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

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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https://hal.archives-ouvertes.fr/hal-01563153
Contributor : Marco Congedo <>
Submitted on : Monday, July 17, 2017 - 12:36:22 PM
Last modification on : Tuesday, May 11, 2021 - 11:37:34 AM
Long-term archiving on: : Saturday, January 27, 2018 - 1:52:12 AM

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  • HAL Id : hal-01563153, version 1

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Marco Congedo, Pedro Luiz Coelho Rodrigues, Florent Bouchard, Alexandre Barachant, Christian Jutten. A Closed-Form Unsupervised Geometry-Aware Dimensionality Reduction Method in the Riemannian Manifold of SPD Matrices. EMBC 2017 - 39th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, IEEE, Jul 2017, Jeju Island, South Korea. pp.3198-3201. ⟨hal-01563153⟩

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