Brain electrical activity discriminant analysis using Reproducing Kernel Hilbert spaces

A deep an adequate understanding of the human brain functions has been an objective for interdisciplinar teams of scientists. Different types of technological acquisition methodologies, allow to capture some particular data that is related with brain activity. Commonly, the more used strategies are related with the brain electrical activity, where reflected neuronal interactions are reflected in the scalp and obtained via electrode arrays as time series. The processing of this type of brain electrical activity (BEA) data, poses some challenges that should be addressed carefully due their intrinsic properties. BEA in known to have a nonstationaty behavior and a high degree of variability dependenig of the stimulus or responses that are being adressed..

Discriminating imagined and non-imagined tasks in the motor cortex area: entropy-complexity plane with a wavelet decomposition

Electroencephalograms reflect the electrical activity of the brain, which can be considered ruled by a chaotic nonlinear dynamics. We consider human electroencephalogram recordings during different motor type activities, and when imagining that they perform this activity. We characterize the different dynamics of the cortex according to distinct motor and imagined movement tasks using an information theory approach and a wavelet decomposition. More specifically, we use the entropy-complexity plane H × C in combination with the wavelet decomposition to precisely quantify the dynamics of the neuronal activity showing that the current theoretical framework allows us to distinguish realized and imagined tasks within the cortex.Instituto de Física de Líquidos y Sistemas Biológico

Empirical Characterization of the Temporal Dynamics of EEG Spectral Components

The properties of time-domain electroencephalographic data have been studied extensively. There has however been no attempt to characterize the temporal evolution of resulting spectral components when successive segments of electroencephalographic data are decomposed. We analyzed resting-state scalp electroencephalographic data from 23 subjects, acquired at 256 Hz, and transformed using 64-point Fast Fourier Transform with a Hamming window. KPSS and Nason tests were administered to study the trend- and wide sense stationarity respectively of the spectral components. Thereafter, the Rosenstein algorithm for dynamic evolution was applied to determine the largest Lyapunov exponents of each component’s temporal evolution. We found that the evolutions were wide sense stationary for time scales up to 8 s, and had significant interactions, especially between spectral series in the frequency ranges 0–4 Hz, 12–24 Hz, and 32-128 Hz. The spectral series were generally non-chaotic, with average largest Lyapunov exponent of 0. The results show that significant information is contained in all frequency bands, and that the interactions between bands are complicated and time-varying

Adaptive nonlinear multivariate brain connectivity analysis of motor imagery movements using graph theory

Recent studies on motor imagery (MI)-based brain computer interaction (BCI) reported that the interaction of spatially separated brain areas in forms of functional or effective connectivity leads to a better insight of brain neural patterns during MI movements and can provide useful features for BCIs. However, existing studies suffer from unrealistic assumptions or technical weaknesses for processing brain signals, such as stationarity, linearity and bivariate analysis framework. Besides, volume conduction effect as a critical challenge in this area and the role of subcortical regions in connectivity analysis have not been considered and studied well. In this thesis, the neurophysiological connectivity patterns of healthy human brain during different MI movements are deeply investigated. At first, an adaptive nonlinear multivariate statespace model known as dual extended Kalman filter is proposed for connectivity pattern estimation. Several frequency domain functional and effective connectivity estimators are developed for nonlinear non-stationary signals. Evaluation results show superior parameter tracking performance and hence more accurate connectivity analysis by the proposed model. Secondly, source-space time-varying nonlinear multivariate brain connectivity during feet, left hand, right hand and tongue MI movements is investigated in a broad frequency range by using the developed connectivity estimators. Results reveal the similarities and the differences between MI tasks in terms of involved regions, density of interactions, distribution of interactions, functional connections and information flows. Finally, organizational principles of brain networks of MI movements measured by all considered connectivity estimators are extensively explored by graph theoretical approach where the local and global graph structures are quantified by computing different graph indexes. Results report statistical significant differences between and within the MI tasks by using the graph indexes extracted from the networks formed particularly by normalized partial directed coherence. This delivers promising distinctive features of the MI tasks for non-invasive BCI applications

Connectivity Analysis in EEG Data: A Tutorial Review of the State of the Art and Emerging Trends

