Mean Field Independent Component Analysis Research Articles

Multiple adulterants detection in turmeric powder using Vis-SWNIR hyperspectral imaging followed by multivariate curve resolution and classification techniques

In the present contribution, visible and short wavelengths of near infrared hyperspectral imaging (Vis-SWNIR-HSI) combined with different chemometric techniques is proposed as a novel technique for turmeric authentication and multiple adulterants (corn flour, rice flour, starch, wheat flour, and zedoary) detection. In this regard, twenty-three samples of turmeric were collected as whole rhizomes or powdered from seven countries and then their VIS-SWNIR hyperspectral images were obtained in 400–1000 nm using SPECIM IQ HSI device. Two multivariate resolution techniques of multivariate curve resolution-alternating least squares (MCR-ALS) and mean-field independent component analysis (MF-ICA) were used to extract pure spatial and spectral profiles of the components, and their results were compared by projecting their solutions in the area of feasible solutions (AFSs). Then, the distribution maps of turmeric component obtained using MCR-ALS and MF-ICA were used for authentication. Principal component analysis (PCA) was used to find the pattern of authentic samples using their distribution maps. Additionally, data-driven soft independent modeling of class analogy (DD-SIMCA) was employed to find boundary between authentic and adulterated turmeric samples. On this matter, good class modelling results with sensitivity of 95 % and specificity of 100 % were obtained. Finally, partial least squares-discriminant analysis (PLS-DA) was utilized for discrimination of the of adulternats and their in binary and multi-class classification modes. On this matter, PLS-DA accuracies were acceptable for binary and mixed samples which confirmed the validity of the proposed method.

Mutual information map as a new way for exploring the independence of chemically meaningful solutions in two-component analytical data

In the present contribution, a new approach based on mutual information (MI) is proposed for exploring the independence of feasible solutions in two component systems. Investigating how independent are different feasible solutions can be a way to bridge the gap between independent component analysis (ICA) and multivariate curve resolution (MCR) approaches and, to the best of our knowledge, has not been investigated before. For this purpose, different chromatographic and hyperspectral imaging (HSI) datasets were simulated, considering different noise levels and different degrees of overlap for two-component systems. Feasible solutions were then calculated by both grid search (GS) and Lawton-Sylvester (LS) plots. MI map which is the plot of MI vs. rotation matrix elements was used to estimate the degree of independence between different solutions. Inspection of the results showed that the different solutions in the feasible bands correspond to different MI values and that those values are lower for spectral profiles (more independent) than for concentration profiles (more dependent) as expected from the duality concept and the opposite is true. In addition, component profiles are found near more dependent solutions for concentration profiles and near less dependent solutions for spectral profiles which is due to the fact that “independence” constraint was applied to the spectral profiles in ICA algorithms. The performance of three well-known ICA algorithms (mean-field independent component analysis (MF-ICA), mutual information-based least dependent component analysis (MILCA) and joint approximate diagonalization of eigenmatrices (JADE)) as well as MCR-alternating least squares (MCR-ALS) were investigated. MI maps showed that the solutions of MF-ICA and MCR-ALS are in the feasible bands but the MILCA and JADE solutions which are just based on the independence maximization are outside the MI maps.

BAL and non-BAL quasars: continuum, emission, and absorption properties establish a common parent sample

ABSTRACT Using a sample of ≃144 000 quasars from the Sloan Digital Sky Survey Data Release 14, we investigate the outflow properties, evident in both absorption and emission, of high-ionization broad absorption line (BAL) and non-BAL quasars with redshifts 1.6 ≲ $z$ ≤ 3.5 and luminosities 45.3 erg s−1 < log10(Lbol) < 48.2 erg s−1. Key to the investigation is a continuum and emission-line reconstruction scheme, based on mean-field independent component analysis, that allows the kinematic properties of the C iv λ1550 emission line to be compared directly for both non-BAL and BAL quasars. C iv emission blueshift and equivalent width (EW) measurements are thus available for both populations. Comparisons of the emission-line and BAL trough properties reveal strong systematic correlations between the emission and absorption properties. The dependence of quantitative outflow indicators on physical properties such as quasar luminosity and luminosity relative to Eddington luminosity is also shown to be essentially identical for the BAL and non-BAL populations. There is an absence of BALs in quasars with the hardest spectral energy distributions (SEDs), revealed by the presence of strong He ii λ1640 emission, large C iv λ1550 emission EW, and no measurable blueshift. In the remainder of the C iv emission blueshift versus EW space, BAL and non-BAL quasars are present at all locations; for every BAL quasar, it is possible to identify non-BAL quasars with the same emission-line outflow properties and SED hardness. The co-location of BAL and non-BAL quasars as a function of emission-line outflow and physical properties is the key result of our investigation, demonstrating that (high-ionization) BALs and non-BALs represent different views of the same underlying quasar population.

