Multi-way Decomposition Research Articles

Europium-Doped Ceria-Gadolinium Mixed Oxides: PARAFAC Analysis and High-Resolution Emission Spectroscopy under Cryogenic Conditions for Structural Analysis.

Gadolinium-doped ceria or gadolinium-stabilized ceria (GDC) is an important technical material due to its ability to conduct O2- ions, e.g., used in solid oxide fuel cells operated at intermediate temperature as an electrolyte, diffusion barrier, and electrode component. We have synthesized Ce1-xGdxO2-y:Eu3+ (0 ≤ x ≤ 0.4) nanoparticles (11-15 nm) using a scalable spray pyrolysis method, which allows the continuous large-scale technical production of such materials. Introducing Eu3+ ions in small amounts into ceria and GDC as spectroscopic probes can provide detailed information about the atomic structure and local environments and allows us to monitor small structural changes. This study presents a novel approach to structurally elucidate europium-doped Ce1-xGdxO2-y:Eu3+ nanoparticles by way of Eu3+ spectroscopy, processing the spectroscopic data with the multiway decomposition method parallel factor (PARAFAC) analysis. In order to perform the deconvolution of spectra, data sets of excitation wavelength, emission wavelength, and time are required. Room temperature, time-resolved emission spectra recorded at λex = 464 nm show that Gd3+ doping results in significantly altered emission spectra compared to pure ceria. The PARAFAC analysis for the pure ceria samples reveals a high-symmetry species (which can also be probed directly via the CeO2 charge transfer band) and a low-symmetry species. The GDC samples yield two low-symmetry spectra in the same experiment. High-resolution emission spectra recorded under cryogenic conditions after probing the 5D0-7F0 transition at λex = 575-583 nm revealed additional variation in the low-symmetry Eu3+ sites in pure ceria and GDC. The total luminescence spectra of CeO2-y:Eu3+ showed Eu3+ ions located in at least three slightly different coordination environments with the same fundamental symmetry, whereas the overall hypsochromic shift and increased broadening of the 5D0-7F0 excitation in the GDC samples, as well as the broadened spectra after deconvolution point to less homogeneous environments. The data of the Gd3+-containing samples indicates that the average charge density around the Eu3+ ions in the lattice is decreased with increasing Gd3+ and oxygen vacancy concentration. For reference, the Judd-Ofelt parameters of all spectra were calculated. PARAFAC proves to be a powerful tool to analyze lanthanide spectra in crystalline solid materials, which are characterized by numerous Stark transitions and where measurements usually yield a superposition of different contributions to any given spectrum.

A novel time–frequency–space method with parallel factor theory for big data analysis in condition monitoring of complex system

The spatial information of the signal is neglected by the conventional frequency/time decompositions such as the fast Fourier transformation, principal component analysis, and independent component analysis. Framing of the data being as a three-way array indexed by channel, frequency, and time allows the application of parallel factor analysis, which is known as a unique multi-way decomposition. The parallel factor analysis was used to decompose the wavelet transformed ongoing diagnostic channel–frequency–time signal and each atom is trilinearly decomposed into spatial, spectral, and temporal signature. The time–frequency–space characteristics of the single-source fault signal was extracted from the multi-source dynamic feature recognition of mechanical nonlinear multi-failure mode and the corresponding relationship between the nonlinear variable, multi-fault mode, and multi-source fault features in time, frequency, and space was obtained. In this article, a new method for the multi-fault condition monitoring of slurry pump based on parallel factor analysis and continuous wavelet transform was developed to meet the requirements of automatic monitoring and fault diagnosis of industrial process production lines. The multi-scale parallel factorization theory was studied and a three-dimensional time–frequency–space model reconstruction algorithm for multi-source feature factors that improves the accuracy of mechanical fault detection and intelligent levels was proposed.

Spatial and Temporal Characteristics of Visual Field Progression in Glaucoma Assessed by Parallel Factor Analysis.

PurposeTo explore spatial and temporal characteristics of glaucomatous visual field (VF) progression through multi-way decomposition of data.MethodsSix serial VF exams with intervals of 6.0 ± 1.0 months in 121 pre-perimetric glaucoma eyes and 80 perimetric glaucoma eyes were arranged into a three-dimensional cube. The data were decomposed using parallel factor analysis.ResultsThree tri-linear components (i.e., spatial scores, temporal loadings, and subject-specific loadings) were identified. Component 1 clearly showed differences between superior and inferior hemispheres, linear trends over time, and wide variability in perimetric glaucoma. Findings were compatible with well-known characteristics of glaucomatous VF defects. Component 2 showed nasal and central areas in contrast with superior, inferior, and temporal peripheral locations, whereas component 3 showed a contrast between nasal and temporal hemispheres. Both components 2 and 3 failed to show clear temporal trends.ConclusionsIdentification of spatio-temporal patterns shows new possibilities for a multi-way decomposition methodology for earlier diagnosis and prediction of glaucomatous VF progression.

