Author name cluster

Andreas Ziehe

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

10 papers

1 author row

NeurIPS Conference 2012 Conference Paper

Learning Invariant Representations of Molecules for Atomization Energy Prediction

Grégoire Montavon
Katja Hansen
Siamac Fazli
Matthias Rupp
Franziska Biegler
Andreas Ziehe
Alexandre Tkatchenko
Anatole Lilienfeld

The accurate prediction of molecular energetics in chemical compound space is a crucial ingredient for rational compound design. The inherently graph-like, non-vectorial nature of molecular data gives rise to a unique and difficult machine learning problem. In this paper, we adopt a learning-from-scratch approach where quantum-mechanical molecular energies are predicted directly from the raw molecular geometry. The study suggests a benefit from setting flexible priors and enforcing invariance stochastically rather than structurally. Our results improve the state-of-the-art by a factor of almost three, bringing statistical methods one step closer to the holy grail of ''chemical accuracy''.

PDF Details

YNIMG Journal 2008 Journal Article

Combining sparsity and rotational invariance in EEG/MEG source reconstruction

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

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.

Details DOI

NeurIPS Conference 2008 Conference Paper

Estimating vector fields using sparse basis field expansions

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

We introduce a novel framework for estimating vector fields using sparse basis field expansions (S-FLEX). The notion of basis fields, which are an extension of scalar basis functions, arises naturally in our framework from a rotational invariance requirement. We consider a regression setting as well as inverse problems. All variants discussed lead to second-order cone programming formulations. While our framework is generally applicable to any type of vector field, we focus in this paper on applying it to solving the EEG/MEG inverse problem. It is shown that significantly more precise and neurophysiologically more plausible location and shape estimates of cerebral current sources from EEG/MEG measurements become possible with our method when comparing to the state-of-the-art.

PDF Details

NeurIPS Conference 2005 Conference Paper

Analyzing Coupled Brain Sources: Distinguishing True from Spurious Interaction

Guido Nolte
Andreas Ziehe
Frank Meinecke
Klaus-Robert Müller

When trying to understand the brain, it is of fundamental importance to analyse (e. g. from EEG/MEG measurements) what parts of the cortex interact with each other in order to infer more accurate models of brain activity. Common techniques like Blind Source Separation (BSS) can estimate brain sources and single out artifacts by using the underlying assumption of source signal independence. However, physiologically interesting brain sources typically interact, so BSS will--by construction-- fail to characterize them properly. Noting that there are truly interacting sources and signals that only seemingly interact due to effects of volume conduction, this work aims to contribute by distinguishing these effects. For this a new BSS technique is proposed that uses anti-symmetrized cross-correlation matrices and subsequent diagonalization. The resulting decomposition consists of the truly interacting brain sources and suppresses any spurious interaction stemming from volume conduction. Our new concept of interacting source analysis (ISA) is successfully demonstrated on MEG data.

PDF Details

JMLR Journal 2004 Journal Article

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

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. [abs] [ pdf ] [ ps.gz ] [ ps ]

PDF Details

JMLR Journal 2003 Journal Article

Blind Separation of Post-nonlinear Mixtures using Linearizing Transformations and Temporal Decorrelation

Andreas Ziehe
Motoaki Kawanabe
Stefan Harmeling
Klaus-Robert Müller

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 non-parametric statistics---to approximately invert the componentwise non-linear 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. [abs] [ pdf ][ ps.gz ][ ps ]

PDF Details

NeurIPS Conference 2001 Conference Paper

Estimating the Reliability of ICA Projections

Frank Meinecke
Andreas Ziehe
Motoaki Kawanabe
Klaus-Robert Müller

When applying unsupervised learning techniques like ICA or tem(cid: 173) poral decorrelation, a key question is whether the discovered pro(cid: 173) jections are reliable. In other words: can we give error bars or can we assess the quality of our separation? We use resampling meth(cid: 173) ods to tackle these questions and show experimentally that our proposed variance estimations are strongly correlated to the sepa(cid: 173) ration error. We demonstrate that this reliability estimation can be used to choose the appropriate ICA-model, to enhance signifi(cid: 173) cantly the separation performance, and, most important, to mark the components that have a actual physical meaning. Application to 49-channel-data from an magneto encephalography (MEG) ex(cid: 173) periment underlines the usefulness of our approach.

PDF Details

NeurIPS Conference 2001 Conference Paper

Kernel Feature Spaces and Nonlinear Blind Souce Separation

Stefan Harmeling
Andreas Ziehe
Motoaki Kawanabe
Klaus-Robert Müller

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 in- trinsic dimension and to ﬁnd an orthonormal basis of this submanifold. In doing so, computations get much simpler and more important our theoretical framework allows to derive elegant kernelized blind source separation (BSS) algorithms for arbitrary invertible nonlinear mixings. Experiments demonstrate the good performance and high computational efﬁciency of our kTDSEP algorithm for the problem of nonlinear BSS.

PDF Details

NeurIPS Conference 1999 Conference Paper

Unmixing Hyperspectral Data

Lucas Parra
Clay Spence
Paul Sajda
Andreas Ziehe
Klaus-Robert Müller

In hyperspectral imagery one pixel typically consists of a mixture of the reflectance spectra of several materials, where the mixture coefficients correspond to the abundances of the constituting ma(cid: 173) terials. We assume linear combinations of reflectance spectra with some additive normal sensor noise and derive a probabilistic MAP framework for analyzing hyperspectral data. As the material re(cid: 173) flectance characteristics are not know a priori, we face the problem of unsupervised linear unmixing. The incorporation of different prior information (e. g. positivity and normalization of the abun(cid: 173) dances) naturally leads to a family of interesting algorithms, for example in the noise-free case yielding an algorithm that can be understood as constrained independent component analysis (ICA). Simulations underline the usefulness of our theory.

PDF Details

NeurIPS Conference 1996 Conference Paper

Adaptive On-line Learning in Changing Environments

Noboru Murata
Klaus-Robert Müller
Andreas Ziehe
Shun-ichi Amari

An adaptive on-line algorithm extending the learning of learning idea is proposed and theoretically motivated. Relying only on gra(cid: 173) dient flow information it can be applied to learning continuous functions or distributions, even when no explicit loss function is gi(cid: 173) ven and the Hessian is not available. Its efficiency is demonstrated for a non-stationary blind separation task of acoustic signals.

PDF Details