This paper describes the background noise estimation technique of the tensor product expansion with absolute error (TPE-AE) to estimate multiple sources. The electroencephalogram (EEG) signal produced by the saccadic eye movement is adopted to analyze relationship between a brain function and a human activity. The electrooculogram (EOG) generated by eye movements yields significant problems for the EEG analysis. The denoising of EOG artifacts is important task to perform an accurate analysis. In this paper, the two types of TPE-AE are proposed to estimates EOG and other components in EEG during eye movement. One technique estimates two outer products using median filter based TPE-AE. The another technique uses a reference signal to separate the two sources. We show that the proposed method is effective to estimate and separate two sources in EEG.

We present a cascade neural network for blind source extraction. We propose a family of unconstrained optimization criteria, from which we derive a learning rule that can extract a single source signal from a linear mixture of source signals. To prevent the newly extracted source signal from being extracted again in the next processing unit, we propose another unconstrained optimization criterion that uses knowledge of this signal. From this criterion, we then derive a learning rule that deflates from the mixture the newly extracted signal. By virtue of blind extraction and deflation processing, the presented cascade neural network can cope with a practical case where the number of mixed signals is equal to or larger than the number of sources, with the number of sources not known in advance. We prove analytically that the proposed criteria both for blind extraction and deflation processing have no spurious equilibria. In addition, the proposed criteria do not require whitening of mixed signals. We also demonstrate the validity and performance of the presented neural network by computer simulation experiments.

Nonnegative matrix factorization (NMF) and its extensions such as Nonnegative Tensor Factorization (NTF) have become prominent techniques for blind sources separation (BSS), analysis of image databases, data mining and other information retrieval and clustering applications. In this paper we propose a family of efficient algorithms for NMF/NTF, as well as sparse nonnegative coding and representation, that has many potential applications in computational neuroscience, multi-sensory processing, compressed sensing and multidimensional data analysis. We have developed a class of optimized local algorithms which are referred to as Hierarchical Alternating Least Squares (HALS) algorithms. For these purposes, we have performed sequential constrained minimization on a set of squared Euclidean distances. We then extend this approach to robust cost functions using the alpha and beta divergences and derive flexible update rules. Our algorithms are locally stable and work well for NMF-based blind source separation (BSS) not only for the over-determined case but also for an under-determined (over-complete) case (i.e., for a system which has less sensors than sources) if data are sufficiently sparse. The NMF learning rules are extended and generalized for N-th order nonnegative tensor factorization (NTF). Moreover, these algorithms can be tuned to different noise statistics by adjusting a single parameter. Extensive experimental results confirm the accuracy and computational performance of the developed algorithms, especially, with usage of multi-layer hierarchical NMF approach [3].

Anomalous environmental electromagnetic (EM) radiation waves have been reported as the portents of earthquakes. Our study's goal is predicting earthquakes using EM radiation waves by detecting some anomalies. We have been measuring the Extremely Low Frequency (ELF) range EM radiation waves all over Japan. However, the recorded data contain signals unrelated to earthquakes. These signals, as noise, confound earthquake prediction efforts. In this paper, we propose an efficient method of global signal elimination and enhancement local signals using Independent Component Analysis (ICA). We evaluated the effectiveness of this method.

Spatio-temporal decorrelation is the task of eliminating correlations between associated signals in spatial domain as well as in time domain. In this paper, we present a simple but efficient adaptive algorithm for spatio-temporal decorrelation. For the task of spatio-temporal decorrelation, we consider a dynamic recurrent network and calculate the associated natural gradient for the minimization of an appropriate optimization function. The natural gradient based spatio-temporal decorrelation algorithm is applied to the task of blind deconvolution of linear single input multiple output (SIMO) system and its performance is compared to the spatio-temporal anti-Hebbian learning rule.

Magnetoencephalography (MEG) is a powerful and non-invasive technique for measuring human brain activity with a high temporal resolution. The motivation for studying MEG data analysis is to extract the essential features from measured data and represent them corresponding to the human brain functions. In this paper, a novel MEG data analysis method based on independent component analysis (ICA) approach with pre-processing and post-processing multistage procedures is proposed. Moreover, several kinds of ICA algorithms are investigated for analyzing MEG single-trial data which is recorded in the experiment of phantom. The analyzed results are presented to illustrate the effectiveness and high performance both in source decomposition by ICA approaches and source localization by equivalent current dipoles fitting method.

