Blind separation of auditory event-related brain responses into independent components

Averaged event-related potential (ERP) data recorded from the human scalp reveal electroencephalographic (EEG) activity that is reliably time-locked and phase-locked to experimental events. We report here the application of a method based on information theory that decomposes one or more ERPs recorded at multiple scalp sensors into a sum of components with fixed scalp distributions and sparsely activated, maximally independent time courses. Independent component analysis (ICA) decomposes ERP data into a number of components equal to the number of sensors. The derived components have distinct but not necessarily orthogonal scalp projections. Unlike dipole-fitting methods, the algorithm does not model the locations of their generators in the head. Unlike methods that remove second-order correlations, such as principal component analysis (PCA), ICA also minimizes higher-order dependencies. Applied to detected—and undetected—target ERPs from an auditory vigilance experiment, the algorithm derived ten components that decomposed each of the major response peaks into one or more ICA components with relatively simple scalp distributions. Three of these components were active only when the subject detected the targets, three other components only when the target went undetected, and one in both cases. Three additional components accounted for the steady-state brain response to a 39-Hz background click train. Major features of the decomposition proved robust across sessions and changes in sensor number and placement. This method of ERP analysis can be used to compare responses from multiple stimuli, task conditions, and subject states.

Spatially independent activity patterns in functional MRI data during the Stroop color-naming task

A method is given for determining the time course and spatial extent of consistently and transiently task-related activations from other physiological and artifactual components that contribute to functional MRI (fMRI) recordings. Independent component analysis (ICA) was used to analyze two fMRI data sets from a subject performing 6-min trials composed of alternating 40-sec Stroop color-naming and control task blocks. Each component consisted of a fixed three-dimensional spatial distribution of brain voxel values (a “map”) and an associated time course of activation. For each trial, the algorithm detected, without a priori knowledge of their spatial or temporal structure, one consistently task-related component activated during each Stroop task block, plus several transiently task-related components activated at the onset of one or two of the Stroop task blocks only. Activation patterns occurring during only part of the fMRI trial are not observed with other techniques, because their time courses cannot easily be known in advance. Other ICA components were related to physiological pulsations, head movements, or machine noise. By using higher-order statistics to specify stricter criteria for spatial independence between component maps, ICA produced improved estimates of the temporal and spatial extent of task-related activation in our data compared with principal component analysis (PCA). ICA appears to be a promising tool for exploratory analysis of fMRI data, particularly when the time courses of activation are not known in advance.

Application of principal component analysis in phase-shifting photoelasticity

Principal component analysis phase shifting (PCA) is a useful tool for fringe pattern demodulation in phase shifting interferometry. The PCA has no restrictions on background intensity or fringe modulation, and it is a self-calibrating phase sampling algorithm (PSA). Moreover, the technique is well suited for analyzing arbitrary sets of phase-shifted interferograms due to its low computational cost. In this work, we have adapted the standard phase shifting algorithm based on the PCA to the particular case of photoelastic fringe patterns. Compared with conventional PSAs used in photoelasticity, the PCA method does not need calibrated phase steps and, given that it can deal with an arbitrary number of images, it presents good noise rejection properties, even for complicated cases such as low order isochromatic photoelastic patterns. © 2016 Optical Society of America.

Characterization of spatial–temporal patterns in dynamic speckle sequences using principal component analysis

Abstract. Speckle is being used as a characterization tool for the analysis of the dynamics of slow-varying phenomena occurring in biological and industrial samples at the surface or near-surface regions. The retrieved data take the form of a sequence of speckle images. These images contain information about the inner dynamics of the biological or physical process taking place in the sample. Principal component analysis (PCA) is able to split the original data set into a collection of classes. These classes are related to processes showing different dynamics. In addition, statistical descriptors of speckle images are used to retrieve information on the characteristics of the sample. These statistical descriptors can be calculated in almost real time and provide a fast monitoring of the sample. On the other hand, PCA requires a longer computation time, but the results contain more information related to spatial–temporal patterns associated to the process under analysis. This contribution merges both descriptions and uses PCA as a preprocessing tool to obtain a collection of filtered images, where statistical descriptors are evaluated on each of them. The method applies to slow-varying biological and industrial processes.