Joint approximate diagonalization of eigenmatrices as a high-throughput approach for analysis of hyphenated and comprehensive two-dimensional gas chromatographic data

The objective of the present work is development of joint approximate diagonalization of eigenmatrices (JADE) as a member of independent component analysis (ICA) family, for the analysis of gas chromatography-mass spectrometry (GC–MS) and comprehensive two-dimensional gas chromatography-mass spectrometry (GC×GC–MS) data to address incomplete separation problem occurred during the analysis of complex sample matrices. In this regard, simulated GC–MS and GC×GC–MS data sets with different number of components, different degree of overlap and noise were evaluated. In the case of simultaneous analysis of multiple samples, column-wise augmentation for GC–MS and column-wise super-augmentation for GC×GC–MS was used before JADE analysis. The performance of JADE was evaluated in terms of statistical parameters of lack of fit (LOF), mutual information (MI) and Amari index as well as analytical figures of merit (AFOMs) obtained from calibration curves. In addition, the area of feasible solutions (AFSs) was calculated by two different approaches of MCR-BANDs and polygon inflation algorithm (FACPACK). Furthermore, JADE performance was compared with multivariate curve resolution-alternating least squares (MCR-ALS) and other ICA algorithms of mean-field ICA (MFICA) and mutual information least dependent component analysis (MILCA). In all cases, JADE could successfully resolve the elution and spectral profiles in GC–MS and GC×GC–MS data with acceptable statistical and calibration parameters and their solutions were in AFSs. To check the applicability of JADE in real cases, JADE was used for resolution and quantification of phenanthrene and anthracene in aromatic fraction of heavy fuel oil (HFO) analyzed by GC×GC–MS. Surprisingly, pure elution and spectral profiles of target compounds were properly resolved in the presence of baseline and interferences using JADE. Once more, the performance of JADE was compared with MCR-ALS in real case. On this matter, the mutual information (MI) values were 1.01 and 1.13 for resolved profiles by JADE and MCR-ALS, respectively. In addition, LOD values (μg/mL) were respectively 1.36 and 1.24 for phenanthrene and 1.26 and 1.09 for anthracene using MCR-ALS and JADE which showed outperformance of JADE over MCR-ALS.

Interpreting the ionization sequence in star-forming galaxy emission-line spectra

High ionization star forming (SF) galaxies are easily identified with strong emission line techniques such as the BPT diagram, and form an obvious ionization sequence on such diagrams. We use a locally optimally emitting cloud model to fit emission line ratios that constrain the excitation mechanism, spectral energy distribution, abundances and physical conditions along the star-formation ionization sequence. Our analysis takes advantage of the identification of a sample of pure star-forming galaxies, to define the ionization sequence, via mean field independent component analysis. Previous work has suggested that the major parameter controlling the ionization level in SF galaxies is the metallicity. Here we show that the observed SF- sequence could alternatively be interpreted primarily as a sequence in the distribution of the ionizing flux incident on gas spread throughout a galaxy. Metallicity variations remain necessary to model the SF-sequence, however, our best models indicate that galaxies with the highest and lowest observed ionization levels (outside the range -0.37 < log [O III]/H\b{eta} < -0.09) require the variation of an additional physical parameter other than metallicity, which we determine to be the distribution of ionizing flux in the galaxy.

