Inductive means and sequences applied to online classi cation of EEG

07/11/2017
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The translation of brain activity into user command, through Brain-Computer Interfaces (BCI), is a very active topic in machine learning and signal processing. As commercial applications and out-of-the-lab solutions are proposed, there is an increased pressure to provide online algorithms and real-time implementations. Electroencephalography (EEG) systems o er lightweight and wearable solutions, at the expense of signal quality. Approaches based on covariance matrices have demonstrated good robustness to noise and provide a suitable representation for classi cation tasks, relying on advances in Riemannian geometry. We propose to equip the minimum distance to mean (MDM) classi er with a new family of means, based on the inductive mean, for block-online classi cation tasks and to embed the inductive mean in an incremental learning algorithm for online classi cation of EEG.

Inductive means and sequences applied to online classication of EEG

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application/pdf Inductive means and sequences applied to online classi cation of EEG Estelle Massart, Sylvain Chevallier
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The translation of brain activity into user command, through Brain-Computer Interfaces (BCI), is a very active topic in machine learning and signal processing. As commercial applications and out-of-the-lab solutions are proposed, there is an increased pressure to provide online algorithms and real-time implementations. Electroencephalography (EEG) systems o er lightweight and wearable solutions, at the expense of signal quality. Approaches based on covariance matrices have demonstrated good robustness to noise and provide a suitable representation for classi cation tasks, relying on advances in Riemannian geometry. We propose to equip the minimum distance to mean (MDM) classi er with a new family of means, based on the inductive mean, for block-online classi cation tasks and to embed the inductive mean in an incremental learning algorithm for online classi cation of EEG.
Inductive means and sequences applied to online classication of EEG
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Inductive means and sequences applied to online classification of EEG Estelle M. Massart1 , Sylvain Chevallier2 1 ICTEAM Institute, Université catholique de Louvain, Belgium 2 LISV, Université de Versailles Saint-Quentin, France Abstract. The translation of brain activity into user command, through Brain-Computer Interfaces (BCI), is a very active topic in machine learn- ing and signal processing. As commercial applications and out-of-the-lab solutions are proposed, there is an increased pressure to provide on- line algorithms and real-time implementations. Electroencephalography (EEG) systems offer lightweight and wearable solutions, at the expense of signal quality. Approaches based on covariance matrices have demon- strated good robustness to noise and provide a suitable representation for classification tasks, relying on advances in Riemannian geometry. We propose to equip the minimum distance to mean (MDM) classifier with a new family of means, based on the inductive mean, for block-online classification tasks and to embed the inductive mean in an incremental learning algorithm for online classification of EEG. 1 Introduction Real-time recording and decoding of brain signals allow to control a large va- riety of systems, such as wheelchairs, exoskeletons, robotic arms or other types of Brain-Computer Interface (BCI) devices [3]. With electroencephalography (EEG), the brain signal is recorded at the surface of the head (on the scalp), offering a simple setup that does not require surgery as it is the case for invasive recording methods. The signal quality of EEG is lower than with invasive meth- ods and the recording is very sensitive to noise, nonetheless possible applications offer promising results [11]. As technologies and signal processing techniques are more and more mature, out-of-the-lab applications and commercial systems are the focus of growing interests [3]. These applications and systems rely on a small number of electrodes for recording and low-cost hardware for signal processing. Thus the denoising and classification algorithms should work online and with a reasonable computational load. One of the most challenging issues with EEG- based BCI is to harness the individual variability of brain signals, which could change from hour-to-hour for a user and are highly variable from one user to the other. Among all the methods considered in the literature for EEG signal process- ing, the ones relying on covariance matrices were shown numerically to achieve good performances [12]. In this approach, a portion of the EEG signal is repre- sented by a covariance matrix, whose elements correspond to the covariance of 2 Estelle M. Massart, Sylvain Chevallier the signals recorded with different electrodes, possibly filtered around different frequencies. The fact that covariance matrices belong to a non-Euclidean space – the manifold of symmetric positive definite (SPD) matrices – calls for efficient classifiers adapted to that geometry. In this paper, we work with the Minimum Distance to Mean (MDM) clas- sifier, initially proposed in [2]. This classifier assigns covariance matrices to the class with the closest mean. The classification results were shown to depend heavily on the mean and distance definition used, and many possibilities were compared in [5]. In the following we will distinguish the offline setting, where the classifier’s parameters are selected and evaluated using all available data, the block-online setting, where the classifier is parametrized on a first batch of data (usually the beginning of a session) and evaluated on another batch of data (the rest of the session), and the online setting, where there is no data available beforehand from the user and the classifier is assessed directly on new data. We equip here this classifier with a new family of means based on the so-called in- ductive mean, which has the main advantage of being computed incrementally, a key property when working in an online setting. This property was already used in [4] for k-means clustering. We show numerically that the use of these new means achieves a classification accuracy in a block-online framework com- parable to the most accurate nonparametric mean: the Riemannian barycenter with respect to the affine-invariant metric (less than 1% of difference on aver- age), while their computation cost is lower. We also propose a variant of the online classification algorithm proposed in [6]. In our algorithm, the means of the classes are adapted online, following an incremental learning scheme. Start- ing from classes learned with other users, the goal is to enable the algorithm to progressively fit with the observed data of a new user. The paper is organized as follows. Section 2 is devoted to block-online classi- fication: we define the MDM classifier and the family of means we use, and com- pare numerically the classification results with other state-of-the-art methods. In Section 3, we present our incremental learning algorithm for online classification. 2 Offline and block-online classification of EEG The proposed approaches are applied on steady-state visual evoked potentials (SSVEP), that is brain responses to visual stimuli, but are valid on other kinds of BCI stimuli. In a SSVEP experiment, blinking LEDs are placed at different locations in the visual field of a user. The LEDs are blinking at F different frequencies (freq1, . . . , freqF ). The subject is either asked to focus on one specific blinking LED (with a known frequency) or to focus on a location without LED (resting state). The blinking LED elicit induced oscillations in the brain, which are visible in the EEG. The goal is to determine based on the EEG if the user is focusing on a blinking LED and if so, on which one. We summarize in Algorithm 1 the block-online classification method pro- posed in [5]. Each time that the user is asked to focus on a stimulus, the portion of the EEG recording following the cue onset (the time at which the user was Inductive means and sequences applied to online... 3 instructed to focus on the blinking LED) is first transformed into a covariance matrix and then classified using the MDM classifier. The means of the classes are estimated beforehand, based on a collection of labelled data, according to the offline training scheme detailed in Algorithm 2. Algorithm 1 Block-online classification - MDM algorithm Inputs: Σ̄(k) , the mean of the class k, for k = 1, . . . , K (obtained using Algo- rithm 2) and an unlabelled EEG trial X ∈ RC×N (with C the number of electrodes and N the number of time samples). Output: k̂, the predicted label of X. 1: Compute Σ̂, an estimate of the covariance matrix of X (see Section 2.1). 2: Define the class label associated to trial X as k̂