A semi-parametric hybrid neural model for nonlinear blind signal separation

Nonlinear blind signal separation is an important but rather difficult problem. Any general nonlinear independent component analysis algorithm for such a problem should specify which solution it tries to find. Several recent neural networks for separating the post nonlinear blind mixtures are limited to the diagonal nonlinearity, where there is no cross-channel nonlinearity. In this paper, a new semi-parametric hybrid neural network is proposed to separate the post nonlinearly mixed blind signals where cross-channel disturbance is included. This hybrid network consists of two cascading modules, which are a neural nonlinear module for approximating the post nonlinearity and a linear module for separating the predicted linear blind mixtures. The nonlinear module is a semi-parametric expansion made up of two sub-networks, one of which is a linear model and the other of which is a three-layer perceptron. These two sub-networks together produce a "weak" nonlinear operator and can approach relatively strong nonlinearity by tuning parameters. A batch learning algorithm based on the entropy maximization and the gradient descent method is deduced. This model is successfully applied to a blind signal separation problem with two sources. Our simulation results indicate that this hybrid model can effectively approach the cross-channel post nonlinearity and achieve a good visual quality as well as a high signal-to-noise ratio in some cases.     

Advances in blind source separation (BSS) and independent component analysis (ICA) for nonlinear mixtures

In this paper, we review recent advances in blind source separation (BSS) and independent component analysis (ICA) for nonlinear mixing models. After a general introduction to BSS and ICA, we discuss in more detail uniqueness and separability issues, presenting some new results. A fundamental difficulty in the nonlinear BSS problem and even more so in the nonlinear ICA problem is that they provide non-unique solutions without extra constraints, which are often implemented by using a suitable regularization. In this paper, we explore two possible approaches. The first one is based on structural constraints. Especially, post-nonlinear mixtures are an important special case, where a nonlinearity is applied to linear mixtures. For such mixtures, the ambiguities are essentially the same as for the linear ICA or BSS problems. The second approach uses Bayesian inference methods for estimating the best statistical parameters, under almost unconstrained models in which priors can be easily added. In the later part of this paper, various separation techniques proposed for post-nonlinear mixtures and general nonlinear mixtures are reviewed.     

Flexible nonlinear blind signal separation in the complex domain

This paper introduces an Independent Component Analysis (ICA) approach to the separation of nonlinear mixtures in the complex domain. Source separation is performed by a complex INFOMAX approach. The neural network which realizes the separation employs the so called "Mirror Model" and is based on adaptive activation functions, whose shape is properly modified during learning. Nonlinear functions involved in the processing of complex signals are realized by pairs of spline neurons called "splitting functions", working on the real and the imaginary part of the signal respectively. Theoretical proof of existence and uniqueness of the solution under proper assumptions is also provided. In particular a simple adaptation algorithm is derived and some experimental results that demonstrate the effectiveness of the proposed solution are shown.     

The distressed brain: a group blind source separation analysis on tinnitus

Background

Tinnitus, the perception of a sound without an external sound source, can lead to variable amounts of distress.

Methodology

In a group of tinnitus patients with variable amounts of tinnitus related distress, as measured by the Tinnitus Questionnaire (TQ), an electroencephalography (EEG) is performed, evaluating the patients'' resting state electrical brain activity. This resting state electrical activity is compared with a control group and between patients with low (N = 30) and high distress (N = 25). The groups are homogeneous for tinnitus type, tinnitus duration or tinnitus laterality. A group blind source separation (BSS) analysis is performed using a large normative sample (N = 84), generating seven normative components to which high and low tinnitus patients are compared. A correlation analysis of the obtained normative components'' relative power and distress is performed. Furthermore, the functional connectivity as reflected by lagged phase synchronization is analyzed between the brain areas defined by the components. Finally, a group BSS analysis on the Tinnitus group as a whole is performed.

Conclusions

Tinnitus can be characterized by at least four BSS components, two of which are posterior cingulate based, one based on the subgenual anterior cingulate and one based on the parahippocampus. Only the subgenual component correlates with distress. When performed on a normative sample, group BSS reveals that distress is characterized by two anterior cingulate based components. Spectral analysis of these components demonstrates that distress in tinnitus is related to alpha and beta changes in a network consisting of the subgenual anterior cingulate cortex extending to the pregenual and dorsal anterior cingulate cortex as well as the ventromedial prefrontal cortex/orbitofrontal cortex, insula, and parahippocampus. This network overlaps partially with brain areas implicated in distress in patients suffering from pain, functional somatic syndromes and posttraumatic stress disorder, and might therefore represent a specific distress network.     