Detecting H II Regions in “Pure” Starburst Galaxies with SDSS Data

AbstractThe relationship between active galactic nuclei (AGN) and starburst galaxies is poorly understood, partially due to galaxies exhibiting both AGN and starburst activity. To better understand the connection, we analyze a sample of “pure” AGN or starburst at redshift z = 0.1 selected using mean field independent component analysis (MFICA). Simulations of starburst galaxy emission suggests that the locally optimally-emitting cloud (LOC) model can fit observations and improve our ability to distinguish the impact of differences in metallicity, ionization parameter, and ionizing flux. To test for the existence of such clouds in our galaxy sample, we examine the Sloan Digital Sky Survey (SDSS) images of our pure galaxies. At this distance, even large star-forming H II regions (e.g. 30 Doradus) only fill part of an SDSS pixel. However, we compare the morphology of the distant galaxies to more nearby ones (i.e. NGC 4713, NGC 4038/4039) to estimate the number of larger H II regions. While the clumpiness parameter of a galaxy in theory might indicate the existence of these regions, a straightforward calculation of the clumpiness parameter is ineffective for galaxies at z = 0.1. Typically, one subtracts a smoothed version of a galaxy image from the same image. We instead test a different approach to establish a smooth image and thus better identify the clumps. We subtract the smoother infrared z-band from the sharper ultraviolet u-band. We test this procedure using NGC 4713, a nearby starburst galaxy, artificially degraded to match images of our “pure” starburst galaxies.

A two-step super-Gaussian independent component analysis approach for fMRI data

Independent component analysis (ICA) has been widely applied to functional magnetic resonance imaging (fMRI) data analysis. Although ICA assumes that the sources underlying data are statistically independent, it usually ignores sources’ additional properties, such as sparsity. In this study, we propose a two-step super-GaussianICA (2SGICA) method that incorporates the sparse prior of the sources into the ICA model. 2SGICA uses the super-Gaussian ICA (SGICA) algorithm that is based on a simplified Lewicki-Sejnowski’s model to obtain the initial source estimate in the first step. Using a kernel estimator technique, the source density is acquired and fitted to the Laplacian function based on the initial source estimates. The fitted Laplacian prior is used for each source at the second SGICA step. Moreover, the automatic target generation process for initial value generation is used in 2SGICA to guarantee the stability of the algorithm. An adaptive step size selection criterion is also implemented in the proposed algorithm. We performed experimental tests on both simulated data and real fMRI data to investigate the feasibility and robustness of 2SGICA and made a performance comparison between InfomaxICA, FastICA, mean field ICA (MFICA) with Laplacian prior, sparse online dictionary learning (ODL), SGICA and 2SGICA. Both simulated and real fMRI experiments showed that the 2SGICA was most robust to noises, and had the best spatial detection power and the time course estimation among the six methods.

Performance assessment of chemometric resolution methods utilized for extraction of pure components from overlapped signals in gas chromatography–mass spectrometry

Multivariate resolution technique is a set of mathematical tools that uncovers the underlying profiles from a set of measurements of time evolving chemical systems. This technique was proposed for resolving the overlapping GC–MS peaks into pure chromatogram and mass spectra. In this paper, several common resolution chemometric techniques in GC–MS resolution such as mean field-independent component analysis (MF-ICA), multivariate curve resolution-alternating least squares (MCR-ALS), and multivariate curve resolution-objective function minimization (MCR-FMIN) were investigated. The obtained solutions using chemometric methods are assessed by lack of fit (LOF) and R2. Results show that all solutions by fulfilling the same constraints have same performance in resolving high overlapping peaks. Also, the differences obtained in each case should be related to the unresolved rotational ambiguity.Among the different ambiguities such as intensity, permutation and rotation in resolution methods, rotational ambiguity is the most difficult and critical one. Because of rotational ambiguity, there is a set of feasible MCR solutions, which explain equally well the observed experimental data, and fulfill sufficiently the imposed constraints of the system. So in these methods, a range of feasible solutions exist. The rotational ambiguities of the profiles are a challenging fact which complicates the development of stable and universal self-modeling curve resolution (SMCR) algorithms. The relative component contribution (RCC) function values for the component profiles obtained by the different methods are calculated by MCR-BANDS. The values of RCC for these three methods are equivalent. Rotational ambiguities of the solutions of SMCR methods can be reduced by applying suitable constraints. The obtained results show, using data sets, which are arranged in a single augmented data matrix could be the best solution for reducing or removing of rotational ambiguity.

