Detecting synchronization clusters in multivariate time series via coarse-graining of Markov chains

Synchronization cluster analysis is an approach to the detection of underlying structures in data sets of multivariate time series, starting from a matrix R of bivariate synchronization indices. A previous method utilized the eigenvectors of R for cluster identification, analogous to several recent attempts at group identification using eigenvectors of the correlation matrix. All of these approaches assumed a one-to-one correspondence of dominant eigenvectors and clusters, which has however been shown to be wrong in important cases. We clarify the usefulness of eigenvalue decomposition for synchronization cluster analysis by translating the problem into the language of stochastic processes, and derive an enhanced clustering method harnessing recent insights from the coarse-graining of finite-state Markov processes. We illustrate the operation of our method using a simulated system of coupled Lorenz oscillators, and we demonstrate its superior performance over the previous approach. Finally we investigate the question of robustness of the algorithm against small sample size, which is important with regard to field applications.Comment: Follow-up to arXiv:0706.3375. Journal submission 9 Jul 2007. Published 19 Dec 200

die Theorie selbstreferentieller Systeme und der Konstruktivismus

Einleitung I. Maturana 1\. Der Organismus als autopoietisches System 2\. Die Geschlossenheit des Nervensystems 3\. Kognition, Kommunikation, Beobachtung 4\. Erkenntnis II. Roth 1\. Verhältnis zu Maturana 2\. Neurobiologische Befunde und Konsequenzen 3\. Die Unwirklichkeit der »Realität« 4\. Die Konstruktivität des Wahrnehmungsapparats 5\. Physik als intendierte Realität III. Luhmann 1\. Systemtheorie 2\. Erkenntnistheoretische Überlegungen in den »Sozialen Systemen« 3\. »Operativer Konstruktivismus« Beobachtung–Differenz–Umwelt–Metatheorie Schluß: Konstruktivismus als naturale OntologieDas Thema der Arbeit ist die Frage, welche Konsequenzen im Bereich der Erkenntnistheorie sich aus denjenigen wissenschaftlichen Ansätzen ableiten lassen, die am Begriff des Systems orientiert sind. Ihr Inhalt besteht in der Darstellung systemtheoretischer Konzepte und ihrer erkenntnistheoretischen Konsequenzen bei Maturana, Roth und Luhmann, sowie in deren Kritik auf der Ebene der System- wie auch der Erkenntnistheorie, mit der Absicht, durch eigene Überlegungen einen Beitrag zur Klärung und Fortentwicklung einer systemtheoretisch angeleiteten Erkenntnistheorie zu leisten. Resultate sind, daß die überwiegend konstruktivistische erkenntnistheoretische Haltung der drei Autoren sich nur bedingt mit systemtheoretischen Argumenten rechtfertigen läßt, und daß die zugrundegelegte Theorie selbstreferentieller Systeme generell noch nicht den Stand erreicht hat, auf dem sich zuverlässig Schlüsse ziehen lassen. Abschließend wird kurz die Idee von Systemtheorie als einer »naturalen Ontologie« skizziert.Elektronische Version von 200

Eigenvalue Decomposition as a Generalized Synchronization Cluster Analysis

Motivated by the recent demonstration of its use as a tool for the detection and characterization of phase-shape correlations in multivariate time series, we show that eigenvalue decomposition can also be applied to a matrix of indices of bivariate phase synchronization strength. The resulting method is able to identify clusters of synchronized oscillators, and to quantify their strength as well as the degree of involvement of an oscillator in a cluster. Since for the case of a single cluster the method gives similar results as our previous approach, it can be seen as a generalized Synchronization Cluster Analysis, extending its field of application to more complex situations. The performance of the method is tested by applying it to simulation data.Comment: Submitted Oct 2005, accepted Jan 2006, "published" Oct 2007, actually available Jan 200

