Mixing and non-mixing local minima of the entropy contrast for blind source separation

In this paper, both non-mixing and mixing local minima of the entropy are analyzed from the viewpoint of blind source separation (BSS); they correspond respectively to acceptable and spurious solutions of the BSS problem. The contribution of this work is twofold. First, a Taylor development is used to show that the \textit{exact} output entropy cost function has a non-mixing minimum when this output is proportional to \textit{any} of the non-Gaussian sources, and not only when the output is proportional to the lowest entropic source. Second, in order to prove that mixing entropy minima exist when the source densities are strongly multimodal, an entropy approximator is proposed. The latter has the major advantage that an error bound can be provided. Even if this approximator (and the associated bound) is used here in the BSS context, it can be applied for estimating the entropy of any random variable with multimodal density.Comment: 11 pages, 6 figures, To appear in IEEE Transactions on Information Theor

On the conditions for valid objective functions in blind separation of independent and dependent sources

It is well known that independent sources can be blindly detected and separated, one by one, from linear mixtures by identifying local extrema of certain objective functions (contrasts), like negentropy, Non-Gaussianity measures, kurtosis, etc. It was also suggested in [1], and verified in practice in [2,4], that some of these measures remain useful for particular cases with dependent sources, but not much work has been done in this respect and a rigorous theoretical ground still lacks. In this paper, it is shown that, if a specific type of pairwise dependence among sources exists, called Linear Conditional Expectation (LCE) law, then a family of objective functions are valid for their separation. Interestingly, this particular type of dependence arises in modeling material abundances in the spectral unmixing problem of remote sensed images. In this work, a theoretical novel approach is used to analyze Shannon entropy (SE), Non-Gaussianity (NG) measure and absolute moments of arbitrarily order, i.e. Generic Absolute (GA) moments for the separation of sources allowing them to be dependent. We provide theoretical results that show the conditions under which sources are isolated by searching for a maximum or a minimum. Also, simple and efficient algorithms based on Parzen windows estimations of probability density functions (pdfs) and Newton-Raphson iterations are proposed for the separation of dependent or independent sources. A set of simulation results on synthetic data and an application to the blind spectral unmixing problem are provided in order to validate our theoretical results and compare these algorithms against FastICA and a very recently proposed algorithm for dependent sources, the Bounded Component Analysis algorithm (BCA). It is shown that, for dependent sources verifying the LCE law, the NG measure provides the best separation results.Fil: Caiafa, Cesar Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto Argentino de Radioastronomia (i); Argentina. Universidad de Buenos Aires. Facultad de Ingeniería; Argentin

Redundancy reduction for computational audition, a unifying approach

Thesis (Ph.D.)--Massachusetts Institute of Technology, School of Architecture and Planning, Program in Media Arts and Sciences, 2001.Includes bibliographical references (p. 113-120).Computational audition has always been a subject of multiple theories. Unfortunately very few place audition in the grander scheme of perception, and even fewer facilitate formal and robust definitions as well as efficient implementations. In our work we set forth to address these issues. We present mathematical principles that unify the objectives of lower level listening functions, in an attempt to formulate a global and plausible theory of computational audition. Using tools to perform redundancy reduction, and adhering to theories of its incorporation in a perceptual framework, we pursue results that support our approach. Our experiments focus on three major auditory functions, preprocessing, grouping and scene analysis. For auditory preprocessing, we prove that it is possible to evolve cochlear-like filters by adaptation to natural sounds. Following that and using the same principles as in preprocessing, we present a treatment that collapses the heuristic set of the gestalt auditory grouping rules, down to one efficient and formal rule. We successfully apply the same elements once again to form an auditory scene analysis foundation, capable of detection, autonomous feature extraction, and separation of sources in real-world complex scenes. Our treatment was designed in such a manner so as to be independent of parameter estimations and data representations specific to the auditory domain. Some of our experiments have been replicated in other domains of perception, providing equally satisfying results, and a potential for defining global ground rules for computational perception, even outside the realm of our five senses.Paris Smaragdis.Ph.D

Analyse en Composantes Indépendantes Multidimensionnelles via des cumulants d’ordres variés