Interpreting the ionization sequence in AGN emission-line spectra

We investigate the physical cause of the great range in the ionization level seen in the spectra of narrow lined active galactic nuclei (AGN). Mean field independent component analysis identifies examples of individual SDSS galaxies whose spectra are not dominated by emission due to star formation (SF), which we designate as AGN. We assembled high S/N ratio composite spectra of a sequence of these AGN defined by the ionization level of their narrow-line regions (NLR), extending down to very low-ionization cases. We used a local optimally emitting cloud (LOC) model to fit emission-line ratios in this AGN sequence. These included the weak lines that can be measured only in the co-added spectra, providing consistency checks on strong line diagnostics. After integrating over a wide range of radii and densities our models indicate that the radial extent of the NLR is the major parameter in determining the position of high to moderate ionization AGN along our sequence, providing a physical interpretation for their systematic variation. Higher ionization AGN contain optimally emitting clouds that are more concentrated towards the central continuum source than in lower ionization AGN. Our LOC models indicate that for the objects that lie on our AGN sequence, the ionizing luminosity is anticorrelated with the NLR ionization level, and hence anticorrelated with the radial concentration and physical extent of the NLR. A possible interpretation that deserves further exploration is that the ionization sequence might be an age sequence where low ionization objects are older and have systematically cleared out their central regions by radiation pressure. We consider that our AGN sequence instead represents a mixing curve of SF and AGN spectra, but argue that while many galaxies do have this type of composite spectra, our AGN sequence appears to be a special set of objects with negligible SF excitation.

Classification and analysis of emission-line galaxies using mean field independent component analysis

We present an analysis of the optical spectra of narrow emission-line galaxies, based on mean field independent component analysis (MFICA). Samples of galaxies were drawn from the Sloan Digital Sky Survey (SDSS) and used to generate compact sets of `continuum' and `emission-line' component spectra. These components can be linearly combined to reconstruct the observed spectra of a wider sample of galaxies. Only 10 components - five continuum and five emission line - are required to produce accurate reconstructions of essentially all narrow emission-line galaxies; the median absolute deviations of the reconstructed emission-line fluxes, given the signal-to-noise ratio (S/N) of the observed spectra, are 1.2-1.8 sigma for the strong lines. After applying the MFICA components to a large sample of SDSS galaxies we identify the regions of parameter space that correspond to pure star formation and pure active galactic nucleus (AGN) emission-line spectra, and produce high S/N reconstructions of these spectra. The physical properties of the pure star formation and pure AGN spectra are investigated by means of a series of photoionization models, exploiting the faint emission lines that can be measured in the reconstructions. We are able to recreate the emission line strengths of the most extreme AGN case by assuming the central engine illuminates a large number of individual clouds with radial distance and density distributions, f(r) ~ r^gamma and g(n) ~ n^beta, respectively. The best fit is obtained with gamma = -0.75 and beta = -1.4. From the reconstructed star formation spectra we are able to estimate the starburst ages. These preliminary investigations serve to demonstrate the success of the MFICA-based technique in identifying distinct emission sources, and its potential as a tool for the detailed analysis of the physical properties of galaxies in large-scale surveys.

