Non-negative Independent Component Analysis Research Articles

Biologically plausible single-layer networks for nonnegative independent component analysis.

An important problem in neuroscience is to understand how brains extract relevant signals from mixtures of unknown sources, i.e., perform blind source separation. To model how the brain performs this task, we seek a biologically plausible single-layer neural network implementation of a blind source separation algorithm. For biological plausibility, we require the network to satisfy the following three basic properties of neuronal circuits: (i) the network operates in the online setting; (ii) synaptic learning rules are local; and (iii) neuronal outputs are nonnegative. Closest is the work by Pehlevan et al.(Neural Comput 29:2925-2954, 2017), which considers nonnegative independent component analysis (NICA), a special case of blind source separation that assumes the mixture is a linear combination of uncorrelated, nonnegative sources. They derive an algorithm with a biologically plausible 2-layer network implementation. In this work, we improve upon their result by deriving 2 algorithms for NICA, each with a biologically plausible single-layer network implementation. The first algorithm maps onto a network with indirect lateral connections mediated by interneurons. The second algorithm maps onto a network with direct lateral connections and multi-compartmental output neurons.

Unmixing multi-spectral photoacoustic sources in human carotid plaques using non-negative independent component analysis

Multi-spectral photoacoustic imaging (MSPAI) is promising for morphology assessment of carotid plaques; however, obtaining unique spectral characteristics of chromophores is cumbersome. We used MSPAI and non-negative independent component analysis (ICA) to unmix distinct signal sources in human carotid plaques blindly. The feasibility of the method was demonstrated on a plaque phantom with hemorrhage and cholesterol inclusions, and plaque endarterectomy samples ex vivo. Furthermore, the results were verified with histology using Masson's trichrome staining. Results showed that ICA could separate recent hemorrhages from old hemorrhages. Additionally, the signatures of cholesterol inclusion were also captured for the phantom experiment. Artifacts were successfully removed from signal sources. Histologic examinations showed high resemblance with the unmixed components and confirmed the morphologic distinction between recent and mature hemorrhages. In future pre-clinical studies, unmixing could be used for morphology assessment of intact human plaque samples.

Application of non-negative ICA for unmixing of Hyperion data

Independent Component Analysis (ICA) is based on the linear mixture model of hyperspectral data and has been widely used in various blind source separations. Non-negative ICA considers non negativity constraint in addition to independency of components and the results will therefore be more real because negative signal sources in an image are not physically meaningful. The non-negative Independent Component Analysis (ICA) was used for detection and mapping of endmembers on a Hyperspectral dataset in this study. This paper surveys the capability of non-negative ICA for endmember detection and unmixing of Hyperion data in a geological terrain. In this research, a small part of the Hyperion scene was processed using the geodesic search algorithm to distinguish the Independent Components (ICs) of the image. The dataset was first topographically and atmospherically corrected and then data quality assessment was performed for recognizing the bad bands. The applied method for unmixing was able to detect the major minerals in the study scene and resulted in more accurate outcome in comparison to regular ICA. The non-negative ICA algorithm satisfactory identified three ICs, of which one showed considerable abundances in the region. The determined minerals are also more compatible to the geology and lithological features in the region. It therefore can map alterations and minerals abundances with higher accuracy. The abundances map of detected minerals was generated using spectral angle mapper method that proved as a useful tool for this purpose.

Independent component analysis (ICA) algorithms for improved spectral deconvolution of overlapped signals in 1H NMR analysis: application to foods and related products

The major challenge facing NMR spectroscopic mixture analysis is the overlapping of signals and the arising impossibility to easily recover the structures for identification of the individual components and to integrate separated signals for quantification. In this paper, various independent component analysis (ICA) algorithms [mutual information least dependent component analysis (MILCA); stochastic non-negative ICA (SNICA); joint approximate diagonalization of eigenmatrices (JADE); and robust, accurate, direct ICA algorithm (RADICAL)] as well as deconvolution methods [simple-to-use-interactive self-modeling mixture analysis (SIMPLISMA) and multivariate curve resolution-alternating least squares (MCR-ALS)] are applied for simultaneous (1)H NMR spectroscopic determination of organic substances in complex mixtures. Among others, we studied constituents of the following matrices: honey, soft drinks, and liquids used in electronic cigarettes. Good quality spectral resolution of up to eight-component mixtures was achieved (correlation coefficients between resolved and experimental spectra were not less than 0.90). In general, the relative errors in the recovered concentrations were below 12%. SIMPLISMA and MILCA algorithms were found to be preferable for NMR spectra deconvolution and showed similar performance. The proposed method was used for analysis of authentic samples. The resolved ICA concentrations match well with the results of reference gas chromatography-mass spectrometry as well as the MCR-ALS algorithm used for comparison. ICA deconvolution considerably improves the application range of direct NMR spectroscopy for analysis of complex mixtures.