The author deals with the problem of multidimensional independent component analysis (MICA) which is the natural generalization of the ordinary problem of independent component analysis (ICA). First, in order to facilitate the use of higher-order cumulants, we present new formulas for the cumulant matrices of a real random vector from its moment matrices. In addition to the usual matrix operations, these formulas use only the Kronecker product, the vec operator and some commutation matrices. These formulas lend themselves to examine more closely the specific structures of cumulant matrices and provide results on the ranks of these matrices that characterize the dependence between random variables composing the random vector. The main practical interest of our matrix formulas lies in much easier cumulant evaluation and faster computation than the conventional method based on repeated use of the Leonov and Shiryaev formulas. In the second part of this thesis, we show that under the usual assumptions of the independent multidimensional component analysis, contracted cumulant matrices at any statistical order are all block diagonalizable in the same basis. We derive an algorithm for solving MICA by block diagonalization and compare the results obtained to the orders 3-6, between them and with other methods, on several synthetic signals. Simple examples are developed to justify the need to combine different levels to ensure the best separation. We also prove that the easiest case to deal with is the case of mixtures of sources that have different dimensions. In the last part of this thesis we propose a set of methods that operate only the higher- order statistics. Under certain additional assumptions, these methods are shown to completely solve the noisy MICA problem without second-order whitening by joint block diagonalization of a cumulant matrices set coming from statistics of orders strictly higher than four. A comparison with the second-order based whitening MICA methods for the separation of fetal and maternal electrical activities (measured using three electrodes placed on the mother’s abdomen) shows that this new family is better suited to this application : it allow an almost perfect separation of these two contributions.L’auteur s’intéresse au problème de l’analyse en composantes indépendantes multidimensionnelles (ACIM) qui est la généralisation naturelle du problème ordinaire de l’analyse en composantes indépendantes (ACI). Tout d’abord, afin de faciliter l’utilisation des cumulants des ordres supérieurs, nous présentons de nou- velles formules pour le calcul matriciel des matrices de cumulants d’un vecteur aléatoire réel à partir de ses matrices de moments. Outre les opérations matricielles usuelles, ces formules utilisent uniquement le produit de Kronecker, l’opérateur vec et des matrices de commutation. Nous pouvons immédiatement à partir de ces formules examiner de plus près les structures particulières des matrices de cumulants et ainsi donner des résultats sur les rangs de ces matrices qui caractérisent la dépendance entre les variables aléatoires constituant le vecteur aléatoire. L’intérêt pratique principal de nos formules matricielles réside certainement dans une évaluation des cumulants beaucoup plus aisée et rapide qu’avec la méthode usuelle basée sur une utilisation répétée des formules de Leonov et Shiryaev. Dans la deuxième partie de cette thèse, nous montrons que sous les hypothèses usuelles de l’analyse en composantes indépendantes mul- tidimensionnelles, les matrices de cumulants contractées à un ordre statistique quelconque sont toutes bloc-diagonalisables dans la même base. Nous en déduisons des algorithmes de résolution d’ACIM par bloc-diagonalisation conjointe et comparons les résultats obtenus aux ordres 3 à 6, entre eux et avec d’autres méthodes, sur quelques signaux synthétiques. Des exemples simples ont élaborés afin de justifier la nécessité de combiner des ordres différents pour garantir la meilleure séparation. Nous prouvons aussi que le cas le plus simple à traiter est celui de mélanges de sources qui ont différentes dimensions. Dans la dernière partie de cette thèse nous proposons une famille de méthodes qui exploitent uniquement les sta- tistiques d’ordres supérieurs à deux. Sous certaines hypothèses supplémentaires, ces méthodes permettent après un blanchiment d’ordre quatre des observations de résoudre complètement le problème ACIM bruité en bloc diagonalisant conjointement un ensemble de matrices de cumulants issues des statistiques d’ordres supérieurs strictement à quatre. Une comparaison avec les méthodes ACIM à blanchiment d’ordre deux pour la séparation des activités électriques foetale et maternelle (mesurées via trois électrodes placées sur l’abdomen de la mère) montre que cette nouvelle famille est mieux adaptée à cette application : elles permettent une séparation quasi parfaite de ces deux contributions

Investigation of neural activity in Schizophrenia during resting-state MEG : using non-linear dynamics and machine-learning to shed light on information disruption in the brain

