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Due to the volume conduction multichannel electroencephalogram (EEG) recordings give a rather blurred image of brain activity. Therefore spatial filters are extremely useful in single-trial analysis in order to improve the signal-to-noise ratio. There are powerful methods from machine learning and signal processing that permit the optimization of(More)
We propose a method for the classification of matrices. We use a linear classifier with a novel regularization scheme based on the spectral <i>l</i><inf>1</inf>-norm of its coefficient matrix. The spectral regularization not only provides a principled way of complexity control but also enables automatic determination of the rank of the coefficient matrix.(More)
We propose a framework for signal analysis of electroencephalography (EEG) that unifies tasks such as feature extraction, feature selection, feature combination, and classification, which are often independently tackled conventionally, under a regularized empirical risk minimization problem. The features are automatically learned, selected and combined(More)
We study a new class of structured Schatten norms for tensors that includes two recently proposed norms (" overlapped " and " latent ") for convex-optimization-based tensor decomposition. Based on the properties of the structured Schatten norms, we analyze the performance of " latent " approach for tensor decomposition, which was empirically found to(More)
Generative neural samplers are probabilistic models that implement sampling using feedforward neural networks: they take a random input vector and produce a sample from a probability distribution defined by the network weights. These models are expressive and allow efficient computation of samples and derivatives, but cannot be used for computing(More)
The variational Bayesian (VB) approximation is known to be a promising approach to Bayesian estimation, when the rigorous calculation of the Bayes posterior is intractable. The VB approximation has been successfully applied to matrix factorization (MF), offering automatic dimensionality selection for principal component analysis. Generally, finding the VB(More)
Brain-Computer Interfaces can suffer from a large variance of the subject conditions within and across sessions. For example vigilance fluctuations in the individual , variable task involvement, workload etc. alter the characteristics of EEG signals and thus challenge a stable BCI operation. In the present work we aim to define features based on a variant(More)
We propose a novel approach to solving the electro-/magnetoencephalographic (EEG/MEG) inverse problem which is based upon a decomposition of the current density into a small number of spatial basis fields. It is designed to recover multiple sources of possibly different extent and depth, while being invariant with respect to phase angles and rotations of(More)
We propose a novel technique to assess functional brain connectivity in electroencephalographic (EEG)/magnetoencephalographic (MEG) signals. Our method, called sparsely connected sources analysis (SCSA), can overcome the problem of volume conduction by modeling neural data innovatively with the following ingredients: 1) the EEG/MEG is assumed to be a linear(More)
We analyze the statistical performance of a recently proposed convex tensor decomposition algorithm. Conventionally tensor decomposition has been formulated as non-convex optimization problems, which hindered the analysis of their performance. We show under some conditions that the mean squared error of the convex method scales linearly with the quantity we(More)