An Improved Multiplicative Updating Algorithm for Nonnegative Independent Component Analysis

This paper addresses nonnegative independent component analysis (NICA), with the aim to realize the blind separation of nonnegative well-grounded independent source signals, which arises in many practical applications but is hardly ever explored. Recently, Bertrand and Moonen presented a multiplicative NICA (M-NICA) algorithm using multiplicative update and subspace projection. Based on the principle of the mutual correlation minimization, we propose another novel cost function to evaluate the diagonalization level of the correlation matrix, and apply the multiplicative exponentiated gradient (EG) descent update to it to maintain nonnegativity. An efficient approach referred to as the EG-NICA algorithm is derived and its validity is confirmed by numerous simulations conducted on different types of source signals. Results show that the separation performance of the proposed EG-NICA algorithm is superior to that of the previous M-NICA algorithm, with a better unmixing accuracy. In addition, its convergence speed is adjustable by an appropriate user-defined learning rate.

An Improved Multiplicative Updating Algorithm for Nonnegative Independent Component Analysis

This paper addresses nonnegative independent component analysis (NICA), with the aim to realize the blind separation of nonnegative well-grounded independent source signals, which arises in many practical applications but is hardly ever explored. Recently, Bertrand and Moonen presented a multiplicative NICA (M-NICA) algorithm using multiplicative update and subspace projection. Based on the principle of the mutual correlation minimization, we propose another novel cost function to evaluate the diagonalization level of the correlation matrix, and apply the multiplicative exponentiated gradient (EG) descent update to it to maintain nonnegativity. An efficient approach referred to as the EG-NICA algorithm is derived and its validity is confirmed by numerous simulations conducted on different types of source signals. Results show that the separation performance of the proposed EG-NICA algorithm is superior to that of the previous M-NICA algorithm, with a better unmixing accuracy. In addition, its convergence speed is adjustable by an appropriate user-defined learning rate.

Quantifying brain tumor tissue abundance in HR-MAS spectra using non-negative blind source separation techniques

Given high-resolution magic angle spinning (HR-MAS) spectra from several glial tumor subjects, our goal is to differentiate between tumor tissue types by separating the different sources that contribute to the profile of each spectrum. Blind source separation techniques are applied for obtaining characteristic profiles for necrosis, highly cellular tumor and border tumor tissue and providing the contribution (abundance) of each of these tumor tissue types to the profile of each spectrum. The problem is formulated as a non-negative source separation problem. Non-negative matrix factorization, convex analysis of non-negative sources and non-negative independent component analysis methods are considered. The results are in agreement with the pathology obtained by the histopathological examination that succeeded the HR-MAS measurements. Furthermore, an analysis to verify to which extent the dimension of the input space, the input features and the number of sources to be extracted from the HR-MAS data could influence the performance of the source separation is presented. Copyright © 2012 John Wiley & Sons, Ltd.

Remote Sensing Image Fusion Based on Integer Wavelet Transformation and Ordered Nonnegative Independent Component Analysis

A novel remote sensing image fusion method is proposed based on integer wavelet transformation and ordered nonnegative independent component analysis (IWT-ONICA) to take advantage of the IWT characteristics of multi-resolution and high-speed computation and the fact that independent component analysis can remove higher-order redundancy. The proposed method is applied to the fusion of IKONOS satellite images. Statistical and visual results show that IWT-ONICA is superior to other fusion algorithms in terms of clarity and visual effect, while evaluation indicators such as the peak signal-to-noise ratio, correlation coefficient, spectral angle mapper, and relative dimensionless global error confirm its superior performance.

Simultaneous Identification and Quantitative Determination of Amino Acids in Mixture by NMR Spectroscopy Using Chemometric Resolution

ABSTRACT Nuclear magnetic resonance (NMR) spectroscopy receives increasing interest in biological and metabolomic studies. It is still, however, a great challenge to analyze the NMR spectra of multicomponent samples, containing overlapping responses of the compositions. In this work, nonnegative independent component analysis (nonnegative ICA) and immune algorithm (IA) were employed for simultaneous identification and quantitative determination of three amino acids in mixture samples from measured multicomponent NMR signals. Results show that the correlation coefficients (R) between the extracted and measured spectra are higher than 0.97 and that those between the calculated relative contents and experimental ones are higher than 0.99. The method may provide an alternative technique for analyzing multicomponent samples like biofluids by using NMR spectroscopy.

