Andreas Ziehe

Publications

• An Algebraic Method for Approximate Rank One Factorization of Rank Deficient Matrices.

  Franz J. Király, Andreas Ziehe, Klaus-Robert Müller

  Latent Variable Analysis and Signal Separation - 10th International Conference, LVA/ICA 2012, Tel Aviv, Israel, March 12-15, 2012. Proceedings; 01/2012

• Comparison of Granger Causality and Phase Slope Index.

  Guido Nolte, Andreas Ziehe, Nicole Krämer, Florin Popescu, Klaus-Robert Müller

  Journal of Machine Learning Research - Proceedings Track. 01/2010; 6:267-276.
• 7.33

  Impact points

  Robustly estimating the flow direction of information in complex physical systems.

  Guido Nolte, Andreas Ziehe, Vadim V Nikulin, Alois Schlögl, Nicole Krämer, Tom Brismar, Klaus-Robert Müller

  Physical review letters. 06/2008; 100(23):234101.

  We propose a new measure (phase-slope index) to estimate the direction of information flux in multivariate time series. This measure (a) is insensitive to mixtures of independent sources, (b) gives meaningful results even if the phase spectrum is not linear, and (c) properly weights contributions fr... [more] We propose a new measure (phase-slope index) to estimate the direction of information flux in multivariate time series. This measure (a) is insensitive to mixtures of independent sources, (b) gives meaningful results even if the phase spectrum is not linear, and (c) properly weights contributions from different frequencies. These properties are shown in extended simulations and contrasted to Granger causality which yields highly significant false detections for mixtures of independent sources. An application to electroencephalography data (eyes-closed condition) reveals a clear front-to-back information flow.
• 5.74

  Impact points

  Combining sparsity and rotational invariance in EEG/MEG source reconstruction.

  Stefan Haufe, Vadim V Nikulin, Andreas Ziehe, Klaus-Robert Müller, Guido Nolte

  NeuroImage. 06/2008;

  We introduce Focal Vector Field Reconstruction (FVR), a novel technique for the inverse imaging of vector fields. The method was designed to simultaneously achieve two goals: a) invariance with respect to the orientation of the coordinate system, and b) a preference for sparsity of the solutions and... [more] We introduce Focal Vector Field Reconstruction (FVR), a novel technique for the inverse imaging of vector fields. The method was designed to simultaneously achieve two goals: a) invariance with respect to the orientation of the coordinate system, and b) a preference for sparsity of the solutions and their spatial derivatives. This was achieved by defining the regulating penalty function, which renders the solutions unique, as a global l(1)-norm of local l(2)-norms. We show that the method can be successfully used for solving the EEG inverse problem. In the joint localization of 2-3 simulated dipoles, FVR always reliably recovers the true sources. The competing methods have limitations in distinguishing close sources because their estimates are either too smooth (LORETA, Minimum l(1)-norm) or too scattered (Minimum l(2)-norm). In both noiseless and noisy simulations, FVR has the smallest localization error according to the Earth Mover's Distance (EMD), which is introduced here as a meaningful measure to compare arbitrary source distributions. We also apply the method to the simultaneous localization of left and right somatosensory N20 generators from real EEG recordings. Compared to its peers FVR was the only method that delivered correct location of the source in the somatosensory area of each hemisphere in accordance with neurophysiological prior knowledge.

• Robustly estimating the flow direction of information in complex physical systems

  Guido Nolte, Andreas Ziehe, Vadim V Nikulin, Alois Schlögl, Nicole Krämer, Tom Brismar, Klaus-Robert Müller

  12/2007;

  We propose a new measure to estimate the direction of information flux in multivariate time series from complex systems. This measure, based on the slope of the phase spectrum (Phase Slope Index) has invariance properties that are important for applications in real physical or biological systems: (a... [more] We propose a new measure to estimate the direction of information flux in multivariate time series from complex systems. This measure, based on the slope of the phase spectrum (Phase Slope Index) has invariance properties that are important for applications in real physical or biological systems: (a) it is strictly insensitive to mixtures of arbitrary independent sources, (b) it gives meaningful results even if the phase spectrum is not linear, and (c) it properly weights contributions from different frequencies. Simulations of a class of coupled multivariate random data show that for truly unidirectional information flow without additional noise contamination our measure detects the correct direction as good as the standard Granger causality. For random mixtures of independent sources Granger Causality erroneously yields highly significant results whereas our measure correctly becomes non-significant. An application of our novel method to EEG data (88 subjects in eyes-closed condition) reveals a strikingly clear front-to-back information flow in the vast majority of subjects and thus contributes to a better understanding of information processing in the brain. Comment: 5 pages, 4 figures

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• 2.40

  Impact points

  Identifying interactions in mixed and noisy complex systems.