ICA BASED DIGITAL IMAGE WATERMARKING BASED ON REDUNDANT DISCRETE WAVELET TRANSFORM

In recent years, access to multimedia data has become much easier due to rapid growth of the internet. While this is usually considered an improvement of everyday life, it also makes unauthorized copying and distributing of multimedia data much easier, therefore presenting a field of watermarking. Many literatures have reported about Discrete Wavelet Transform watermarking techniques for data security. However, DWT based watermarking schemes are found to be less robust against image processing attacks and the shift variance of Wavelet Packet Transform causes inaccurate extraction. In this paper, an attempt is made to develop a watermarking scheme based on RDWT and extraction using Independent Component Analysis (ICA). Various ICA like Fast ICA, Radical ICA, Pearson ICA, Jade ICA, Maximum Likelihood ICA, Mean Field ICA and Kernel ICA are proposed and implemented for extraction. Simulation results reveal that Fast ICA produces better Similarity Measure and Mutual Information over other ICA methods.

Towards obtaining more information from gas chromatography–mass spectrometric data of essential oils: An overview of mean field independent component analysis

Mean field independent component analysis (MF-ICA) along with other chemometric techniques was proposed for obtaining more information from multi-component gas chromatographic–mass spectrometric (GC–MS) signals of essential oils (mandarin and lemon as examples). Using these techniques, some fundamental problems during the GC–MS analysis of essential oils such as varying baseline, presence of different types of noise and co-elution have been solved. The parameters affecting MF-ICA algorithm were screened using a 2 5 factorial design. The optimum conditions for MF-ICA algorithm were followed by deconvolution of complex GC–MS peak clusters. The number of independent components (ICs) (chemical constituents) in each peak cluster was estimated using morphological score method. Eigenvalue profiles of evolving factor analysis (EFA) and pure variables from orthogonal projection approach (OPA) were used as initial mixing matrix (chromatograms) in iterative process. The resolved mass spectra were satisfactorily identified using NIST mass spectral search system. Finally, the results of optimized MF-ICA were compared with those obtained using multivariate curve resolution-alternating least square (MCR-ALS), multivariate curve resolution-objective function minimization (MCR-FMIN) and heuristic evolving latent projection (HELP) methods. It is demonstrated that MF-ICA can be used as an alternative method for a quick and accurate analysis of real multi-component problematic systems such as essential oils.

Using mean field approach independent component analysis to fatty acid characterization with overlapped GC–MS signals

In this paper, mean field independent component analysis (MF-ICA) was applied as a deconvolution method to separate complex gas chromatographic–mass spectrometric (GC–MS) signals obtained from fatty acid analysis of fish oil. The separation which is a blind operation was used as a complementary method in identification of the unknown components of a mixture and in quantification purposes, as well. In MF-ICA, the sources (mass spectra) are recovered from the mean of their posterior distributions and mixing matrix (chromatograms) and noise level are estimated through the maximum a posterior (MAP) solution. The number of independent components (ICs) in the overlapping signals can be estimated by the difference between the reconstructed and original GC–MS data. It was found that the chromatographic profiles and the mass spectra of the components in overlapping multicomponent GC–MS data can be accurately recovered with and without previously background correction. The resolved mass spectral sources satisfactory are identified using mass spectral search system. The recovered chromatographic area and the relative content of each analyte considering selected number of ICs are calculated and the results are compared with the ones obtained previously by using heuristic evolving latent projections (HELP) method.

A primary study on resolution of overlapping GC-MS signal using mean-field approach independent component analysis

Independent component analysis (ICA) has been found to be powerful to separate complex signals. However, chemical signals are generally correlated, instead of independent as hypothesized in ICA. In this study, mean-field independent component analysis (MF-ICA) was investigated to resolve the overlapping gas chromatographic-mass spectrometric (GC-MS) signal. In MF-ICA, the sources are estimated from the mean of their posterior distribution. The mixing matrix and noise level are found through the maximum a posterior (MAP) solution. By simulated signals, results show that for cases of the slightly correlated (or overlapped) sources, both the sources (MS) and mixing matrix (chromatogram) can be almost correctly estimated by specification of the nonnegative (positive) priors for the mixing matrix and sources. However, when the sources are highly correlated, no good results can be obtained, although acceptable estimated sources can be obtained somehow for database matching. For experimental overlapping GC-MS data, reasonable results are obtained, because MS spectra of different homologous compounds in GC-MS analysis of a mixture are not generally correlated very much. Therefore, ICA should be an alternate tool for resolution of overlapping chemical signals, although further works are still needed.