Blind separation of non-negative source signals using multiplicative updates and subspace projection

In this paper, we consider a noise-free blind source separation problem with independent non-negative source signals, also known as non-negative independent component analysis (NICA). We assume that the source signals are well-grounded, which means that they have a non-vanishing pdf in a positive neighborhood of zero. We propose a novel algorithm, referred to as multiplicative NICA (M-NICA), which uses multiplicative updates together with a subspace projection based correction step to reconstruct the original source signals from the observed linear mixtures, and which is based only on second order statistics. A multiplicative update has the facilitating property that it preserves non-negativity, and does not depend on a user-defined learning rate, as opposed to gradient based updates such as in the non-negative PCA (NPCA) algorithm. We provide batch mode simulations of M-NICA and compare its performance to NPCA, for different types of signals. It is observed that M-NICA generally yields a better unmixing accuracy, but converges slower than NPCA. Especially when the amount of data samples is small, M-NICA significantly outperforms NPCA. Furthermore, a sliding window implementation of both algorithms is described and simulated, where M-NICA is observed to provide the best results.

Robust demarcation of basal cell carcinoma by dependent component analysis-based segmentation of multi-spectral fluorescence images

This study was designed to demonstrate robust performance of the novel dependent component analysis (DCA)-based approach to demarcation of the basal cell carcinoma (BCC) through unsupervised decomposition of the red–green–blue (RGB) fluorescent image of the BCC. Robustness to intensity fluctuation is due to the scale invariance property of DCA algorithms, which exploit spectral and spatial diversities between the BCC and the surrounding tissue. Used filtering-based DCA approach represents an extension of the independent component analysis (ICA) and is necessary in order to account for statistical dependence that is induced by spectral similarity between the BCC and surrounding tissue. This generates weak edges what represents a challenge for other segmentation methods as well. By comparative performance analysis with state-of-the-art image segmentation methods such as active contours (level set), K-means clustering, non-negative matrix factorization, ICA and ratio imaging we experimentally demonstrate good performance of DCA-based BCC demarcation in two demanding scenarios where intensity of the fluorescent image has been varied almost two orders of magnitude.

EEG source imaging with spatio‐temporal tomographic nonnegative independent component analysis

This article describes a spatio-temporal EEG/MEG source imaging (ESI) that extracts a parsimonious set of "atoms" or components, each the outer product of both a spatial and a temporal signature. The sources estimated are localized as smooth, minimally overlapping patches of cortical activation that are obtained by constraining spatial signatures to be nonnegative (NN), orthogonal, sparse, and smooth-in effect integrating ESI with NN-ICA. This constitutes a generalization of work by this group on the use of multiple penalties for ESI. A multiplicative update algorithm is derived being stable, fast and converging within seconds near the optimal solution. This procedure, spatio-temporal tomographic NN ICA (STTONNICA), is equally able to recover superficial or deep sources without additional weighting constraints as tested with simulations. STTONNICA analysis of ERPs to familiar and unfamiliar faces yields an occipital-fusiform atom activated by all faces and a more frontal atom that only is active with familiar faces. The temporal signatures are at present unconstrained but can be required to be smooth, complex, or following a multivariate autoregressive model.

Characterization of radix rehmanniae processing procedure using FT-IR spectroscopy through nonnegative independent component analysis

A method is proposed for monitoring the radix rehmanniae proparate processing procedure and determining the endpoint of the process using attenuated total reflectance (ATR) FT-IR through nonnegative independent component analysis (ICA). In the proposed method, ATR FT-IR spectra of the samples were firstly measured at different steaming periods. Then, nonnegative ICA was used for direct estimation of the feature spectra of the pure components in the mixture without pre-separation and other prior information. The estimated independent components (ICs) and their variation of the relative concentrations were used to characterize the processing procedure and determine the endpoint. The results show that the estimated three ICs are consistent with that of the chemical components in the mixtures, i.e. catalpol/rehmaionoside, glucose, and other compounds that nearly keep invariant during the processing procedure. The endpoint determined by the IR-ICA method is 15 h, which was located in the range obtained by expert sensory analysis, whereas the endpoint determined by the traditional sensory analysis is 14-17 h and even 14-20 h, which showed the significant deviation of the endpoints determined by different operators.

Extraction of chemical information from complex analytical signals by a non-negative independent component analysis

Extraction of chemical information of the components from a complex analytical signal has been a great challenge in chemometrical studies for complex sample analysis. Independent component analysis (ICA) has been widely applied in complex signal separation, including the multicomponent overlapping signals in analytical chemistry. Difficulties, however, still exist in the application of ICA in chemical signal processing because chemical signals of different components are generally correlated and non-negative, instead of independence as hypothesized in ICA. In this study, a non-negative ICA method is proposed by means of a post rotation of the independent components (ICs) and applied to the extraction of the chemical information of the components from the signals of complex samples. Raman spectra of pharmaceutical tablets and gas chromatography-mass spectrometry (GC-MS) data of cigarette smoke are qualitatively analyzed. The results show that the Raman spectrum of the active substance in the pharmaceutical tablets and the mass spectra of the components in the overlapping GC-MS signal can be effectively and accurately extracted by using the proposed method.

