TY - JOUR A1 - Meinecke, Frank C. A1 - Ziehe, Andreas A1 - Kurths, Jürgen A1 - Müller, Klaus-Robert T1 - Measuring phase synchronization of superimposed signals N2 - Phase synchronization is an important phenomenon that occurs in a wide variety of complex oscillatory processes. Measuring phase synchronization can therefore help to gain fundamental insight into nature. In this Letter we point out that synchronization analysis techniques can detect spurious synchronization, if they are fed with a superposition of signals such as in electroencephalography or magnetoencephalography data. We show how techniques from blind source separation can help to nevertheless measure the true synchronization and avoid such pitfalls Y1 - 2005 SN - 0031-9007 ER - TY - JOUR A1 - Nolte, Guido A1 - Meinecke, Frank C. A1 - Ziehe, Andreas A1 - Müller, Klaus-Robert T1 - Identifying interactions in mixed and noisy complex systems N2 - We present a technique that identifies truly interacting subsystems of a complex system from multichannel data if the recordings are an unknown linear and instantaneous mixture of the true sources. The method is valid for arbitrary noise structure. For this, a blind source separation technique is proposed that diagonalizes antisymmetrized cross- correlation or cross-spectral matrices. The resulting decomposition finds truly interacting subsystems blindly and suppresses any spurious interaction stemming from the mixture. The usefulness of this interacting source analysis is demonstrated in simulations and for real electroencephalography data Y1 - 2006 UR - http://pre.aps.org/ U6 - https://doi.org/10.1103/Physreve.73.051913 ER - TY - JOUR A1 - Ziehe, Andreas A1 - Laskov, Pavel A1 - Nolte, G A1 - Müller, Klaus-Robert T1 - A fast algorithm for joint diagonalization with non-orthogonal transformations and its application to blind source separation N2 - A new efficient algorithm is presented for joint diagonalization of several matrices. The algorithm is based on the Frobenius-norm formulation of the joint diagonalization problem, and addresses diagonalization with a general, non- orthogonal transformation. The iterative scheme of the algorithm is based on a multiplicative update which ensures the invertibility of the diagonalizer. The algorithm's efficiency stems from the special approximation of the cost function resulting in a sparse, block-diagonal Hessian to be used in the computation of the quasi-Newton update step. Extensive numerical simulations illustrate the performance of the algorithm and provide a comparison to other leading diagonalization methods. The results of such comparison demonstrate that the proposed algorithm is a viable alternative to existing state-of-the-art joint diagonalization algorithms. The practical use of our algorithm is shown for blind source separation problems Y1 - 2004 ER - TY - JOUR A1 - Müller, Klaus-Robert A1 - Vigario, R. A1 - Meinecke, Frank C. A1 - Ziehe, Andreas T1 - Blind source separation techniques for decomposing event-related brain signals N2 - Recently blind source separation (BSS) methods have been highly successful when applied to biomedical data. This paper reviews the concept of BSS and demonstrates its usefulness in the context of event-related MEG measurements. In a first experiment we apply BSS to artifact identification of raw MEG data and discuss how the quality of the resulting independent component projections can be evaluated. The second part of our study considers averaged data of event-related magnetic fields. Here, it is particularly important to monitor and thus avoid possible overfitting due to limited sample size. A stability assessment of the BSS decomposition allows to solve this task and an additional grouping of the BSS components reveals interesting structure, that could ultimately be used for gaining a better physiological modeling of the data Y1 - 2004 SN - 0218-1274 ER - TY - JOUR A1 - Ziehe, Andreas A1 - Kawanabe, Motoaki A1 - Harmeling, Stefan T1 - Blind separation of post-nonlinear mixtures using linearizing transformations and temporal decorrelation N2 - We propose two methods that reduce the post-nonlinear blind source separation problem (PNL-BSS) to a linear BSS problem. The first method is based on the concept of maximal correlation: we apply the alternating conditional expectation (ACE) algorithm-a powerful technique from nonparametric statistics-to approximately invert the componentwise nonlinear functions. The second method is a Gaussianizing transformation, which is motivated by the fact that linearly mixed signals before nonlinear transformation are approximately Gaussian distributed. This heuristic, but simple and efficient procedure works as good as the ACE method. Using the framework provided by ACE, convergence can be proven. The optimal transformations obtained by ACE coincide with the sought-after inverse functions of the