Robust artifactual independent component classification for BCI practitioners

Objective. EEG artifacts of non-neural origin can be separated from neural signals by independent component analysis (ICA). It is unclear (1) how robustly recently proposed artifact classifiers transfer to novel users, novel paradigms or changed electrode setups, and (2) how artifact cleaning by a machine learning classifier impacts the performance of brain–computer interfaces (BCIs). Approach. Addressing (1), the robustness of different strategies with respect to the transfer between paradigms and electrode setups of a recently proposed classifier is investigated on offline data from 35 users and 3 EEG paradigms, which contain 6303 expert-labeled components from two ICA and preprocessing variants. Addressing (2), the effect of artifact removal on single-trial BCI classification is estimated on BCI trials from 101 users and 3 paradigms. Main results. We show that (1) the proposed artifact classifier generalizes to completely different EEG paradigms. To obtain similar results under massively reduced electrode setups, a proposed novel strategy improves artifact classification. Addressing (2), ICA artifact cleaning has little influence on average BCI performance when analyzed by state-of-the-art BCI methods. When slow motor-related features are exploited, performance varies strongly between individuals, as artifacts may obstruct relevant neural activity or are inadvertently used for BCI control. Significance. Robustness of the proposed strategies can be reproduced by EEG practitioners as the method is made available as an EEGLAB plug-in.EC/FP7/224631/EU/Tools for Brain-Computer Interaction/TOBIBMBF, 01GQ0850, Verbundprojekt: Bernstein Fokus Neurotechnologie - Nichtinvasive Neurotechnologie für Mensch-Maschine Interaktion - Teilprojekte A1, A3, A4, B4, W3, ZentrumDFG, 194657344, EXC 1086: BrainLinks-BrainTool

Searchlight-based multi-voxel pattern analysis of fMRI by cross-validated MANOVA

Multi-voxel pattern analysis (MVPA) is a fruitful and increasingly popular complement to traditional univariate methods of analyzing neuroimaging data. We propose to replace the standard ‘decoding’ approach to searchlight-based MVPA, measuring the performance of a classifier by its accuracy, with a method based on the multivariate form of the general linear model. Following the well-established methodology of multivariate analysis of variance (MANOVA), we define a measure that directly characterizes the structure of multi-voxel data, the pattern distinctness D. Our measure is related to standard multivariate statistics, but we apply cross-validation to obtain an unbiased estimate of its population value, independent of the amount of data or its partitioning into ‘training’ and ‘test’ sets. The estimate can therefore serve not only as a test statistic, but also as an interpretable measure of multivariate effect size. The pattern distinctness generalizes the Mahalanobis distance to an arbitrary number of classes, but also the case where there are no classes of trials because the design is described by parametric regressors. It is defined for arbitrary estimable contrasts, including main effects (pattern differences) and interactions (pattern changes). In this way, our approach makes the full analytical power of complex factorial designs known from univariate fMRI analyses available to MVPA studies. Moreover, we show how the results of a factorial analysis can be used to obtain a measure of pattern stability, the equivalent of ‘cross-decoding’

Mental states as macrostates emerging from brain electrical dynamics

Psychophysiological correlations form the basis for different medical and scientific disciplines, but the nature of this relation has not yet been fully understood. One conceptual option is to understand the mental as “emerging” from neural processes in the specific sense that psychology and physiology provide two different descriptions of the same system. Stating these descriptions in terms of coarser- and finer-grained system states (macro- and microstates), the two descriptions may be equally adequate if the coarse-graining preserves the possibility to obtain a dynamical rule for the system. To test the empirical viability of our approach, we describe an algorithm to obtain a specific form of such a coarse-graining from data, and illustrate its operation using a simulated dynamical system. We then apply the method to an electroencephalographic recording, where we are able to identify macrostates from the physiological data that correspond to mental states of the subject

Valid population inference for information-based imaging: From the second-level t-test to prevalence inference

In multivariate pattern analysis of neuroimaging data, ‘second-level’ inference is often performed by entering classification accuracies into a t-test vs chance level across subjects. We argue that while the random-effects analysis implemented by the t-test does provide population inference if applied to activation differences, it fails to do so in the case of classification accuracy or other ‘information-like’ measures, because the true value of such measures can never be below chance level. This constraint changes the meaning of the population-level null hypothesis being tested, which becomes equivalent to the global null hypothesis that there is no effect in any subject in the population. Consequently, rejecting it only allows to infer that there are some subjects in which there is an information effect, but not that it generalizes, rendering it effectively equivalent to fixed-effects analysis. This statement is supported by theoretical arguments as well as simulations. We review possible alternative approaches to population inference for information-based imaging, converging on the idea that it should not target the mean, but the prevalence of the effect in the population. One method to do so, ‘permutation-based information prevalence inference using the minimum statistic’, is described in detail and applied to empirical data

