Mixture Models for Multidimensional Positive Data Clustering with Applications to Image Categorization and Retrieval

Model-based approaches have become important tools to model data and infer knowledge. Such approaches are often used for clustering and object recognition which are crucial steps in many applications, including but not limited to, recommendation systems, search engines, cyber security, surveillance and object tracking. Many of these applications have the urgent need to reduce the semantic gap of data representation between the system level and the human being understandable level. Indeed, the low level features extracted to represent a given object can be confusing to machines which cannot differentiate between very similar objects trivially distinguishable by human beings (e.g. apple vs tomato). Such a semantic gap between the system and the user perception for data, makes the modeling process hard to be designed basing on the features space only. Moreover those models should be flexible and updatable when new data are introduced to the system. Thus, apart from estimating the model parameters, the system should be somehow informed how new data should be perceived according to some criteria in order to establish model updates. In this thesis we propose a methodology for data representation using a hierarchical mixture model basing on the inverted Dirichlet and the generalized inverted Dirichlet distributions. The proposed approach allows to model a given object class by a set of components deduced by the system and grouped according to labeled training data representing the human level semantic. We propose an update strategy to the system components that takes into account adjustable metrics representing users perception. We also consider the "page zero" problem in image retrieval systems when a given user does not possess adequate tools and semantics to express what he/she is looking for, while he/she can visually identify it. We propose a statistical framework that enables users to start a search process and interact with the system in order to find their target "mental image". Finally we propose to improve our models by using a variational Bayesian inference to learn generalized inverted Dirichlet mixtures with features selection. The merit of our approaches is evaluated using extensive simulations and real life applications

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