On Riemannian tools for classification improvement in Brain-Computer Interfaces

Abstract

A Brain Computer Interface (BCI) or Brain Machine Interface (BMI) is a device that allows the exchange of information between the brain of a person and a computer without the need of physical interaction. This technology promises to change the way in which we interact with machines, but it is not yet affordable, robust or quick enough to substitute other classic human to machine interfaces for the general public. This being said, the lack of need of interaction makes them a very promising solution that would provide people with severe motor disabilities with a new way of interacting with their surroundings, improving their quality of life. The most extended method of extracting information about brain activity and the one used for this project is the Electroencefalogram (EEG). This device consists of multiple electrodes mounted on a helmet-like structure that is placed on the user’s scalp. The electrodes detect the sum of action potentials from large populations of neurons on the brain’s cortex. The main advantages of this technique are the relative low cost of the device, portability, and the high temporal resolution and ease of use of a non invasive technique. This is not free of disadvantages, as the method suffers from a low signal to noise ratio, low robustness to interference, low spatial resolution and the effects of inter and intra session drift, that is, the movement of the electrodes during and between sessions produce variations on the acquisition of the signal. There are also multiple paradigms in the field of BCI, each one of them focusing on a different brain signal. This work is centered around the Motor Imagery Brain Computer Interface (MI-BCI), which differs from other BCIs in the fact that it directly decodes the intention of the user without the need of inducing a specific response in the brain by presenting an stimulus. This approach is considered to be more natural and can be more comfortable, but also requires a higher level of mental effort and proficiency from part of the user. The MI-BCI is based on a signal of unknown origin that is produced on the sensorymotor cortex, responsible for voluntary movements and touch among others, the Sensorimotor Rhythms (SMR). This signal is atenuated when the person performs or thinks about performing a movement, which is called an Event Related Desynchronization (ERD) and amplified when going back to the idling state, an Event Related Synchronization (ERS). As the brain is a distributed system, the origin of these events can be estimated and is related to the movement that the person imagined. In an implementation, these movements are limited to a discrete set of posibilities and each one is mapped to a computer instruction, allowing the unidirectional transfer of information between brain and machine. The classical machine learning approach to this problem has been to use very specific signal processing techniques to extract relevant features for this problem that can then be fed to a general classification algorithm. The main tecnique is known as Common Spatial Patterns (CSP) followed by classification with Linear Discriminant Analysis (LDA) or Support Vector Machine (SVM). This has some advantages such as a relative low requirement of training samples, but also lacks the capability of generalisation, and a system fine tuned for one user cannot be used for other users or even for another session from the same user reliably. In this work we study an alternative framework that uses the covariance matrices of the EEG signals as observations and exploits the Riemannian geometry of Symmetric Positive Definite (SPD) matrices to classify them in their natural space. This is not only a more general signal processing approach that has been used in other fields of research, but also opens the possibility of transfering some information between users and sessions, which may result in a more robust system or in a system that requires less data for training. This is crucial for the usability of MI-BCI because recording a training session before each use of the system is mentally exhausting and time consuming.