  Guido Nolte, Frank C Meinecke, Andreas Ziehe, Klaus-Robert Müller

  Physical review. E, Statistical, nonlinear, and soft matter physics. 06/2006; 73(5 Pt 1):051913.

  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 pr... [more] 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.

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• 7.33

  Impact points

  Measuring phase synchronization of superimposed signals.

  Frank C Meinecke, Andreas Ziehe, Jürgen Kurths, Klaus-Robert Müller

  Physical review letters. 04/2005; 94(8):084102.

  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 synchr... [more] 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.

• Analyzing Coupled Brain Sources: Distinguishing True from Spurious Interaction.

  Guido Nolte, Andreas Ziehe, Frank C. Meinecke, Klaus-Robert Müller

  Advances in Neural Information Processing Systems 18 [Neural Information Processing Systems, NIPS 2005, December 5-8, 2005, Vancouver, British Columbia, Canada]; 01/2005

• Journal of Machine Learning Research 5 (2004) 777--800 Submitted 12/03; Revised 5/04; Published 7/04 A Fast Algorithm for Joint Diagonalization with Non-orthogonal

  Andreas Ziehe, Pavel Laskov, Kekul Estrasse, Guido Nolte

  10/2004;

  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 b... [more] 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.

• Journal of Machine Learning Research 4 (2003) 1319-1338 Submitted 10/02; Published 12/03 Blind Separation of Post-nonlinear Mixtures using Linearizing

  Andreas Ziehe, Motoaki Kawanabe, Stefan Harmeling, Te-won Lee, Jean-francois Cardoso, Erkki Oja, Shun-ichi Amari

  06/2004;

  We propose two methods that reduce the post-nonlinear blind source separation problem (PNLBSS) 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 statisti... [more] We propose two methods that reduce the post-nonlinear blind source separation problem (PNLBSS) 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 nonlinearities. 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.

• A Fast Algorithm for Joint Diagonalization with Non-orthogonal Transformations and its Application to Blind Source Separation.

  Andreas Ziehe, Pavel Laskov, Guido Nolte, Klaus-Robert Müller

  Journal of Machine Learning Research. 01/2004; 5:777-800.

• Blind Source Separation Techniques for Decomposing Event-Related Brain Signals.

  Klaus-Robert Müller, Ricardo Vigário, Frank C. Meinecke, Andreas Ziehe

  I. J. Bifurcation and Chaos. 01/2004; 14:773-791.

• Approximate Joint Diagonalization Using a Natural Gradient Approach.

  Arie Yeredor, Andreas Ziehe, Klaus-Robert Müller

  Independent Component Analysis and Blind Signal Separation, Fifth International Conference, ICA 2004, Granada, Spain, September 22-24, 2004, Proceedings; 01/2004

• Nonlinear Blind Source Separation Using Kernel Feature Spaces

  Stefan Harmeling, Andreas Ziehe, Motoaki Kawanabe, Benjamin Blankertz

  10/2003;

  In this work we propose a kernel-based blind source separation (BSS) algorithm that can perform nonlinear BSS for general invertible nonlinearities. For our kTDSEP algorithm we have to go through four steps: (i) adapting to the intrinsic dimension of the data mapped to feature space , (ii) finding a... [more] In this work we propose a kernel-based blind source separation (BSS) algorithm that can perform nonlinear BSS for general invertible nonlinearities. For our kTDSEP algorithm we have to go through four steps: (i) adapting to the intrinsic dimension of the data mapped to feature space , (ii) finding an orthonormal basis of this submanifold, (iii) mapping the data into the subspace of spanned by this orthonormal basis, and (iv) applying temporal decorrelation BSS (TDSEP) to the mapped data. After demixing we get a number of irrelevant components and the original sources. To find out which ones are the components of interest, we propose a criterion that allows to identify the original sources. The excellent performance of kTDSEP is demonstrated in experiments on nonlinearly mixed speech data.

