Approximate Rank-Detecting Factorization of Low-Rank Tensors

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

Learning with Algebraic Invariances, and the Invariant Kernel Trick

When solving data analysis problems it is important to integrate prior knowledge and/or structural invariances. This paper contributes by a novel framework for incorporating algebraic invariance structure into kernels. In particular, we show that algebraic properties such as sign symmetries in data, phase independence, scaling etc. can be included easily by essentially performing the kernel trick twice. We demonstrate the usefulness of our theory in simulations on selected applications such as sign-invariant spectral clustering and underdetermined ICA

Robustly estimating the flow direction of information in complex physical systems

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 figure

TDSEP - an efficient algorithm for blind separation using time structure

An algorithm for blind source separation based on several time-delayed second-order correlation matrices is proposed. The technique to construct the unmixing matrix employs first a whitening step and then an approximate simultaneous diagonalisation of several time-delayed second-order correlation matrices. Its efficiency and stability are demonstrated for linear artificial mixtures with 17 sources. 1 Introduction Blind source separation is an increasingly popular data analysis technique. It has been applied successfully to the so called cocktail party problem (e.g. [9, 3, 2, 5, 7, 12, 1]) and to various problems in biomedical data processing (e.g. [10, 13, 14]). Usually it is assumed that the observed signals x are constituted of linearly mixed sources s, which are unknown, but mutually statistically independent. x i (t) = n X j=1 a ij s j (t) 1 i; j n i:e: x = As: (1) Since neither s nor the mixing process A are known and we have to estimate the inverse C of the mixing matrix b..

An Approach to Blind Source Separation Based on Temporal Structure of Speech Signals

In this paper we introduce a new technique for blind source separation of speech signals. We focus on the temporal structure of the signals in contrast to most other major approaches to this problem. The idea is to apply the decorrelation method proposed by Molgedey and Schuster in the time-frequency domain. We show some results of experiments with both artificially controlled data and speech data recorded in the real environment

JADE TD : Combining Higher-Order Statistics And Temporal Information For Blind Source Separation (with Noise)

So far blind separation algorithms have been either using information from higher order statistics or from time structure in the data. We propose the use of an error function that merges both types of information and obtain the JADE TD algorithm. This way we combine the virtues of both ingredients: the TDSEP and the JADE algorithm. We investigate the performance and usefulness of the new algorithm in several experimental scenarios. A particularly interesting scenario is the robustness of blind separation in the presence of noise, where the measuring noise effectively doubles the number of sources and therefore leads to large separation errors for blind separation algorithms. To still allow for separation in the presence of noise, we propose to use time delayed covariance matrices for the whitening step and for the estimation of the subsequent rotation step, accordingly, also delayed cumulant information is taken into account. This technique makes use of the fact that the autocorrelatio..

Blind separation of post-nonlinear mixtures using gaussianizing transformations and temporal decorrelation

At the previous workshop (ICA2001) we proposed the ACE-TD method that reduces the post-nonlinear blind source separation problem (PNL BSS) to a linear BSS problem [18]. The method utilizes the Alternating Conditional Expectation (ACE) algorithm to approximately invert the (post-)nonlinear functions. In this contribution, we propose an alternative procedure called 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 yields similar results as the ACE method and can thus be used as a fast and effective equalization method. After equalizing the nonlinearities, temporal decorrelation separation (TDSEP) allows us to recover the source signals. Numerical simulations on realistic examples are performed to compare “Gauss-TD ” with “ACE-TD”. 1

Artifact Reduction in magnetoneurography . . .

Artifacts in magnetoneurography (MNG) data due to endogenous biological noise sources, e.g. heart signal, can be four orders of magnitude higher than the signal of interest. Therefore it is important to establish effective artifact reduction methods. We propose a blind source separation algorithm using only second order temporal correlations for cleaning bio-magnetic measurements of evoked responses in the peripheral nervous system. The algorithm showed its efficiency by eliminating disturbances originating from biological and technical noise sources and successfully extracting the signal of interest. This yields a significant improvement of the neuro-magnetic source analysis

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

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