Blind source separation methods for deconvolution of complex signals in cancer biology

Two blind source separation methods (Independent Component Analysis and Non-negative Matrix Factorization), developed initially for signal processing in engineering, found recently a number of applications in analysis of large-scale data in molecular biology. In this short review, we present the common idea behind these methods, describe ways of implementing and applying them and point out to the advantages compared to more traditional statistical approaches. We focus more specifically on the analysis of gene expression in cancer. The review is finalized by listing available software implementations for the methods described.     

Rival Penalized Competitive Learning based approach for discrete-valued source separation

This paper presents an approach based on Rival Penalized Competitive Learning (RPCL) rules for discrete-valued source separation. In this approach, we first build a connection between the source number and the cluster number of observations. Then, we use the RPCL rule to automatically find out the correct number of clusters such that the source number is determined. Moreover, we tune the de-mixing matrix based on the cluster centers instead of the observation themselves, whereby the noise interference is considerably reduced. The experiments have shown that this new approach not only quickly and automatically determines the number of sources, but also is insensitive to the noise in performing blind source separation.     

Least-squares methods for identifying biochemical regulatory networks from noisy measurements

Background  

We consider the problem of identifying the dynamic interactions in biochemical networks from noisy experimental data. Typically, approaches for solving this problem make use of an estimation algorithm such as the well-known linear Least-Squares (LS) estimation technique. We demonstrate that when time-series measurements are corrupted by white noise and/or drift noise, more accurate and reliable identification of network interactions can be achieved by employing an estimation algorithm known as Constrained Total Least Squares (CTLS). The Total Least Squares (TLS) technique is a generalised least squares method to solve an overdetermined set of equations whose coefficients are noisy. The CTLS is a natural extension of TLS to the case where the noise components of the coefficients are correlated, as is usually the case with time-series measurements of concentrations and expression profiles in gene networks.     

Testing of instantaneity hypothesis for blind source separation of extensor indicis and extensor digiti minimi surface electromyograms

Human muscle activity can be assessed with surface electromyography (SEMG). Depending on electrode location and size, the recording volume under the sensor is likely to measure electrical potentials emanating from muscles other than the muscle of interest. This crosstalk issue makes interpretation of SEMG data difficult. The purpose of this paper was to study a crosstalk reduction technique called blind source separation (BSS). Most straightforward separation techniques rely on linearity and instantaneity (LI) of signal mixtures on the sensors. Literature on BSS for SEMG often makes hypothesis of linearity and instantaneity of the mixing model. Using simulation of SEMG mixtures and real SEMG recordings on the human extensor indicis (EI) and extensor digiti minimi (EDM) muscles during a task consisting of selective successive activations of EI and EDM muscles, cross-correlation between the sensors was proven to be directly dependent on instantaneity of the sources. Instantaneity hypothesis testing on real SEMG recordings showed that source instantaneity hypothesis is very sensitive to electrode location along the fibers direction. Source separation gains using JADE BSS algorithm depend strongly on instantaneity hypothesis. Using LI BSS on SEMG requires great attention to electrode positioning; we provide a tool to test these on EI/EDM muscles.     

pcaMethods--a bioconductor package providing PCA methods for incomplete data

pcaMethods is a Bioconductor compliant library for computing principal component analysis (PCA) on incomplete data sets. The results can be analyzed directly or used to estimate missing values to enable the use of missing value sensitive statistical methods. The package was mainly developed with microarray and metabolite data sets in mind, but can be applied to any other incomplete data set as well. AVAILABILITY: http://www.bioconductor.org     

PCA based population generation for genetic network optimization

A gene regulatory network (GRN) represents a set of genes and its regulatory interactions. The inference of the regulatory interactions between genes is usually carried out using an appropriate mathematical model and the available gene expression profile. Among the various models proposed for GRN inference, our recently proposed Michaelis–Menten based ODE model provides a good trade-off between the computational complexity and biological relevance. This model, like other known GRN models, also uses an evolutionary algorithm for parameter estimation. Considering various issues associated with such population based stochastic optimization approaches (e.g. diversity, premature convergence due to local optima, accuracy, etc.), it becomes important to seed the initial population with good individuals which are closer to the optimal solution. In this paper, we exploit the inherent strength of principal component analysis (PCA) in a novel manner to initialize the population for GRN optimization. The benefit of the proposed method is validated by reconstructing in silico and in vivo networks of various sizes. For the same level of accuracy, the approach with PCA based initialization shows improved convergence speed.     

Methods for cell separation based on sedimentation

Summary A modified Erlenmeyer flask and a sedimentation chamber have been used for separation of cells from suspension. Preliminary investigations show an efficiency in the separation of more than 80% with yeast cells. Fermentations with the Erlenmeyer flask as separator show a 4–5 times increased cell density for both hybridomas and yeast cells.     