Environ 25% de la population mondiale est atteinte de troubles psychiatriques qui sont typiquement associés à des problèmes comportementaux, fonctionnels et/ou cognitifs et dont les corrélats neurophysiologiques sont encore très mal compris. Non seulement ces dysfonctionnements réduisent la qualité de vie des individus touchés, mais ils peuvent aussi devenir un fardeau pour les proches et peser lourd dans l’économie d’une société. Cibler les mécanismes responsables du fonctionnement atypique du cerveau en identifiant des biomarqueurs plus robustes permettrait le développement de traitements plus efficaces. Ainsi, le premier objectif de cette thèse est de contribuer à une meilleure caractérisation des changements dynamiques cérébraux impliqués dans les troubles mentaux, plus précisément dans la schizophrénie et les troubles d’humeur. Pour ce faire, les premiers chapitres de cette thèse présentent, en intégral, deux revues de littératures systématiques que nous avons menées sur les altérations de connectivité cérébrale, au repos, chez les patients schizophrènes, dépressifs et bipolaires. Ces revues révèlent que, malgré des avancées scientifiques considérables dans l’étude de l’altération de la connectivité cérébrale fonctionnelle, la dimension temporelle des mécanismes cérébraux à l’origine de l’atteinte de l’intégration de l’information dans ces maladies, particulièrement de la schizophrénie, est encore mal comprise. Par conséquent, le deuxième objectif de cette thèse est de caractériser les changements cérébraux associés à la schizophrénie dans le domaine temporel. Nous présentons deux études dans lesquelles nous testons l’hypothèse que la « disconnectivité temporelle » serait un biomarqueur important en schizophrénie. Ces études explorent les déficits d’intégration temporelle en schizophrénie, en quantifiant les changements de la dynamique neuronale dite invariante d’échelle à partir des données magnétoencéphalographiques (MEG) enregistrés au repos chez des patients et des sujets contrôles. En particulier, nous utilisons (1) la LRTCs (long-range temporal correlation, ou corrélation temporelle à longue-distance) calculée à partir des oscillations neuronales et (2) des analyses multifractales pour caractériser des modifications de l’activité cérébrale arythmique. Par ailleurs, nous développons des modèles de classification (en apprentissage-machine supervisé) pour mieux cerner les attributs corticaux et sous-corticaux permettant une distinction robuste entre les patients et les sujets sains. Vu que ces études se basent sur des données MEG spontanées enregistrées au repos soit avec les yeux ouvert, ou les yeux fermées, nous nous sommes par la suite intéressés à la possibilité de trouver un marqueur qui combinerait ces enregistrements. La troisième étude originale explore donc l’utilité des modulations de l’amplitude spectrale entre yeux ouverts et fermées comme prédicteur de schizophrénie. Les résultats de ces études démontrent des changements cérébraux importants chez les patients schizophrènes au niveau de la dynamique d’invariance d’échelle. Elles suggèrent une dégradation du traitement temporel de l’information chez les patients, qui pourrait être liée à leurs symptômes cognitifs et comportementaux. L’approche multimodale de cette thèse, combinant la magétoencéphalographie, analyses non-linéaires et apprentissage machine, permet de mieux caractériser l’organisation spatio-temporelle du signal cérébrale au repos chez les patients atteints de schizophrénie et chez des individus sains. Les résultats fournissent de nouvelles preuves supportant l’hypothèse d’une « disconnectivité temporelle » en schizophrénie, et étendent les recherches antérieures, en explorant la contribution des structures cérébrales profondes et en employant des mesures non-linéaires avancées encore sous-exploitées dans ce domaine. L’ensemble des résultats de cette thèse apporte une contribution significative à la quête de nouveaux biomarqueurs de la schizophrénie et démontre l’importance d’élucider les altérations des propriétés temporelles de l’activité cérébrales intrinsèque en psychiatrie. Les études présentées offrent également un cadre méthodologique pouvant être étendu à d’autres psychopathologie, telles que la dépression.Psychiatric disorders affect nearly a quarter of the world’s population. These typically bring about debilitating behavioural, functional and/or cognitive problems, for which the underlying neural mechanisms are poorly understood. These symptoms can significantly reduce the quality of life of affected individuals, impact those close to them, and bring on an economic burden on society. Hence, targeting the baseline neurophysiology associated with psychopathologies, by identifying more robust biomarkers, would improve the development of effective treatments. The first goal of this thesis is thus to contribute to a better characterization of neural dynamic alterations in mental health illnesses, specifically in schizophrenia and mood disorders. Accordingly, the first chapter of this thesis presents two systematic literature reviews, which investigate the resting-state changes in brain connectivity in schizophrenia, depression and bipolar disorder patients. Great strides have been made in neuroimaging research in identifying alterations in functional connectivity. However, these two reviews reveal a gap in the knowledge about the temporal basis of the neural mechanisms involved in the disruption of information integration in these pathologies, particularly in schizophrenia. Therefore, the second goal of this thesis is to characterize the baseline temporal neural alterations of schizophrenia. We present two studies for which we hypothesize that the resting temporal dysconnectivity could serve as a key biomarker in schizophrenia. These studies explore temporal integration deficits in schizophrenia by quantifying neural alterations of scale-free dynamics using resting-state magnetoencephalography (MEG) data. Specifically, we use (1) long-range temporal correlation (LRTC) analysis on oscillatory activity and (2) multifractal analysis on arrhythmic brain activity. In addition, we develop classification models (based on supervised machine-learning) to detect the cortical and sub-cortical features that allow for a robust division of patients and healthy controls. Given that these studies are based on MEG spontaneous brain activity, recorded at rest with either eyes-open or eyes-closed, we then explored the possibility of finding a distinctive feature that would combine both types of resting-state recordings. Thus, the third study investigates whether alterations in spectral amplitude between eyes-open and eyes-closed conditions can be used as a possible marker for schizophrenia. Overall, the three studies show changes in the scale-free dynamics of schizophrenia patients at rest that suggest a deterioration of the temporal processing of information in patients, which might relate to their cognitive and behavioural symptoms. The multimodal approach of this thesis, combining MEG, non-linear analyses and machine-learning, improves the characterization of the resting spatiotemporal neural organization of schizophrenia patients and healthy controls. Our findings provide new evidence for the temporal dysconnectivity hypothesis in schizophrenia. The results extend on previous studies by characterizing scale-free properties of deep brain structures and applying advanced non-linear metrics that are underused in the field of psychiatry. The results of this thesis contribute significantly to the identification of novel biomarkers in schizophrenia and show the importance of clarifying the temporal properties of altered intrinsic neural dynamics. Moreover, the presented studies offer a methodological framework that can be extended to other psychopathologies, such as depression