nonlinearitics. After equalizing the nonlinearities, temporal decorrelation separation (TDSEP) allows us to recover the source signals. Numerical simulations testing "ACE-TD" and "Gauss-TD" on realistic examples are performed with excellent results Y1 - 2004 SN - 1532-4435 ER - TY - THES A1 - Ziehe, Andreas T1 - Blind source separation based on joint diagonalization of matrices with applications in biomedical signal processing T1 - Blinde Signalquellentrennung beruhend auf simultaner Diagonalisierung von Matrizen mit Anwendungen in der biomedizinischen Signalverarbeitung T1 - Blinde Signalquellentrennung beruhend auf simultaner Diagonalisierung von Matrizen mit Anwendungen in der biomedizinischen Signalverarbeitung N2 - This thesis is concerned with the solution of the blind source separation problem (BSS). The BSS problem occurs frequently in various scientific and technical applications. In essence, it consists in separating meaningful underlying components out of a mixture of a multitude of superimposed signals. In the recent research literature there are two related approaches to the BSS problem: The first is known as Independent Component Analysis (ICA), where the goal is to transform the data such that the components become as independent as possible. The second is based on the notion of diagonality of certain characteristic matrices derived from the data. Here the goal is to transform the matrices such that they become as diagonal as possible. In this thesis we study the latter method of approximate joint diagonalization (AJD) to achieve a solution of the BSS problem. After an introduction to the general setting, the thesis provides an overview on particular choices for the set of target matrices that can be used for BSS by joint diagonalization. As the main contribution of the thesis, new algorithms for approximate joint diagonalization of several matrices with non-orthogonal transformations are developed. These newly developed algorithms will be tested on synthetic benchmark datasets and compared to other previous diagonalization algorithms. Applications of the BSS methods to biomedical signal processing are discussed and exemplified with real-life data sets of multi-channel biomagnetic recordings. N2 - Diese Arbeit befasst sich mit der Lösung des Problems der blinden Signalquellentrennung (BSS). Das BSS Problem tritt häufig in vielen wissenschaftlichen und technischen Anwendungen auf. Im Kern besteht das Problem darin, aus einem Gemisch von überlagerten Signalen die zugrundeliegenden Quellsignale zu extrahieren. In wissenschaftlichen Publikationen zu diesem Thema werden hauptsächlich zwei Lösungsansätze verfolgt: Ein Ansatz ist die sogenannte "Analyse der unabhängigen Komponenten", die zum Ziel hat, eine lineare Transformation V der Daten X zu finden, sodass die Komponenten Un der transformierten Daten U = V X (die sogenannten "independent components") so unabhängig wie möglich sind. Ein anderer Ansatz beruht auf einer simultanen Diagonalisierung mehrerer spezieller Matrizen, die aus den Daten gebildet werden. Diese Möglichkeit der Lösung des Problems der blinden Signalquellentrennung bildet den Schwerpunkt dieser Arbeit. Als Hauptbeitrag der vorliegenden Arbeit präsentieren wir neue Algorithmen zur simultanen Diagonalisierung mehrerer Matrizen mit Hilfe einer nicht-orthogonalen Transformation. Die neu entwickelten Algorithmen werden anhand von numerischen Simulationen getestet und mit bereits bestehenden Diagonalisierungsalgorithmen verglichen. Es zeigt sich, dass unser neues Verfahren sehr effizient und leistungsfähig ist. Schließlich werden Anwendungen der BSS Methoden auf Probleme der biomedizinischen Signalverarbeitung erläutert und anhand von realistischen biomagnetischen Messdaten wird die Nützlichkeit in der explorativen Datenanalyse unter Beweis gestellt. KW - Signaltrennung KW - Mischung KW - Diagonalisierung KW - Bioelektrisches Signal KW - Magnetoencephalographie KW - Elektroencephalographie KW - Signalquellentrennung KW - Matrizen-Eigenwertaufgabe KW - Simultane Diagonalisierung KW - Optimierungsproblem KW - blind source separation KW - BSS KW - ICA KW - independent component analysis KW - approximate joint diagonalization KW - EEG KW - MEG Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-5694 ER - TY - JOUR A1 - Wübbeler, G. A1 - Ziehe, Andreas A1 - Mackert, B.-M. A1 - Müller, Klaus-Robert A1 - Trahms, L. A1 - Curio, Gabriel T1 - Independent component analysis of noninvasively recorded cortical magnetic DC-fields in humans Y1 - 2000 ER - TY - JOUR A1 - Ziehe, Andreas A1 - Müller, Klaus-Robert A1 - Nolte, G. A1 - Mackert, B.-M. A1 - Curio, Gabriel T1 - Artifact reduction in magnetoneurography based on time-delayed second-order correlations Y1 - 2000 ER - TY - JOUR A1 - Parra, L. A1 - Spence, C. A1 - Sajda, P. A1 - Ziehe, Andreas A1 - Müller, Klaus-Robert T1 - Unmixing hyperspectral data Y1 - 2000 ER -