Inverse diffusion methods for data peak separation

Previous methods for separation of overlapping data peaks include geometrical assessment and Fourier deconvolution. On the basis of inverse diffusion theory, we present new separation methods suitable for convenient programming and rapid calculation of Gaussian area contributions. Both continuum and discrete inverse diffusion models are described. Example computations are given for biological data: density gradient centrifugation, isoelectric focusing electrophoresis, and high-pressure liquid chromatography.     

A new method for the extraction of fetal ECG from the dependent abdominal signals using blind source separation and adaptive noise cancellation techniques

Background

The electrocardiogram (ECG) is a diagnostic tool that records the electrical activity of the heart, and depicts it as a series of graph-like tracings, or waves. Being able to interpret these details allows diagnosis of a wide range of heart problems. Fetal electrocardiogram (FECG) extraction has an important impact in medical diagnostics during the mother pregnancy period. Since the observed FECG signals are often mixed with the maternal ECG (MECG) and the noise induced by the movement of electrodes or by mother motion, the separation process of the ECG signal sources from the observed data becomes quite complicated. One of its complexity is when the ECG sources are dependent, thus, in this paper we introduce a new approach of blind source separation (BSS) in the noisy context for both independent and dependent ECG signal source. This approach consist in denoising the observed ECG signals using a bilateral total variation (BTV) filter; then minimizing the Kullbak-Leibler divergence between copula densities to separate the FECG signal from the MECG one.

Results

We present simulation results illustrating the performance of our proposed method. We will consider many examples of independent/dependent source component signals. The results will be compared with those of the classical method called independent component analysis (ICA) under the same conditions. The accuracy of source estimation is evaluated through a criterion, called again the signal-to-noise-ratio (SNR). The first experiment shows that our proposed method gives accurate estimation of sources in the standard case of independent components, with performance around 27 dB in term of SNR. In the second experiment, we show the capability of the proposed algorithm to successfully separate two noisy mixtures of dependent source components - with classical criterion devoted to the independent case - fails, and that our method is able to deal with the dependent case with good performance.

Conclusions

In this work, we focus specifically on the separation of the ECG signal sources taken from skin two electrodes located on a pregnant woman’s body. The ECG separation is interpreted as a noisy linear BSS problem with instantaneous mixtures. Firstly, a denoising step is required to reduce the noise due to motion artifacts using a BTV filter as a very effective one-pass filter for denoising. Then, we use the Kullbak-Leibler divergence between copula densities to separate the fetal heart rate from the mother one, for both independent and dependent cases.

     

Improved methods for separation of human cytokeratins.

The cytokeratins from human bladder and esophageal epithelia were separated using chromatographic techniques. The cytokeratins were first extracted from fresh autopsy tissue using high and low salt buffers. Urea, 8.0-9.5 M, was used to solubilize the resulting cytokeratin pellet. Imidazole was found to increase the solubility of the pellet but reducing agents such as 2-mercaptoethanol were not beneficial. DEAE ion exchange chromatography produced three fractions which were analyzed by using one and two-dimensional electrophoresis. The third fraction was shown to contain the acidic cytokeratins and was further fractionated on a moderately polar reverse phase HPLC column using an acetonitrile elution gradient. Tetramethylammonium tetrafluoroborate was added to the mobile phase to react with any unreacted silanol groups on the stationary phase, and trifluoroacetic acid was added to ion pair with the protein. HPLC fractions of the acidic proteins from human esophagus revealed seven reproducible peaks. All seven peaks were shown by Western blotting to contain an epitope found on cytokeratin 13. The results suggest that the isolation and separation procedures have produced a series of peptide products which all retain a similar epitope but which vary significantly in their hydrophobic characteristics.     

A linear framework for time-scale separation in nonlinear biochemical systems

Cellular physiology is implemented by formidably complex biochemical systems with highly nonlinear dynamics, presenting a challenge for both experiment and theory. Time-scale separation has been one of the few theoretical methods for distilling general principles from such complexity. It has provided essential insights in areas such as enzyme kinetics, allosteric enzymes, G-protein coupled receptors, ion channels, gene regulation and post-translational modification. In each case, internal molecular complexity has been eliminated, leading to rational algebraic expressions among the remaining components. This has yielded familiar formulas such as those of Michaelis-Menten in enzyme kinetics, Monod-Wyman-Changeux in allostery and Ackers-Johnson-Shea in gene regulation. Here we show that these calculations are all instances of a single graph-theoretic framework. Despite the biochemical nonlinearity to which it is applied, this framework is entirely linear, yet requires no approximation. We show that elimination of internal complexity is feasible when the relevant graph is strongly connected. The framework provides a new methodology with the potential to subdue combinatorial explosion at the molecular level.     

New methods for separation and recovery of biomolecules.

New methods and applications in the separation of biomolecules are reviewed, with an emphasis on the large-scale recovery of proteins. Highlights include the advent of flow-through particles in perfusion chromatography, which allows for very high flow rates, while retaining a high chromatographic efficiency.