Phase synchronization analysis of event-related brain potentials in language processing

Das Forschungsthema Synchronisation bildet einen Schnittpunkt von Nichtlinearer Dynamik und Neurowissenschaft. So hat zum einen neurobiologische Forschung gezeigt, daß die Synchronisation neuronaler Aktivität einen wesentlichen Aspekt der Funktionsweise des Gehirns darstellt. Zum anderen haben Fortschritte in der physikalischen Theorie zur Entdeckung des Phänomens der Phasensynchronisation geführt. Eine dadurch motivierte Datenanalysemethode, die Phasensynchronisations-Analyse, ist bereits mit Erfolg auf empirische Daten angewandt worden. Die vorliegende Dissertation knüpft an diese konvergierenden Forschungslinien an. Ihren Gegenstand bilden methodische Beiträge zur Fortentwicklung der Phasensynchronisations-Analyse, sowie deren Anwendung auf ereigniskorrelierte Potentiale, eine besonders in den Kognitionswissenschaften wichtige Form von EEG-Daten. Die methodischen Beiträge dieser Arbeit bestehen zum ersten in einer Reihe spezialisierter statistischer Tests auf einen Unterschied der Synchronisationsstärke in zwei verschiedenen Zuständen eines Systems zweier Oszillatoren. Zweitens wird im Hinblick auf den viel-kanaligen Charakter von EEG-Daten ein Ansatz zur multivariaten Phasensynchronisations-Analyse vorgestellt. Zur empirischen Untersuchung neuronaler Synchronisation wurde ein klassisches Experiment zur Sprachverarbeitung repliziert, in dem der Effekt einer semantischen Verletzung im Satzkontext mit demjenigen der Manipulation physischer Reizeigenschaften (Schriftfarbe) verglichen wird. Hier zeigt die Phasensynchronisations-Analyse eine Verringerung der globalen Synchronisationsstärke für die semantische Verletzung sowie eine Verstärkung für die physische Manipulation. Im zweiten Fall läßt sich der global beobachtete Synchronisationseffekt mittels der multivariaten Analyse auf die Interaktion zweier symmetrisch gelegener Gehirnareale zurückführen. Die vorgelegten Befunde zeigen, daß die physikalisch motivierte Methode der Phasensynchronisations-Analyse einen wesentlichen Beitrag zur Untersuchung ereigniskorrelierter Potentiale in den Kognitionswissenschaften zu leisten vermag.The topic of synchronization forms a link between nonlinear dynamics and neuroscience. On the one hand, neurobiological research has shown that the synchronization of neuronal activity is an essential aspect of the working principle of the brain. On the other hand, recent advances in the physical theory have led to the discovery of the phenomenon of phase synchronization. A method of data analysis that is motivated by this finding - phase synchronization analysis - has already been successfully applied to empirical data. The present doctoral thesis ties up to these converging lines of research. Its subject are methodical contributions to the further development of phase synchronization analysis, as well as its application to event-related potentials, a form of EEG data that is especially important in the cognitive sciences. The methodical contributions of this work consist firstly in a number of specialized statistical tests for a difference in the synchronization strength in two different states of a system of two oscillators. Secondly, in regard of the many-channel character of EEG data an approach to multivariate phase synchronization analysis is presented. For the empirical investigation of neuronal synchronization a classic experiment on language processing was replicated, comparing the effect of a semantic violation in a sentence context with that of the manipulation of physical stimulus properties (font color). Here phase synchronization analysis detects a decrease of global synchronization for the semantic violation as well as an increase for the physical manipulation. In the latter case, by means of the multivariate analysis the global synchronization effect can be traced back to an interaction of symmetrically located brain areas. The findings presented show that the method of phase synchronization analysis motivated by physics is able to provide a relevant contribution to the investigation of event-related potentials in the cognitive sciences

About the derivation of the SCA algorithm

In Allefeld & Kurths [2004], we introduced an approach to multivariate phase synchronization analysis in the form of a Synchronization Cluster Analysis (SCA). A statistical model of a synchronization cluster was described, and an abbreviated instruction on how to apply this model to empirical data was given, while an implementation of the corresponding algorithm was (and is) available from the authors. In this letter, the complete details on how the data analysis algorithm is to be derived from the model are filled in