In this paper, we discuss a neural network approach for blind signal extraction of temporally correlated sources. Assuming autoregressive models of source signals, we propose a very simple neural network model and an efficient on-line adaptive algorithm that extract, from linear mixtures, a temporally correlated source with an arbitrary distribution, including a colored Gaussian source and a source with extremely low value (or even zero) of kurtosis. We then combine these extraction processing units with deflation processing units to extract such sources sequentially in a cascade fashion. Theory and simulations show that the proposed neural network successfully extracts all arbitrarily distributed, but temporally correlated source signals from linear mixtures.

In many applications of Independent Component Analysis (ICA) and Blind Source Separation (BSS) estimated sources signals and the mixing or separating matrices have some special structure or some constraints are imposed for the matrices such as symmetries, orthogonality, non-negativity, sparseness and specified invariant norm of the separating matrix. In this paper we present several algorithms and overview some known transformations which allows us to preserve several important constraints.

In this paper we consider blind source separation (BSS) problem of signals which are spatially uncorrelated of order four, but temporally correlated of order four (for instance speech or biomedical signals). For such type of signals we propose a new sufficient condition for separation using fourth order statistics, stating that the separation is possible, if the source signals have distinct normalized cumulant functions (depending on time delay). Using this condition we show that the BSS problem can be converted to a symmetric eigenvalue problem of a generalized cumulant matrix Z(4)(b) depending on L-dimensional parameter b, if this matrix has distinct eigenvalues. We prove that the set of parameters b which produce Z(4)(b) with distinct eigenvalues form an open subset of RL, whose complement has a measure zero. We propose a new separating algorithm which uses Jacobi's method for joint diagonalization of cumulant matrices depending on time delay. We empasize the following two features of this algorithm: 1) The optimal number of matrices for joint diago- nalization is 100-150 (established experimentally), which for large dimensional problems is much smaller than those of JADE; 2) It works well even if the signals from the above class are, additionally, white (of order two) with zero kurtosis (as shown by an example).

This paper addresses a maximum likelihood method for source separation in the case of overdetermined mixtures corrupted by additive white Gaussian noise. We consider an approximate likelihood which is based on the Laplace approximation and develop a natural gradient adaptation algorithm to find a local maximum of the corresponding approximate likelihood. We present a detailed mathematical derivation of the algorithm using the Lie group invariance. Useful behavior of the algorithm is verified by numerical experiments.

In this paper we develop a new family of on-line adaptive learning algorithms for blind separation of time delayed and convolved sources. The algorithms are derived for feedforward and fully connected feedback (recurrent) neural networks on basis of modified natural gradient approach. The proposed algorithms can be considered as generalization and extension of existing algorithms for instantaneous mixture of unknown source signals. Preliminary computer simulations confirm validity and high performance of the proposed algorithms.

This paper presents novel techniques for blind separation and blind extraction of instantaneously mixed binary sources, which are suitable for the case with less sensors than sources. First, a solvability analysis is presented for a general case. Necessary and sufficient conditions for recoverability of all or some part of sources are derived. A new deterministic blind separation algorithm is then proposed to estimate the mixing matrix and separate all sources efficiently in the noise-free or low noise level case. Next, using the Maximum Likelihood (ML) approach for robust estimation of centers of clusters, we have extended the algorithm for high additive noise case. Moreover, a new sequential blind extraction algorithm has been developed, which enables us not only to extract the potentially separable sources but also estimate their number. The sources can be extracted in a specific order according to their dominance (strength) in the mixtures. At last, simulation results are presented to illustrate the validity and high performance of the algorithms.

Gray scale images are represented by recurrent neural subnetworks which together with a competition layer create an associative memory. The single recurrent subnetwork Ni implements a stochastic nonlinear fractal operator Fi, constructed for the given image fi. We show that under realstic assumptions F has a unique attractor which is located in the vicinity of the original image. Therefore one subnetwork represents one original image. The associative recall is implemented in two stages. Firstly, the competition layer finds the most invariant subnetwork for the given input noisy image g. Next, the selected recurrent subnetwork in few (5-10) global iterations produces high quality approximation of the original image. The degree of invariance for the subnetwork Ni on the inprt g is measured by a norm ||g-Fi(g)||. We have experimentally verified that associative recall for images of natural scenes with pixel values in [0, 255] is successful even when Gaussian noise has the standard deviation σ as large as 500. Moreover, the norm, computed only on 10% of pixels chosen randomly from images still successfuly recalls a close approximation of original image. Comparing to Amari-Hopfield associative memory, our solution has no spurious states, is less sensitive to noise, and its network complexity is significantly lower. However, for each new stored image a new subnetwork must be added.