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Riemannian Classification for SSVEP-Based BCI
Published in Chang S. Nam, Anton Nijholt, Fabien Lotte, Brain–Computer Interfaces Handbook, 2018
Sylvain Chevallier, Emmanuel K. Kalunga, Quentin Barthélemy, Florian Yger
After reviewing some of the most robust approaches in features extraction for steady-state visually evoked potentials (SSVEPs), this chapter will present recently introduced tools for signal processing based on a non-Euclidean geometry, namely, the Riemannian geometry. These techniques have demonstrated their benefit on several occasions, leading to winning algorithms in international competitions and to state-of-the-art results on renowned BCI benchmarks. Most of these achievements are built on the theoretical advances of a very active community working on Information Geometry and its applications to signal processing, for example, in radar imagery, computer vision, or finance. A thorough review of the existing Riemannian approaches for BCI is proposed, with its application to SSVEP.
An Information Geometry Approach to Robustness Analysis for the Uncertainty Quantification of Computer Codes
Published in Technometrics, 2022
Clement Gauchy, Jerome Stenger, Roman Sueur, Bertrand Iooss
Figure 2 shows the position of four Gaussian distributions in the half-plane. It is clear that the distributions C and D are more difficult to distinguish than A and B, though in both cases the 2-Wassertein distance W2 (Villani 2009) is the same. The hyperbolic geometry induced by the Fisher information provides a representation in accordance with this intuition. Indeed, the two red dashed curves are the geodesics between points A and B, and C and D. We observe that the Fisher distance between A and B is greater than between C and D. This illustrates how information geometry provides a well-grounded framework to measure statistical dissimilarities in probability measure spaces.
A mosaic of Chu spaces and Channel Theory I: Category-theoretic concepts and tools
Published in Journal of Experimental & Theoretical Artificial Intelligence, 2019
Chris Fields, James F. Glazebrook
Simplicial complexes over an information space provide the structure needed to define an information geometry. To each simplicial complex is associated the polyhedron or geometric realisation of , denoted , formed from the set of all functions satisfying: if , then the set is a simplex of ;.