Estadística Aplicada a los Recursos Marinos. PCA. Principal Component Analysis

Análisis multivariante de Componentes Principales (PCA)

Drying process of microcrystalline cellulose studied by attenuated total reflection IR spectroscopy with two-dimensional correlation spectroscopy and principal component analysis

Molecular interactions between microcrystalline cellulose (MCC) and water were investigated by attenuated total reflection infrared (ATR/IR) spectroscopy. Moisture-content-dependent IR spectra during a drying process of wet MCC were measured. In order to distinguish overlapping O–H stretching bands arising from both cellulose and water, principal component analysis (PCA) and, generalized two-dimensional correlation spectroscopy (2DCOS) and second derivative analysis were applied to the obtained spectra. Four typical drying stages were clearly separated by PCA, and spectral variations in each stage were analyzed by 2DCOS. In the drying time range of 0–41 min, a decrease in the broad band around 3390 cm−1 was observed, indicating that bulk water was evaporated. In the drying time range of 49–195 min, decreases in the bands at 3412, 3344 and 3286 cm−1 assigned to the O6H6cdots, three dots, centeredO3′ interchain hydrogen bonds (H-bonds), the O3H3cdots, three dots, centeredO5 intrachain H-bonds and the H-bonds in Iβ phase in MCC, respectively, were observed. The result of the second derivative analysis suggests that water molecules mainly interact with the O6H6cdots, three dots, centeredO3′ interchain H-bonds. Thus, the H-bonding network in MCC is stabilized by H-bonds between OH groups constructing O6H6cdots, three dots, centeredO3′ interchain H-bonds and water, and the removal of the water molecules induces changes in the H-bonding network in MCC.

Performance analysis using equivariant kernel density estimator in nonlinear mixture

This paper investigates the performance analysis of separation of mutually independent sources in nonlinear models. The nonlinear mapping constituted by an unsupervised linear mixture is followed by an unknown and invertible nonlinear distortion, are found in many signal processing cases. Generally, blind separation of sources from their nonlinear mixtures is rather difficult. We propose using a kernel density estimator incorporated with equivariant gradient analysis to separate the sources with nonlinear distortion. The kernel density estimator parameters of which are iteratively updated to minimize the output independence expressed as a mutual information criterion. The equivariant gradient algorithm has the form of nonlinear decorrelation to perform the convergence analysis. Experiments are proposed to illustrate these results.

Investigating the performance analysis of EASI algorithm and EKENS algorithm in nonlinear model

This paper investigates the performance of EASI algorithm and the proposed EKENS algorithm for linear and nonlinear mixtures. The proposed EKENS algorithm is based on the modified equivariant algorithm and kernel density estimation. Theory and characteristic of both the algorithms are discussed for blind source separation model. The separation structure of nonlinear mixtures is based on a nonlinear stage followed by a linear stage. Simulations with artificial and natural data demonstrate the feasibility and good performance of the proposed EKENS algorithm.

Probabilistic principal component analysis

Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based upon a probability model. In this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum-likelihood estimation of parameters in a latent variable model closely related to factor analysis. We consider the properties of the associated likelihood function, giving an EM algorithm for estimating the principal subspace iteratively, and discuss the advantages conveyed by the definition of a probability density function for PCA.

Probabilistic principal component analysis

Principal component analysis (PCA) is a ubiquitous technique for data analysis and processing, but one which is not based upon a probability model. In this paper we demonstrate how the principal axes of a set of observed data vectors may be determined through maximum-likelihood estimation of parameters in a latent variable model closely related to factor analysis. We consider the properties of the associated likelihood function, giving an EM algorithm for estimating the principal subspace iteratively, and discuss the advantages conveyed by the definition of a probability density function for PCA.