Microstructural imaging of the human brain with a 'super-scanner': 10 key advantages of ultra-strong gradients for diffusion MRI

The key component of a microstructural diffusion MRI 'super-scanner' is a dedicated high-strength gradient system that enables stronger diffusion weightings per unit time compared to conventional gradient designs. This can, in turn, drastically shorten the time needed for diffusion encoding, increase the signal-to-noise ratio, and facilitate measurements at shorter diffusion times. This review, written from the perspective of the UK National Facility for In Vivo MR Imaging of Human Tissue Microstructure, an initiative to establish a shared 300 mT/m-gradient facility amongst the microstructural imaging community, describes ten advantages of ultra-strong gradients for microstructural imaging. Specifically, we will discuss how the increase of the accessible measurement space compared to a lower-gradient systems (in terms of Δ, b-value, and TE) can accelerate developments in the areas of 1) axon diameter distribution mapping; 2) microstructural parameter estimation; 3) mapping micro-vs macroscopic anisotropy features with gradient waveforms beyond a single pair of pulsed-gradients; 4) multi-contrast experiments, e.g. diffusion-relaxometry; 5) tractography and high-resolution imaging in vivo and 6) post mortem; 7) diffusion-weighted spectroscopy of metabolites other than water; 8) tumour characterisation; 9) functional diffusion MRI; and 10) quality enhancement of images acquired on lower-gradient systems. We finally discuss practical barriers in the use of ultra-strong gradients, and provide an outlook on the next generation of 'super-scanners'

NASA Laser Light Scattering Advanced Technology Development Workshop, 1988

The major objective of the workshop was to explore the capabilities of existing and prospective laser light scattering hardware and to assess user requirements and needs for a laser light scattering instrument in a reduced gravity environment. The workshop addressed experimental needs and stressed hardware development

Novas estratégias de pré-processamento, extração de atributos e classificação em sistemas BCI

