Methods for Single Trial Analysis of Asynchronous EEG Patterns

Processing of electroencephalographic (EEG) signals has mostly focused on analysing correlates that are time-locked to an observable event. However, when the signal is acquired in less controlled environment, like in the context of a brain-computer interface operating in the real-world, this synchronous nature does not hold any longer. The analysis of such signal requires the design of methods that rely less on time-locked nature. These methods are also the requirements for study endogenous processes for which the ground truth of when the process take place in time is not available. In this thesis, we present methods to analyse brain signals, EEG in particular, that are not time-locked to observable events. This thesis documents three major contributions : (i) it proposes a Bayesian formalism to the problem of asynchronous EEG pattern classification, (ii) it shows the importance of generative models to achieve this task and (iii) it shows that such methods can be used to gather information and classify the EEG correlates of decision-making process while classical methods fail at it. First, we propose methods to handle non-time-locked EEG patterns by making the hypothesis that, in each trial, only a part of the signal contains the relevant pattern of interest. This relevant part can appear at any time in the analysis window and differently for each trial. The rest of the trial corresponds to a non-informative part irrelevant to the targeted cognitive task. Starting from a discriminant asynchronous approach handling independently the time-samples in the trial, we extend this method to a generative Bayesian model where each part is formally modelled. This is a main difference compared to the classical approach which usually try to avoid to model the non-informative part. Then, making the assumption that the informative part can be modelled by a time sequence, we adapt the previous method to a Bayesian model of asynchronous template matching which allows the recognition of the time onset of the pattern of interest in each trial. Second, we show the importance of the generative model which, thanks to the Bayesian approach allows us to alleviate the problem of choosing of the hyperparameters of the initial discriminative approach. Compared to the initial discriminant model, us- ing a generative approach leads to use more parameters into the model but whose estimation is helped by the prior we provide. By doing so, we provide a more intuitive way for the experimenter to adapt the method to other problems. Using a generative model and a Bayesian estimation also enables us to improve the generalisation of the model of asynchronous template matching. This model has indeed been tested as benchmark on jittered evoked potential data and has shown to successfully improve the signal-to-noise ratio, recover the evoked response and classify better than classical methods. Finally, we see the importance of asynchronous methods for classification of the EEG correlates of decision-making process. We test this in the context of the study of the exploration/exploitation contrast. Exploration is related to decision making in an uncertain environment. This situation arises a conflict between two opposing needs : gathering information about the environment and exploiting this knowledge in order to optimise the decision. Using an experimental setup that forces the subjects to switch between exploratory or exploitative actions, we show for the first time that it is possible to classify the EEG correlates of the exploratory behaviour. Moreover, we show that synchronous methods fail at classify this contrast thus requiring advanced asynchronous ones. The results also confirm that the brain areas relevant to this switch are mainly the left parietal and medial frontal cortex which is consistent with the neurophysiological findings based on functional magnetic resonance imagery. In addition we have been able to show the importance of alpha rhythm for this contrast. In summary, this thesis provides a formal framework for classification of asynchronous EEG patterns using a generative Bayesian approach. It also provides a methodology to approach the study of EEG correlates of cognitive tasks when little is known about them and when the targeted pattern is reasonably assumed to be non time-locked.

The timing of exploratory decision-making revealed by single-trial topographic EEG analyses

Nicolas Bourdaud, Ricardo Andres Chavarriaga Lozano, Micah Murray, Athina Tzovara

Decision-making in an uncertain environment is driven by two major needs: exploring the environment to gather information or exploiting acquired knowledge to maximize reward. The neural processes underlying exploratory decision-making have been mainly studied by means of functional magnetic resonance imaging, overlooking any information about the time when decisions are made. Here, we carried out an electroencephalography (EEG) experiment, in order to detect the time when the brain generators responsible for these decisions have been sufficiently activated to lead to the next decision. Our analyses, based on a classification scheme, extract time-unlocked voltage topographies during reward presentation and use them to predict the type of decisions made on the subsequent trial. Classification accuracy, measured as the area under the Receiver Operator's Characteristic curve was on average 0.65 across 7 subjects. Classification accuracy was above chance levels already after 516 ms on average, across subjects. We speculate that decisions were already made before this critical period, as confirmed by a positive correlation with reaction times across subjects. On an individual subject basis, distributed source estimations were performed on the extracted topographies to statistically evaluate the neural correlates of decision-making. For trials leading to exploration, there was significantly higher activity in dorsolateral prefrontal cortex and the right supramarginal gyrus; areas responsible for modulating behavior under risk and deduction. No area was more active during exploitation. We show for the first time the temporal evolution of differential patterns of brain activation in an exploratory decision-making task on a single-trial basis.

Elsevier2012

Prior knowledge in Kernel methods

Alexei Pozdnoukhov

Machine Learning is a modern and actively developing field of computer science, devoted to extracting and estimating dependencies from empirical data. It combines such fields as statistics, optimization theory and artificial intelligence. In practical tasks, the general aim of Machine Learning is to construct algorithms able to generalize and predict in previously unseen situations based on some set of examples. Given some finite information, Machine Learning provides ways to exract knowledge, describe, explain and predict from data. Kernel Methods are one of the most successful branches of Machine Learning. They allow applying linear algorithms with well-founded properties such as generalization ability, to non-linear real-life problems. Support Vector Machine is a well-known example of a kernel method, which has found a wide range of applications in data analysis nowadays. In many practical applications, some additional prior knowledge is often available. This can be the knowledge about the data domain, invariant transformations, inner geometrical structures in data, some properties of the underlying process, etc. If used smartly, this information can provide significant improvement to any data processing algorithm. Thus, it is important to develop methods for incorporating prior knowledge into data-dependent models. The main objective of this thesis is to investigate approaches towards learning with kernel methods using prior knowledge. Invariant learning with kernel methods is considered in more details. In the first part of the thesis, kernels are developed which incorporate prior knowledge on invariant transformations. They apply when the desired transformation produce an object around every example, assuming that all points in the given object share the same class. Different types of objects, including hard geometrical objects and distributions are considered. These kernels were then applied for images classification with Support Vector Machines. Next, algorithms which specifically include prior knowledge are considered. An algorithm which linearly classifies distributions by their domain was developed. It is constructed such that it allows to apply kernels to solve non-linear tasks. Thus, it combines the discriminative power of support vector machines and the well-developed framework of generative models. It can be applied to a number of real-life tasks which include data represented as distributions. In the last part of the thesis, the use of unlabelled data as a source of prior knowledge is considered. The technique of modelling the unlabelled data with a graph is taken as a baseline from semi-supervised manifold learning. For classification problems, we use this apporach for building graph models of invariant manifolds. For regression problems, we use unlabelled data to take into account the inner geometry of the input space. To conclude, in this thesis we developed a number of approaches for incorporating some prior knowledge into kernel methods. We proposed invariant kernels for existing algorithms, developed new algorithms and adapted a technique taken from semi-supervised learning for invariant learning. In all these cases, links with related state-of-the-art approaches were investigated. Several illustrative experiments were carried out on real data on optical character recognition, face image classification, brain-computer interfaces, and a number of benchmark and synthetic datasets.

EPFL2006

Prior Knowledge in Kernel Methods

Alexei Pozdnoukhov

École Polytechnique Fédérale de Lausanne2006

Prior knowledge in Kernel methods

Alexei Pozdnoukhov

EPFL2006

Prior Knowledge in Kernel Methods

Alexei Pozdnoukhov

École Polytechnique Fédérale de Lausanne2006