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Communication Dans Un Congrès Année : 2017

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

Résumé

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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Dates et versions

hal-01563153 , version 1 (17-07-2017)

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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, ⟨10.1109/EMBC.2017.8037537⟩. ⟨hal-01563153⟩
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