandre Barachant 1 Christian Jutten 1
* Corresponding author
1 GIPSA-VIBS - VIBS
GIPSA-DIS - Département Images et Signal
Abstract : Riemannian geometry has been found accurate and robust for classifying multidimensional data, for instance, in brain-computer interfaces based on electroencephalography. Given a number of data points on the manifold of symmetric positive-definite matrices, it is often of interest to embed these points in a manifold of smaller dimension. This is necessary for large dimensions in order to preserve accuracy and useful in general to speed up computations. Geometry-aware methods try to accomplish this task while respecting as much as possible the geometry of the original data points. We provide a closed-form solution for this problem in a fully unsupervised setting. Through the analysis of three brain-computer interface data bases we show that our method allows substantial dimensionality reduction without affecting the classification accuracy.
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Marco Congedo, Pedro Rodrigues, Florent Bouchard, Alexandre Barachant, Christian Jutten. A Closed-Form Unsupervised Geometry-Aware Dimensionality Reduction Method in the Riemannian Manifold of SPD Matrices. 39th International Conference of the IEEE Engineering in Medicine and Biology Society, Jeju Island (EMBC'17), IEEE, Jul 2017, Jeju Island, South Korea. pp.3198-3201. ⟨hal-01563153⟩

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