From Euclidean to Riemannian Means Information Geometry for SSVEP Classification

28/10/2015
Publication GSI2015
OAI : oai:www.see.asso.fr:11784:14265

Résumé

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.

From Euclidean to Riemannian Means Information Geometry for SSVEP Classification

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application/pdf From Euclidean to Riemannian Means Information Geometry for SSVEP Classification Emmanuel Kalunga, Sylvain Chevallier, Quentin Barthélemy, Karim Djouani, Yskandar Hamam, Eric Monacelli

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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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From Euclidean to Riemannian Means: Information Geometry for SSVEP Classification Emmanuel K. Kalunga, Sylvain Chevallier, Quentin Barthélemy et al. F’SATI - Tshawne University of Technology (South Africa) LISV - Université de Versailles Saint-Quentin (France) Mensia Technologies (France) sylvain.chevallier@uvsq.fr 28 October 2015 Brain-Computer Interfaces Spatial covariance matrices for BCI Experimental assessment of distances Cerebral interfaces Context Rehabilitation and disability compensation ) Out-of-the-lab solutions ) Open to a wider population Problem Intra-subject variabilities ) Online methods, adaptative algorithms Inter-subject variabilities ) Good generalization, fast convergence Opportunities New generation of BCI (Congedo & Barachant) • Growing interest in EEG community • Large community, available datasets • Challenging situations and problems S. Chevallier 28/10/2015 GSI 2 / 19 Brain-Computer Interfaces Spatial covariance matrices for BCI Experimental assessment of distances Outline Brain-Computer Interfaces Spatial covariance matrices for BCI Experimental assessment of distances S. Chevallier 28/10/2015 GSI 3 / 19 Brain-Computer Interfaces Spatial covariance matrices for BCI Experimental assessment of distances Interaction based on brain activity Brain-Computer Interface (BCI) for non-muscular communication • Medical applications • Possible applications for wider population Recording at what scale ? • Neuron !LFP • Neuronal group !ECoG !SEEG • Brain !EEG !MEG !IRMf !TEP S. Chevallier 28/10/2015 GSI 4 / 19 Brain-Computer Interfaces Spatial covariance matrices for BCI Experimental assessment of distances Interaction loop BCI loop 1 Acquisition 2 Preprocessing 3 Translation 4 User feedback S. Chevallier 28/10/2015 GSI 5 / 19 Brain-Computer Interfaces Spatial covariance matrices for BCI Experimental assessment of distances Electroencephalography Most BCI rely on EEG ) Efficient to capture brain waves • Lightweight system • Low cost • Mature technologies • High temporal resolution • No trepanation S. Chevallier 28/10/2015 GSI 6 / 19 Brain-Computer Interfaces Spatial covariance matrices for BCI Experimental assessment of distances Origins of EEG • Local field potentials • Electric potential difference between dendrite and soma • Maxwell’s equation • Quasi-static approximation • Volume conduction effect • Sensitive to conductivity of brain skull • Sensitive to tissue anisotropies S. Chevallier 28/10/2015 GSI 7 / 19 Brain-Computer Interfaces Spatial covariance matrices for BCI Experimental assessment of distances Experimental paradigms Different brain signals for BCI : • Motor imagery : (de)synchronization in premotor cortex • Evoked responses : low amplitude potentials induced by stimulus Steady-State Visually Evoked Potentials 8 electrodes in occipital region SSVEP stimulation LEDs 13 Hz 17 Hz 21 Hz • Neural synchronization with visual stimulation • No learning required, based on visual attention • Strong induced activation S. Chevallier 28/10/2015 GSI 8 / 19 Brain-Computer Interfaces Spatial covariance matrices for BCI Experimental assessment of distances BCI Challenges Limitations • Data scarsity ) A few sources are non-linearly mixed on all electrodes • Individual variabilities ) Effect of mental fatigue • Inter-session variabilities ) Electronic impedances, localizations of electrodes • Inter-individual variabilities ) State of the art approaches fail with 20% of subjects Desired properties : • Online systems ) Continously adapt to the user’s variations • No calibration phase ) Non negligible cognitive load, raises fatigue • Generic model classifiers and transfert learning ) Use data from one subject to enhance the results for another S. Chevallier 28/10/2015 GSI 9 / 19 Brain-Computer Interfaces Spatial covariance matrices for BCI Experimental assessment of distances Spatial covariance matrices Common approach : spatial filtering • Efficient on clean datasets • Specific to each user and session ) Require user calibration • Two step training with feature selection ) Overfitting risk, curse of dimensionality Working with covariance matrices • Good generalization across subjects • Fast convergence • Existing online algorithms • Efficient implementations S. Chevallier 28/10/2015 GSI 10 / 19 Brain-Computer Interfaces Spatial covariance matrices for BCI Experimental assessment of distances Covariance matrices for EEG • An EEG trial : X 2 RC⇥N , C electrodes, N time samples • Assuming that X ⇠ N(0, ⌃) • Covariance matrices ⌃ belong to MC = ⌃ 2 RC⇥C : ⌃ = ⌃| and x| ⌃x > 0, 8x 2 RC \0 • Mean of the set {⌃i }i=1,...,I is ¯⌃ = argmin⌃2MC PI i=1 dm (⌃i , ⌃) • Each EEG class is represented by its mean • Classification based on those means • How to obtain a robust and efficient algorithm ? Congedo, 2013 S. Chevallier 28/10/2015 GSI 11 / 19 Brain-Computer Interfaces Spatial covariance matrices for BCI Experimental assessment of distances Minimum distance to Riemannian mean Simple and robust classifier • Compute the center ⌃ (k) E of each of the K classes • Assign a given unlabelled ˆ⌃ to the closest class k⇤ = argmin k (ˆ⌃, ⌃ (k) E ) Trajectories on tangent space at mean of all trials ¯⌃µ −4 −2 0 2 4 −4 −2 0 2 4 6 Resting class 13Hz class 21Hz class 17Hz class Delay S. Chevallier 28/10/2015 GSI 12 / 19 Brain-Computer Interfaces Spatial covariance matrices for BCI Experimental assessment of distances Riemannian potato Removing outliers and artifacts Reject any ⌃i that lies too far from the mean of all trials ¯⌃µ z( i ) = i µ > zth , i is d(⌃i , ¯⌃), µ and are the mean and standard deviation of distances { i } I i=1 Raw matrices Riemannian potato filtering S. Chevallier 28/10/2015 GSI 13 / 19 Brain-Computer Interfaces Spatial covariance matrices for BCI Experimental assessment of distances Covariance matrices for EEG-based BCI Riemannian approaches in BCI : • Achieve state of the art results ! performing like spatial filtering or sensor-space methods • Rely on simpler algorithms ! less error-prone, computationally efficient What are the reason of this success ? • Invariances embedded with Riemannian distances ! invariance to rescaling, normalization, whitening ! invariance to electrode permutation or positionning • Equivalent to working in an optimal source space ! spatial filtering are sensitive to outliers and user-specific ! no question on "sensors or sources" methods ) What are the most desirable invariances for EEG ? S. Chevallier 28/10/2015 GSI 14 / 19 Brain-Computer Interfaces Spatial covariance matrices for BCI Experimental assessment of distances Considered distances and divergences Euclidean dE(⌃1, ⌃2) = k⌃1 ⌃2kF Log-Euclidean dLE(⌃1, ⌃2) = klog(⌃1) log(⌃2)kF V. Arsigny et al., 2006, 2007 Affine-invariant dAI(⌃1, ⌃2) = klog(⌃ 1 1 ⌃2)kF T. Fletcher & S. Joshi, 2004 , M. Moakher, 2005 ↵-divergence d↵ D(⌃1, ⌃2) 1<↵<1 = 4 1 ↵2 log det( 1 ↵ 2 ⌃1+ 1+↵ 2 ⌃2) det(⌃1) 1 ↵ 2 det(⌃2) 1+↵ 2 Z. Chebbi & M. Moakher, 2012 Bhattacharyya dB(⌃1, ⌃2) = ⇣ log det 1 2 (⌃1+⌃2) (det(⌃1) det(⌃2))1/2 ⌘1/2 Z. Chebbi & M. Moakher, 2012 S. Chevallier 28/10/2015 GSI 15 / 19 Brain-Computer Interfaces Spatial covariance matrices for BCI Experimental assessment of distances Experimental results • Euclidean distances yield the lowest results ! Usually attributed to the invariance under inversion that is not guaranteed ! Displays swelling effect • Riemannian approaches outperform state-of-the-art methods (CCA+SVM) • ↵-divergence shows the best performances ! but requires a costly optimisation to find the best ↵ value • Bhattacharyya has the lowest computational cost and a good accuracy −1 −0.5 0 0.5 1 20 30 40 50 60 70 80 90 Accuracy(%) Alpha values (α) −1 −0.5 0 0.5 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 CPUtime(s) S. Chevallier 28/10/2015 GSI 16 / 19 Brain-Computer Interfaces Spatial covariance matrices for BCI Experimental assessment of distances Conclusion Working with covariance matrices in BCI • Achieves very good results • Simple algorithms work well : MDM, Riemannian potato • Need for robust and online methods Interesting applications for IG : • Many freely available datasets • Several competitions • Many open source toolboxes for manipulating EEG Several open questions : • Handling electrodes misplacements and others artifacts • Missing data and covariance matrices of lower rank • Inter- and intra-individual variabilities S. Chevallier 28/10/2015 GSI 17 / 19 Brain-Computer Interfaces Spatial covariance matrices for BCI Experimental assessment of distances Thank you ! S. Chevallier 28/10/2015 GSI 18 / 19 Brain-Computer Interfaces Spatial covariance matrices for BCI Experimental assessment of distances Interaction loop BCI loop 1 Acquisition 2 Preprocessing 3 Translation 4 User feedback First systems in early ’70 S. Chevallier 28/10/2015 GSI 19 / 19