Understanding how different areas of the human brain communicate with each other is a crucial issue in neuroscience. The concepts of structural, functional and effective connectivity have been widely exploited to describe the human connectome, consisting of brain networks, their structural connections and functional interactions. Despite high-spatial-resolution imaging techniques such as functional magnetic resonance imaging (fMRI) being widely used to map this complex network of multiple interactions, electroencephalographic (EEG) recordings claim high temporal resolution and are thus perfectly suitable to describe either spatially distributed and temporally dynamic patterns of neural activation and connectivity. In this work, we provide a technical account and a categorization of the most-used data-driven approaches to assess brain-functional connectivity, intended as the study of the statistical dependencies between the recorded EEG signals. Different pairwise and multivariate, as well as directed and non-directed connectivity metrics are discussed with a pros-cons approach, in the time, frequency, and information-theoretic domains. The establishment of conceptual and mathematical relationships between metrics from these three frameworks, and the discussion of novel methodological approaches, will allow the reader to go deep into the problem of inferring functional connectivity in complex networks. Furthermore, emerging trends for the description of extended forms of connectivity (e.g., high-order interactions) are also discussed, along with graph-theory tools exploring the topological properties of the network of connections provided by the proposed metrics. Applications to EEG data are reviewed. In addition, the importance of source localization, and the impacts of signal acquisition and pre-processing techniques (e.g., filtering, source localization, and artifact rejection) on the connectivity estimates are recognized and discussed. By going through this review, the reader could delve deeply into the entire process of EEG pre-processing and analysis for the study of brain functional connectivity and learning, thereby exploiting novel methodologies and approaches to the problem of inferring connectivity within complex networks

An information theoretic learning framework based on Renyi’s α entropy for brain effective connectivity estimation