Evaluation of catalytic pyrolysis of cassava rhizome by principal component analysis

Rhizome of cassava plants (Manihot esculenta Crantz) was catalytically pyrolysed at 500 °C using analytical pyrolysis–gas chromatography/mass spectrometry (Py–GC/MS) method in order to investigate the relative effect of various catalysts on pyrolysis products. Selected catalysts expected to affect bio-oil properties were used in this study. These include zeolites and related materials (ZSM-5, Al-MCM-41 and Al-MSU-F type), metal oxides (zinc oxide, zirconium (IV) oxide, cerium (IV) oxide and copper chromite) catalysts, proprietary commercial catalysts (Criterion-534 and alumina-stabilised ceria-MI-575) and natural catalysts (slate, char and ashes derived from char and biomass). The pyrolysis product distributions were monitored using models in principal components analysis (PCA) technique. The results showed that the zeolites, proprietary commercial catalysts, copper chromite and biomass-derived ash were selective to the reduction of most oxygenated lignin derivatives. The use of ZSM-5, Criterion-534 and Al-MSU-F catalysts enhanced the formation of aromatic hydrocarbons and phenols. No single catalyst was found to selectively reduce all carbonyl products. Instead, most of the carbonyl compounds containing hydroxyl group were reduced by zeolite and related materials, proprietary catalysts and copper chromite. The PCA model for carboxylic acids showed that zeolite ZSM-5 and Al-MSU-F tend to produce significant amounts of acetic and formic acids.

Analysis of magnetoencephaoographic data as a nonlinear dynamical system

This thesis presents the results from an investigation into the merits of analysing Magnetoencephalographic (MEG) data in the context of dynamical systems theory. MEG is the study of both the methods for the measurement of minute magnetic flux variations at the scalp, resulting from neuro-electric activity in the neocortex, as well as the techniques required to process and extract useful information from these measurements. As a result of its unique mode of action - by directly measuring neuronal activity via the resulting magnetic field fluctuations - MEG possesses a number of useful qualities which could potentially make it a powerful addition to any brain researcher's arsenal. Unfortunately, MEG research has so far failed to fulfil its early promise, being hindered in its progress by a variety of factors. Conventionally, the analysis of MEG has been dominated by the search for activity in certain spectral bands - the so-called alpha, delta, beta, etc that are commonly referred to in both academic and lay publications. Other efforts have centred upon generating optimal fits of "equivalent current dipoles" that best explain the observed field distribution. Many of these approaches carry the implicit assumption that the dynamics which result in the observed time series are linear. This is despite a variety of reasons which suggest that nonlinearity might be present in MEG recordings. By using methods that allow for nonlinear dynamics, the research described in this thesis avoids these restrictive linearity assumptions. A crucial concept underpinning this project is the belief that MEG recordings are mere observations of the evolution of the true underlying state, which is unobservable and is assumed to reflect some abstract brain cognitive state. Further, we maintain that it is unreasonable to expect these processes to be adequately described in the traditional way: as a linear sum of a large number of frequency generators. One of the main objectives of this thesis will be to prove that much more effective and powerful analysis of MEG can be achieved if one were to assume the presence of both linear and nonlinear characteristics from the outset. Our position is that the combined action of a relatively small number of these generators, coupled with external and dynamic noise sources, is more than sufficient to account for the complexity observed in the MEG recordings. Another problem that has plagued MEG researchers is the extremely low signal to noise ratios that are obtained. As the magnetic flux variations resulting from actual cortical processes can be extremely minute, the measuring devices used in MEG are, necessarily, extremely sensitive. The unfortunate side-effect of this is that even commonplace phenomena such as the earth's geomagnetic field can easily swamp signals of interest. This problem is commonly addressed by averaging over a large number of recordings. However, this has a number of notable drawbacks. In particular, it is difficult to synchronise high frequency activity which might be of interest, and often these signals will be cancelled out by the averaging process. Other problems that have been encountered are high costs and low portability of state-of-the- art multichannel machines. The result of this is that the use of MEG has, hitherto, been restricted to large institutions which are able to afford the high costs associated with the procurement and maintenance of these machines. In this project, we seek to address these issues by working almost exclusively with single channel, unaveraged MEG data. We demonstrate the applicability of a variety of methods originating from the fields of signal processing, dynamical systems, information theory and neural networks, to the analysis of MEG data. It is noteworthy that while modern signal processing tools such as independent component analysis, topographic maps and latent variable modelling have enjoyed extensive success in a variety of research areas from financial time series modelling to the analysis of sun spot activity, their use in MEG analysis has thus far been extremely limited. It is hoped that this work will help to remedy this oversight.