Orientador: Romis Ribeiro de Faissol AttuxTese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de ComputaçãoResumo: As interfaces cérebro-computador (BCIs) visam controlar um dispositivo externo, utilizando diretamente os sinais cerebrais do usuário. Tais sistemas requerem uma série de etapas para processar e extrair atributos relevantes dos sinais observados para interpretar correta e eficientemente as intenções do usuário. Embora o campo tenha se desenvolvido continuamente e algumas dificuldades tenham sido superadas, ainda é necessário aumentar a capacidade de uso, melhorando sua capacidade de classificação e aumentando a confiabilidade de sua resposta. O objetivo clássico da pesquisa de BCI é apoiar a comunicação e o controle para usuários com comunicação prejudicada devido a doenças ou lesões. Aplicações típicas das BCI são a operação de cursores de interface, programas de escrita de texto ou dispositivos externos, como cadeiras de rodas, robôs e diferentes tipos de próteses. O usuário envia informações moduladas para a BCI, realizando tarefas mentais que produzem padrões cerebrais distintos. A BCI adquire sinais do cérebro do usuário e os traduz em comunicação adequada. Esta tese tem como objetivo desenvolver uma comunicação BCI não invasiva mais rápida e confiável baseada no estudo de diferentes técnicas que atuam nas etapas de processamento do sinal, considerando dois aspectos principais, a abordagem de aprendizado de máquina e a redução da complexidade na tarefa de aprendizado dos padrões mentais pelo usuário. A pesquisa foi focada em dois paradigmas de BCI, Imagética Motora (IM) e o potencial relacionado ao evento P300. Algoritmos de processamento de sinais para a detecção de ambos os padrões cerebrais foram aplicados e avaliados. O aspecto do pré-processamento foi a primeira perspectiva estudada, considerando como destacar a resposta dos fenômenos cerebrais, em relação ao ruído e a outras fontes de informação que talvez distorçam o sinal de EEG; isso em si é um passo que influenciará diretamente a resposta dos seguintes blocos de processamento e classificação. A Análise de Componente Independente (ICA) foi usada em conjunto com métodos de seleção de atributos e diferentes classificadores para separar as fontes originais relacionadas à dessincronização produzida pelo fenômeno de IM; esta foi uma tentativa de criar um tipo de filtro espacial que permitisse o sinal ser pré-processado, reduzindo a influência do ruído. Além disso, os resultados dos valores de classificação foram analisados considerando a comparação com métodos padrão de pré-processamento, como o filtro CAR. Os resultados mostraram que é possível separar os componentes relacionados à atividade motora. A proposta da ICA, em média, foi 4\% mais alta em porcentagem de precisão de classificação do que os resultados obtidos usando o CAR, ou quando nenhum filtro foi usado. O papel dos métodos que estudam a conectividade de diferentes áreas do cérebro foi avaliado como a segunda contribuição deste trabalho; Isso permitiu considerar aspectos que contemplam a complexidade da resposta cerebral de um usuário. A área da BCI precisa de uma interpretação mais profunda do que acontece no nível do cérebro em vários dos fenômenos estudados. A técnica utilizada para construir grafos de conectividade funcional foi a correntropia, esta medida foi utilizada para quantificar a similaridade; uma comparação foi feita usando também, as medidas de correlação de Spearman e Pearson. A conectividade funcional relaciona diferentes áreas do cérebro analisando sua atividade cerebral, de modo que o estudo do grafo foi avaliado utilizando três medidas de centralidade, onde a importância de um nó na rede é medida. Também, dois tipos de classificadores foram testados, comparando os resultados no nível de precisão de classificação. Em conclusão, a correntropia pode trazer mais informações para o estudo da conectividade do que o uso da correlação simples, o que trouxe melhorias nos resultados da classificação, especialmente quando ela foi utilizada com o classificador ELM. Finalmente, esta tese demonstra que os BCIs podem fornecer comunicação efetiva em uma aplicação onde a predição da resposta de classificação foi modelada, o que permitiu a otimização dos parâmetros do processamento de sinal realizado usando o filtro espacial xDAWN e um classificador FLDA para o problema do speller P300, buscando a melhor resposta para cada usuário. O modelo de predição utilizado foi Bayesiano e confirmou os resultados obtidos com a operação on-line do sistema, permitindo otimizar os parâmetros tanto do filtro quanto do classificador. Desta forma, foi visto que usando filtros com poucos canais de entrada, o modelo otimizado deu melhores resultados de acurácia de classificação do que os valores inicialmente obtidos ao treinar o filtro xDAWN para os mesmos casos. Os resultados obtidos mostraram que melhorias nos métodos do transdutor BCI, no pré-processamento, extração de características e classificação constituíram a base para alcançar uma comunicação BCI mais rápida e confiável. O avanço nos resultados da classificação foi obtido em todos os casos, comparado às técnicas que têm sido amplamente utilizadas e já mostraram eficácia para esse tipo de problema. No entanto, ainda há aspectos a considerar da resposta dos sujeitos para tipos específicos de paradigmas, lembrando que sua resposta pode variar ao longo de diferentes dias e as implicações reais disso na definição e no uso de diferentes métodos de processamento de sinalAbstract: Brain-computer interfaces (BCIs) aim to control an external device by directly employing user's brain signals. Such systems require a