The interactions among neural populations distributed across different brain regions are at the core of cognitive and perceptual processing. Therefore, the ability of studying the flow of information within networks of connected neural assemblies is of fundamental importance to understand such processes. In that regard, brain connectivity measures constitute a valuable tool in neuroscience. They allow assessing functional interactions among brain regions through directed or non-directed statistical dependencies estimated from neural time series. Transfer entropy (TE) is one such measure. It is an effective connectivity estimation approach based on information theory concepts and statistical causality premises. It has gained increasing attention in the literature because it can capture purely nonlinear directed interactions, and is model free. That is to say, it does not require an initial hypothesis about the interactions present in the data. These properties make it an especially convenient tool in exploratory analyses. However, like any information-theoretic quantity, TE is defined in terms of probability distributions that in practice need to be estimated from data. A challenging task, whose outcome can significantly affect the results of TE. Also, it lacks a standard spectral representation, so it cannot reveal the local frequency band characteristics of the interactions it detects.Las interacciones entre poblaciones neuronales distribuidas en diferentes regiones del cerebro son el núcleo del procesamiento cognitivo y perceptivo. Por lo tanto, la capacidad de estudiar el flujo de información dentro de redes de conjuntos neuronales conectados es de fundamental importancia para comprender dichos procesos. En ese sentido, las medidas de conectividad cerebral constituyen una valiosa herramienta en neurociencia. Permiten evaluar interacciones funcionales entre regiones cerebrales a través de dependencias estadísticas dirigidas o no dirigidas estimadas a partir de series de tiempo. La transferencia de entropía (TE) es una de esas medidas. Es un enfoque de estimación de conectividad efectiva basada en conceptos de teoría de la información y premisas de causalidad estadística. Ha ganado una atención cada vez mayor en la literatura porque puede capturar interacciones dirigidas puramente no lineales y no depende de un modelo. Es decir, no requiere de una hipótesis inicial sobre las interacciones presentes en los datos. Estas propiedades la convierten en una herramienta especialmente conveniente en análisis exploratorios. Sin embargo, como cualquier concepto basado en teoría de la información, la TE se define en términos de distribuciones de probabilidad que en la práctica deben estimarse a partir de datos. Una tarea desafiante, cuyo resultado puede afectar significativamente los resultados de la TE. Además, carece de una representación espectral estándar, por lo que no puede revelar las características de banda de frecuencia local de las interacciones que detecta.DoctoradoDoctor(a) en IngenieríaContents List of Figures xi List of Tables xv Notation xvi 1 Preliminaries 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Problem statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Probability distribution estimation as an intermediate step in TE computation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.2 The lack of a spectral representation for TE . . . . . . . . . . . . 7 1.3 Theoretical background . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.1 Transfer entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3.2 Granger causality . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3.3 Information theoretic learning from kernel matrices . . . . . . . . 12 1.4 Literature review on transfer entropy estimation . . . . . . . . . . . . . . 14 1.4.1 Transfer entropy in the frequency domain . . . . . . . . . . . . . . 17 1.5 Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.5.1 General aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.5.2 Specific aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.6 Outline and contributions . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.6.1 Kernel-based Renyi’s transfer entropy . . . . . . . . . . . . . . . . 24 1.6.2 Kernel-based Renyi’s phase transfer entropy . . . . . . . . . . . . 24 1.6.3 Kernel-based Renyi’s phase transfer entropy for the estimation of directed phase-amplitude interactions . . . . . . . . . . . . . . . . 25 1.7 EEG databases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Contents ix 1.7.1 Motor imagery . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.7.2 Working memory . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.8 Thesis structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2 Kernel-based Renyi’s transfer entropy 34 2.1 Kernel-based Renyi’s transfer entropy . . . . . . . . . . . . . . . . . . . . 35 2.2 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.2.1 VAR model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.2.2 Modified linear Kus model . . . . . . . . . . . . . . . . . . . . . . 38 2.2.3 EEG data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.2.4 Parameter selection . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.3.1 VAR model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.3.2 Modified linear Kus model . . . . . . . . . . . . . . . . . . . . . . 46 2.3.3 EEG data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.3.4 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3 Kernel-based Renyi’s phase transfer entropy 60 3.1 Kernel-based Renyi’s phase transfer entropy . . . . . . . . . . . . . . . . 61 3.1.1 Phase-based effective connectivity estimation approaches considered in this chapter . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.2 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.2.1 Neural mass models . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.2.2 EEG data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.2.3 Parameter selection . . . . . . . . . . . . . . . . . . . . . . . . . . 67 3.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.3.1 Neural mass models . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.3.2 EEG data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.3.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 4 Kernel-based Renyi’s phase transfer entropy for the estimation of directed phase-amplitude interactions 84 4.1 Kernel-based Renyi’s phase transfer entropy for the estimation of directed phase-amplitude interactions . . . . . . . . . . . . . . . . . . . . . . . . . 85 x Contents 4.1.1 Transfer entropy for directed phase-amplitude interactions . . . . 85 4.1.2 Cross-frequency directionality . . . . . . . . . . . . . . . . . . . . 85 4.1.3 Phase transfer entropy and directed phase-amplitude interactions 86 4.2 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 4.2.1 Simulated phase-amplitude interactions . . . . . . . . . . . . . . . 88 4.2.2 EEG data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 4.2.3 Parameter selection . . . . . . . . . . . . . . . . . . . . . . . . . . 91 4.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.3.1 Simulated phase-amplitude interactions . . . . . . . . . . . . . . . 92 4.3.2 EEG data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.3.3 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 4.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5 Final Remarks 100 5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 5.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 5.3 Academic products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.3.1 Journal papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 5.3.2 Conference papers . . . . . . . . . . . . . . . . . . . . . . . . . . 105 5.3.3 Conference presentations . . . . . . . . . . . . . . . . . . . . . . . 105 Appendix A Kernel methods and Renyi’s entropy estimation 106 A.1 Reproducing kernel Hilbert spaces . . . . . . . . . . . . . . . . . . . . . . 106 A.1.1 Reproducing kernels . . . . . . . . . . . . . . . . . . . . . . . . . 106 A.1.2 Kernel-based learning . . . . . . . . . . . . . . . . . . . . . . . . . 107 A.2 Kernel-based estimation of Renyi’s entropy . . . . . . . . . . . . . . . . . 109 Appendix B Surface Laplacian 113 Appendix C Permutation testing 115 Appendix D Kernel-based relevance analysis 117 Appendix E Cao’s criterion 120 Appendix F Neural mass model equations 122 References 12