• Optimizing Property Codes in Protein Data Reveals Structural Characteristics

  Andreas Ziehe, Hanspeter Herzel

  10/2003;

  We search for assignments of numbers to the amino acids (property codes) that maximize the autocorrelation function signal in given protein sequence data by an iterative method. Our method yields similar results to optimization with the related extended Jacobi method for joint diagonalization and st... [more] We search for assignments of numbers to the amino acids (property codes) that maximize the autocorrelation function signal in given protein sequence data by an iterative method. Our method yields similar results to optimization with the related extended Jacobi method for joint diagonalization and standard optimization tools.

• On-line Learning in Changing Environments with Applications in Supervised and Unsupervised Learning

  Noboru Murata, Motoaki Kawanabe, Andreas Ziehe

  10/2003;

  An adaptive on-line algorithm extending the learning of learning idea is proposed and theoretically motivated. Relying only on gradient ow information it can be applied to learning continuous functions or distributions, even when no explicit loss function is given and the Hessian is not available. T... [more] An adaptive on-line algorithm extending the learning of learning idea is proposed and theoretically motivated. Relying only on gradient ow information it can be applied to learning continuous functions or distributions, even when no explicit loss function is given and the Hessian is not available. The framework is applied for unsupervised and supervised learning. Its eciency is demonstrated for drifting and switching non-stationary blind separation tasks of acoustic signals. Furthermore applications to classi cation (USPS data set) and time-series prediction in changing environments are presented.

• Kernel Feature Spaces and

  Stefan Harmeling, Andreas Ziehe, Motoaki Kawanabe, Klaus-robert Mller

  10/2003;

  In kernel based learning the data is mapped to a kernel feature space of a dimension that corresponds to the number of training data points. In practice, however, the data forms a smaller submanifold in feature space, a fact that has been used e.g. by reduced set techniques for SVMs. We propose a ne... [more] In kernel based learning the data is mapped to a kernel feature space of a dimension that corresponds to the number of training data points. In practice, however, the data forms a smaller submanifold in feature space, a fact that has been used e.g. by reduced set techniques for SVMs. We propose a new mathematical construction that permits to adapt to the intrinsic dimension and to find an orthonormal basis of this submanifold.

• Blind Source Separation Techniques for

  Frank Meinecke, Andreas Ziehe

  10/2003;

  Recently blind source separation (BSS) methods have been highly successfully applied to biomedical data. This paper reviews the concept of BSS and demonstrates its usefulness in the context of eventrelated MEG measurements. In a rst experiment we apply BSS to artifact identi cation of raw MEG data a... [more] Recently blind source separation (BSS) methods have been highly successfully applied to biomedical data. This paper reviews the concept of BSS and demonstrates its usefulness in the context of eventrelated MEG measurements. In a rst experiment we apply BSS to artifact identi cation 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 elds. Here it is particularly important to monitor and thus avoid possible over tting 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.

• Decomposition Algorithms For Analysing Brain Signals

  Jens Kohlmorgen, Andreas Ziehe, Benjamin Blankertz

  10/2003;

  Analyzing biomedical data { e.g. from the brain { we encounter fundamental problems that lie largely in the elds of signal processing and machine learning. The current paper presents at rst a method to deal with non-stationary signals, subsequently the signal processing technique of independent comp... [more] Analyzing biomedical data { e.g. from the brain { we encounter fundamental problems that lie largely in the elds of signal processing and machine learning. The current paper presents at rst a method to deal with non-stationary signals, subsequently the signal processing technique of independent component analysis (ICA) is reviewed. We use EEG recordings of continuous auditory perception as illustration for the discussed algorithms.

• Assessing Reliability Of Ica Projections -- A Resampling Approach

  Frank Meinecke, Andreas Ziehe

  10/2003;

  When applying unsupervised learning techniques like ICA or temporal decorrelation for BSS, a key question is whether the discovered projections are reliable. In other words: can we give error bars or can we assess the quality of our separation ? We use resampling methods to tackle these questions an... [more] When applying unsupervised learning techniques like ICA or temporal decorrelation for BSS, a key question is whether the discovered projections are reliable. In other words: can we give error bars or can we assess the quality of our separation ? We use resampling methods to tackle these questions and show experimentally that our proposed variance estimations are strongly correlated to the separation error. We demonstrate that this reliability estimation can be used to choose an appropriate ICA-model, to enhance significantly the separation performance, and, most important, to mark the components that can really have a physical meaning. An application to data from an MEG -experiment underlines the usefulness of our approach.