series of steps to process and extract relevant features from the observed signals to correctly and efficiently interpret the user's intentions. Although the field has been continuously developing and some difficulties have been overcome, it is still necessary to increase usability by enhancing their classification capacity and increasing the reliability of their response. The classical objective of BCI research is to support communication and control for users with impaired communication due to illness or injury. Typical BCI applications are the operation of interface cursors, spelling programs or external devices, such as wheelchairs, robots and different types of prostheses. The user sends modulated information to the BCI by engaging in mental tasks that produce distinct brain patterns. The BCI acquires signals from the user¿s brain and translates them into suitable communication. This thesis aims to develop faster and more reliable non-invasive BCI communication based on the study of different techniques that serve in the signal processing stages, considering two principal aspects, the machine learning approach, and the reduction of the complexity in the task of learning the mental patterns by the user. Research was focused on two BCI paradigms, Motor Imagery (MI) and the P300 event related potential (ERP). Signal processing algorithms for the detection of both brain patterns were applied and evaluated. The aspect of the pre-processing was the first perspective studied to consider how to highlight the response of brain phenomena, in relation to noise and other sources of information that maybe distorting the EEG signal; this in itself is a step that will directly influence the response of the following blocks of processing and classification. The Independent Component Analysis (ICA) was used in conjunction with feature selection methods and different classifiers to separate the original sources that are related to the desynchronization produced by MI phenomenon; an attempt was made to create a type of spatial filter that pre-processed the signal, reducing the influence of the noise. Furthermore, some of the classifications values were analyzed considering comparison when used other standard pre-processing methods, as the CAR filter. The results showed that it is possible to separate the components related to motor activity. The ICA proposal on average were 4\% higher in percent of classification accuracy than those obtained using CAR, or when no filter was used. The role of methods that study the connectivity of different brain areas were evaluated as the second contribution of this work; this allowed to consider aspects that contemplate the complexity of the brain response of a user. The area of BCI needs a deeper interpretation of what happens at the brain level in several of the studied phenomena. The technique used to build functional connectivity graphs was correntropy, this quantity was used to measure similarity, a comparison was made using also, the Spearman and Pearson correlation. Functional connectivity relates different brain areas activity, so the study of the graph was evaluated using three measures of centrality of graph, where the importance of a node in the network is measured. In addition, two types of classifiers were tested, comparing the results at the level of classification precision. In conclusion, the correntropy can bring more information for the study of connectivity than the use of the simple correlation, which brought improvements in the classification results especially when it was used with the ELM classifier. Finally, this thesis demonstrates that BCIs can provide effective communication in an application where the prediction of the classification response was modeled, which allowed the optimization of the parameters of the signal processing performed using the xDAWN spatial filter and a FLDA classifier for the problem of the P300 speller, seeking the best response for each user. The prediction model used was Bayesian and confirmed the results obtained with the on-line operation of the system, thus allowing to optimize the parameters of both the filter and the classifier. In this way it was seen that using filters with few inputs the optimized model gave better results of acuraccy classification than the values initially obtained when the training ofthe xDAWN filter was made for the same cases. The obtained results showed that improvements in the BCI transducer, pre-processing, feature extraction and classification methods constituted the basis to achieve faster and more reliable BCI communication. The advance in the classification results were obtained in all cases, compared to techniques that have been widely used and had already shown effectiveness for this type of problemsDoutoradoEngenharia de ComputaçãoDoutora em Engenharia Elétrica153311/2014-2CNP

Information theoretic versus cumulant-based contrasts for multimodal source separation

Recently, several authors have emphasized the existence of spurious maxima in usual contrast functions for source separation (e.g., the likelihood and the mutual information) when several sources have multimodal distributions. The aim of this letter is to compare the information theoretic contrasts to cumulant-based ones from the robustness to spurious maxima point of view. Even if all of them tend to measure, in some way, the same quantity, which is the output independence (or equivalently, the output non-Gaussianity), it is shown that in the case of a mixture involving two sources, the kurtosis-based contrast functions are more robust than the information theoretic ones when the source distributions are multimodal