We present an algorithm, AROFAC2, which detects the (CP-)rank of a degree 3 tensor and calculates its factorization into rank-one components. We provide generative conditions for the algorithm to work and demonstrate on both synthetic and real world data that AROFAC2 is a potentially outperforming alternative to the gold standard PARAFAC over which it has the advantages that it can intrinsically detect the true rank, avoids spurious components, and is stable with respect to outliers and non-Gaussian noise.

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''.

The Multiple Signal Classification (MUSIC) algorithm for acoustic imaging most commonly assumes that all sources have undirectional radiation pattern. We here propose a modification of this algorithm such that the concept is applicable for arbitrary directional characteristics of the sources. This is accomplished by fitting for each frequency the real valued amplitudes of the acoustic model rather than assuming a fixed functional form. The mathematical problem can be solved analytically resulting in an eigenvalue problem of a real valued Hamiltonian matrix. The performance is illustrated in simulations using pure monopolar, dipolar and quadrupolar sources.

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.

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.

We propose kTDSEP, a kernel-based algorithm for nonlinear blind source separation (BSS). It combines complementary research fields: kernel feature spaces and BSS using temporal information. This yields an efficient algorithm for nonlinear BSS with invertible nonlinearity. Key assumptions are that the kernel feature space is chosen rich enough to approximate the nonlinearity and that signals of interest contain temporal information. Both assumptions are fulfilled for a wide set of real-world applications. The algorithm works as follows: First, the data are (implicitly) mapped to a high (possibly infinite)—dimensional kernel feature space. In practice, however, the data form a smaller submanifold in feature space—even smaller than the number of training data points—a fact that has already been used by, for example, reduced set techniques for support vector machines. We propose to adapt to this effective dimension as a preprocessing step and to construct an orthonormal basis of this submanifold. The latter dimension-reduction step is essential for making the subsequent application of BSS methods computationally and numerically tractable. In the reduced space, we use a BSS algorithm that is based on second-order temporal decorrelation. Finally, we propose a selection procedure to obtain the original sources from the extracted nonlinear components automatically. Experiments demonstrate the excellent performance and efficiency of our kTDSEP algorithm for several problems of nonlinear BSS and for more than two sources.

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.

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.

We present methods to separate blindly mixed signals recorded in a room. The learning algorithm is based on the information maximization in a single layer neural network. We focus on the implementation of the learning algorithm and on issues that arise when separating speakers in room recordings. We used an infomax approach in a feedforward neural network implemented in the frequency domain using the polynomial filter matrix algebra technique. A fast convergence speed was achieved by using a time-delayed decorrelation method as a preprocessing step. Under minimum-phase mixing conditions this preprocessing step was sufficient for the separation of signals. These methods successfully separated a recorded voice with music in the background (cocktail party problem). Finally, we discuss problems that arise in real world recordings and their potential solutions.