Study of Adaptation Methods Towards Advanced Brain-computer Interfaces

Ph.DDOCTOR OF PHILOSOPH

Graph analysis of functional brain networks: practical issues in translational neuroscience

The brain can be regarded as a network: a connected system where nodes, or units, represent different specialized regions and links, or connections, represent communication pathways. From a functional perspective communication is coded by temporal dependence between the activities of different brain areas. In the last decade, the abstract representation of the brain as a graph has allowed to visualize functional brain networks and describe their non-trivial topological properties in a compact and objective way. Nowadays, the use of graph analysis in translational neuroscience has become essential to quantify brain dysfunctions in terms of aberrant reconfiguration of functional brain networks. Despite its evident impact, graph analysis of functional brain networks is not a simple toolbox that can be blindly applied to brain signals. On the one hand, it requires a know-how of all the methodological steps of the processing pipeline that manipulates the input brain signals and extract the functional network properties. On the other hand, a knowledge of the neural phenomenon under study is required to perform physiological-relevant analysis. The aim of this review is to provide practical indications to make sense of brain network analysis and contrast counterproductive attitudes

Network-based brain computer interfaces: principles and applications

Brain-computer interfaces (BCIs) make possible to interact with the external environment by decoding the mental intention of individuals. BCIs can therefore be used to address basic neuroscience questions but also to unlock a variety of applications from exoskeleton control to neurofeedback (NFB) rehabilitation. In general, BCI usability critically depends on the ability to comprehensively characterize brain functioning and correctly identify the user s mental state. To this end, much of the efforts have focused on improving the classification algorithms taking into account localized brain activities as input features. Despite considerable improvement BCI performance is still unstable and, as a matter of fact, current features represent oversimplified descriptors of brain functioning. In the last decade, growing evidence has shown that the brain works as a networked system composed of multiple specialized and spatially distributed areas that dynamically integrate information. While more complex, looking at how remote brain regions functionally interact represents a grounded alternative to better describe brain functioning. Thanks to recent advances in network science, i.e. a modern field that draws on graph theory, statistical mechanics, data mining and inferential modelling, scientists have now powerful means to characterize complex brain networks derived from neuroimaging data. Notably, summary features can be extracted from these networks to quantitatively measure specific organizational properties across a variety of topological scales. In this topical review, we aim to provide the state-of-the-art supporting the development of a network theoretic approach as a promising tool for understanding BCIs and improve usability

Theoretical and experimental study of P300 ERP in the context of Brain-computer interfaces. Part I: Study and analysis of functional connectivity methods.

Trabajo Fin de Máster en Ingeniería InformáticaThe analysis of connectivity in brain networks has been widely researched and it has been shown that certain cognitive processes require the integration of distributed brain areas. Functional connectivity attempts to statistically quantify the interdependencies between these brain areas. For this study, an analysis of functional connectivity in an ERP context, more specifically on the P300 component using the Granger Causality metric was proposed. To this end, an analysis method is proposed which consists in quantifying the causality in the P300 signal and the non-P300 signal using the MVCG toolbox to determine if there are differences between the two results obtained. In this respect, a dataset from a Brain-Computer Interface (BCI) based on P300 is analyzed. Causality is determined in overlapping windows calculated from the signals under three aspects: i) Using standard electrodes, ii) Using electrodes selected by Bayesian Linear Discriminant Analysis and exhaustive search by forward selection (BLDA-FS), and iii) Using electrodes selected by the coefficient of determination (r2). Based on this analysis, it is shown that the Granger Causality metric is valid to show the existence of a significant connectivity difference between the P300 signal and the non-P300 signal. This measure shows higher connectivity values for the P300 signal and lower connectivity values for the non-P300 signal. Among the three approaches considered, the standard electrodes and the electrodes selected with BLDA-FS were found to be more discriminative in showing differences between P300 and nonP300 connectivity. Furthermore, through this study, it was possible to differentiate the level of functional connectivity between subjects with cognitive disabilities and nondisabled subjects, observing that the measured functional connectivity was higher in subjects without an underlying cognitive pathology. Studying functional connectivity with Granger Causality may help to incorporate this information as new features that allow better detection of the P300 signal and consequently improve the performance of P300-based BCIs