Gene Module Identification from Microarray Data Using Nonnegative Independent Component Analysis

Genes mostly interact with each other to form transcriptional modules for performing single or multiple functions. It is important to unravel such transcriptional modules and to determine how disturbances in them may lead to disease. Here, we propose a non-negative independent component analysis (nICA) approach for transcriptional module discovery. nICA method utilizes the non-negativity constraint to enforce the independence of biological processes within the participated genes. In such, nICA decomposes the observed gene expression into positive independent components, which fits better to the reality of corresponding putative biological processes. In conjunction with nICA modeling, visual statistical data analyzer (VISDA) is applied to group genes into modules in latent variable space. We demonstrate the usefulness of the approach through the identification of composite modules from yeast data and the discovery of pathway modules in muscle regeneration.

Latent variable analysis of Raman spectra for structural characterization of proteins

Latent variable analysis of deep UV resonance Raman spectra was demonstrated to be a powerful tool for characterizing protein secondary structural composition. Non-negative independent component analysis (ICA) and pure variable methods, such as stepwise maximum angle calculation (SMAC) and simple-to-use interactive self-modeling mixture analysis (SIMPLISMA), were employed for examination of 10 deep UV Raman (DUVRR) spectra of lysozyme obtained at various stages of its partial denaturation, the first stage of amyloid fibril formation. The non-negative ICA allowed for extracting the spectrum of the β-sheet from deep UV resonance Raman spectra of lysozyme while principle component analysis (PCA) and multivariate curve resolution (MCR) could not separate the β-sheet constituent as an individual component. No initial guess about the features of the β-sheet spectrum was used. Pure variable methods SMAC and SIMPLISMA were found to resolve three independent spectral components assigned to β-sheet, random coil, and native lysozyme.

Monte Carlo Algorithm for Least Dependent Non-Negative Mixture Decomposition

We propose a simulated annealing algorithm (stochastic non-negative independent component analysis, SNICA) for blind decomposition of linear mixtures of non-negative sources with non-negative coefficients. The demixing is based on a Metropolis-type Monte Carlo search for least dependent components, with the mutual information between recovered components as a cost function and their non-negativity as a hard constraint. Elementary moves are shears in two-dimensional subspaces and rotations in three-dimensional subspaces. The algorithm is geared at decomposing signals whose probability densities peak at zero, the case typical in analytical spectroscopy and multivariate curve resolution. The decomposition performance on large samples of synthetic mixtures and experimental data is much better than that of traditional blind source separation methods based on principal component analysis (MILCA, FastICA, RADICAL) and chemometrics techniques (SIMPLISMA, ALS, BTEM).

Nonnegative independent component analysis based on minimizing mutual information technique

A novel neural network technique for nonnegative independent component analysis is proposed in this letter. Compared with other algorithms, this method can work efficiently even when the source signals are not well grounded. Moreover, this method is insensitive to the particular underlying distribution of the source data. Experimental results demonstrate the advantages of our approach in achieving satisfactory results regardless of whether the source data are well grounded or not.

Geometrical methods for non-negative ICA: Manifolds, Lie groups and toral subalgebras

We explore the use of geometrical methods to tackle the non-negative independent component analysis (non-negative ICA) problem, without assuming the reader has an existing background in differential geometry. We concentrate on methods that achieve this by minimizing a cost function over the space of orthogonal matrices. We introduce the idea of the manifold and Lie group SO ( n ) of special orthogonal matrices that we wish to search over, and explain how this is related to the Lie algebra so ( n ) of skew-symmetric matrices. We describe how familiar optimization methods such as steepest descent and conjugate gradients can be transformed into this Lie group setting, and how the Newton update step has an alternative Fourier version in SO ( n ) . Finally, we introduce the concept of a toral subgroup generated by a particular element of the Lie group or Lie algebra, and explore how this commutative subgroup might be used to simplify searches on our constraint surface. No proofs are presented in this article.

Algorithms for nonnegative independent component analysis

We consider the task of solving the independent component analysis (ICA) problem x=As given observations x, with a constraint of nonnegativity of the source random vector s. We refer to this as nonnegative independent component analysis and we consider methods for solving this task. For independent sources with nonzero probability density function (pdf) p(s) down to s=0 it is sufficient to find the orthonormal rotation y=Wz of prewhitened sources z=Vx, which minimizes the mean squared error of the reconstruction of z from the rectified version y/sup +/ of y. We suggest some algorithms which perform this, both based on a nonlinear principal component analysis (PCA) approach and on a geodesic search method driven by differential geometry considerations. We demonstrate the operation of these algorithms on an image separation problem, which shows in particular the fast convergence of the rotation and geodesic methods and apply the approach to a musical audio analysis task.