Abstract
Brain Computer Interfaces (BCI) based on electroencephalography (EEG) rely on multichannel brain signal processing. Most of the state-of-the-art approaches deal with covariance matrices, and indeed Riemannian geometry has provided a substantial framework for developing new algorithms. Most notably, a straightforward algorithm such as Minimum Distance to Mean yields competitive results when applied with a Riemannian distance. This applicative contribution aims at assessing the impact of several distances on real EEG dataset, as the invariances embedded in those distances have an influence on the classification accuracy. Euclidean and Riemannian distances and means are compared both in term of quality of results and of computational load.
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References
Amari, S.I.: \(\alpha \)-divergence is unique, belonging to both \(f\)-divergence and Bregman divergence classes. IEEE Trans. Inf. Theor. 55(11), 4925–4931 (2009)
Arsigny, V., Fillard, P., Pennec, X., Ayache, N.: Log-Euclidean metrics for fast and simple calculus on diffusion tensors. Magn. Reson. Med. 56(2), 411–421 (2006)
Arsigny, V., Fillard, P., Pennec, X., Ayache, N.: Geometric means in a novel vector space structure on symmetric positive-definite matrices. SIAM J. Matrix Anal. Appl. 29(1), 328–347 (2007)
Barachant, A., Andreev, A., Congedo, M., et al.: The Riemannian potato: an automatic and adaptive artifact detection method for online experiments using Riemannian geometry. In: Proceedings of TOBI Workshop IV, pp. 19–20 (2013)
Barachant, A., Bonnet, S., Congedo, M., Jutten, C.: Multiclass brain-computer interface classification by Riemannian geometry. IEEE Trans. Biomed. Eng. 59(4), 920–928 (2012)
Chebbi, Z., Moakher, M.: Means of Hermitian positive-definite matrices based on the log-determinant \(\alpha \)-divergence function. Linear Algebra Appl. 436(7), 1872–1889 (2012)
Congedo, M., Barachant, A., Andreev, A.: A new generation of brain-computer interface based on Riemannian geometry. arXiv preprint arXiv:1310.8115 (2013)
Fletcher, P.T., Joshi, S.: Principal geodesic analysis on symmetric spaces: statistics of diffusion tensors. In: Sonka, M., Kakadiaris, I.A., Kybic, J. (eds.) CVAMIA/MMBIA 2004. LNCS, vol. 3117, pp. 87–98. Springer, Heidelberg (2004)
Hastie, T., Tibshirani, R., Friedman, J., Hastie, T., Friedman, J., Tibshirani, R.: The Elements of Statistical Learning, vol. 2. Springer, New York (2009)
Johannes, M.G., Pfurtscheller, G., Flyvbjerg, H.: Designing optimal spatial filters for single-trial EEG classification in a movement task. Clin. Neurophysiol. 110(5), 787–798 (1999)
Kalunga, E.K., Chevallier, S., Rabreau, O., Monacelli, E.: Hybrid interface: integrating BCI in multimodal human-machine interfaces. In: 2014 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM), pp. 530–535. IEEE (2014)
Kalunga, E.K., Djouani, K., Hamam, Y., Chevallier, S., Monacelli, E.: SSVEP enhancement based on canonical correlation analysis to improve BCI performances. In: AFRICON 2013, pp. 1–5. IEEE (2013)
Lotte, F., Guan, C.: Regularizing common spatial patterns to improve BCI designs: unified theory and new algorithms. IEEE Trans. Biomed. Eng. 58(2), 355–362 (2011)
Moakher, M.: A differential geometric approach to the geometric mean of symmetric positive-definite matrices. SIAM J. Matrix Anal. Appl. 26(3), 735–747 (2005)
Niedermeyer, E., da Silva, F.L.: Electroencephalography: Basic Principles, Clinical Applications, and Related Fields, 5th edn. Lippincott Williams & Wilkins, Baltimore (2004)
Nielsen, F., Bhatia, R.: Matrix Information Geometry. Springer Publishing Company Incorporated, Heidelberg (2012)
Rivet, B., Souloumiac, A., Attina, V., Gibert, G.: xDAWN algorithm to enhance evoked potentials: application to brain-computer interface. IEEE Trans. Biomed. Eng. 56(8), 2035–2043 (2009)
Schäfer, J., Strimmer, K.: A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Stat. Appl. Genet. Mol. Biol. 4(1) (2005)
Tomioka, R., Aihara, K., Müller, K.R.: Logistic regression for single trial EEG classification. In: NIPS, vol. 19, pp. 1377–1384 (2007)
Wang, S., James, C.J.: Enhancing evoked responses for BCI through advanced ICA techniques. In: MEDSIP, pp. 1–4 (2006)
Yger, F.: A review of kernels on covariance matrices for BCI applications. In: 2013 IEEE International Workshop on Machine Learning for Signal Processing (MLSP), pp. 1–6. IEEE (2013)
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Kalunga, E.K., Chevallier, S., Barthélemy, Q., Djouani, K., Hamam, Y., Monacelli, E. (2015). From Euclidean to Riemannian Means: Information Geometry for SSVEP Classification . In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_64
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DOI: https://doi.org/10.1007/978-3-319-25040-3_64
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