Application of non-linear optimization for estimating Tucker3 solutions

An extension of the non-linear optimization (FMIN) which was previously proposed to the estimation of multivariate curve resolution solutions by Tauler [AnalyticaChimicaActa 595 (2007) 289–298] to the multi-way analysis is reported in this contribution. TuckFMIN is presented for the calculation of Tucker3 solutions by the FMIN.TuckFMIN is heavily relying on the minimization of an objective function which is defined directly from the constraints non-fulfillment. Starting from higher-order singular value decomposition (HO-SVD) loadings, TuckFMIN represents a new approach for obtaining three proper rotation matrices for transforming the HO-SVD loadings to physically and chemically meaningful solutions. Different constraints should be imposed during optimization; sparsity and trilinearity are among new constraints for simplicity of the Tucker3 core and fast and robust convergence in a multi-way decomposition. Simulated fluorescence data was exemplified to evaluate the feasibility of proposed method. For the sake of comparison between different initialization methods, PARAFAC-ALS and HO-SVD loadings were used. LOF (lack of fit) from TuckFMIN modeling is always as same as LOF of HO-SVD and less than LOF of the PARAFAC-ALS for noise free data sets. Despite the PARAFAC-ALS decomposition, TuckFMIN has the best fitting regardless to rank-deficiency or levels of noise. By means of simulation study, it is demonstrated that TuckFMIN can be helpful for faster convergence and obtaining the reproducible results. An experimental 3D fluorescence data set from gold nano-particle (AuNP) interaction with HIV genome are successfully used for evaluating the performance of the TuckFMIN algorithm.

Prediction of Structural Deficiency Ratio of Bridges Based on Multiway Data Factorization

AbstractPrediction of future bridge conditions is essential in bridge management as this provides guidance for strategic planning. The National Bridge Inventory (NBI) database has been used by researchers for this purpose by utilizing Markov Chains and regression approaches. This paper introduces a hybrid method for predictions based on multiway data decomposition and simple exponential smoothing (SES). Multiway decomposition is used due to the multidimensional nature of the utilized bridge data. The simple exponential smoothing technique is utilized to predict the future proportions of structurally deficient bridges, known as the structural deficiency ratio (SD ratio) across the United States. The mean absolute error (MAE) values declined with increasing smoothing factor values, which implies bridge conditions can be reliably predicted based on recent SD ratios and not on distant past ones. With prediction metrics yielding relatively low values, this hybrid approach involving multiway data decomposition ...

PARAFAC Decomposition for Ultrasonic Wave Sensing of Fiber Bragg Grating Sensors: Procedure and Evaluation.

Ultrasonic wave-sensing technology has been applied for the health monitoring of composite structures, using normal fiber Bragg grating (FBG) sensors with a high-speed wavelength interrogation system of arrayed waveguide grating (AWG) filters; however, researchers are required to average thousands of repeated measurements to distinguish significant signals. To resolve this bottleneck problem, this study established a signal-processing strategy that improves the signal-to-noise ratio for the one-time measured signal of ultrasonic waves, by application of parallel factor analysis (PARAFAC) technology that produces unique multiway decomposition without additional orthogonal or independent constraints. Through bandpass processing of the AWG filter and complex wavelet transforms, ultrasonic wave signals are preprocessed as time, phase, and frequency profiles, and then decomposed into a series of conceptual three-way atoms by PARAFAC. While an ultrasonic wave results in a Bragg wavelength shift, antiphase fluctuations can be observed at two adjacent AWG ports. Thereby, concentrating on antiphase features among the three-way atoms, a fitting atom can be chosen and then restored to three-way profiles as a final result. An experimental study has revealed that the final result is consistent with the conventional 1024-data averaging signal, and relative error evaluation has indicated that the signal-to-noise ratio of ultrasonic waves can be significantly improved.

Comprehensive and Comparative Metabolomic Profiling of Wheat, Barley, Oat and Rye Using Gas Chromatography-Mass Spectrometry and Advanced Chemometrics.

Beyond the main bulk components of cereals such as the polysaccharides and proteins, lower concentration secondary metabolites largely contribute to the nutritional value. This paper outlines a comprehensive protocol for GC-MS metabolomic profiling of phenolics and organic acids in grains, the performance of which is demonstrated through a comparison of the metabolite profiles of the main northern European cereal crops: wheat, barley, oat and rye. Phenolics and organic acids were extracted using acidic hydrolysis, trimethylsilylated using a new method based on trimethylsilyl cyanide and analyzed by GC-MS. In order to extract pure metabolite peaks, the raw chromatographic data were processed by a multi-way decomposition method, Parallel Factor Analysis 2. This approach lead to the semi-quantitative detection of a total of 247 analytes, out of which 89 were identified based on RI and EI-MS library match. The cereal metabolome included 32 phenolics, 30 organic acids, 10 fatty acids, 11 carbohydrates and 6 sterols. The metabolome of the four cereals were compared in detail, including low concentration phenolics and organic acids. Rye and oat displayed higher total concentration of phenolic acids, but ferulic, caffeic and sinapinic acids and their esters were found to be the main phenolics in all four cereals. Compared to the previously reported methods, the outlined protocol provided an efficient and high throughput analysis of the cereal metabolome and the acidic hydrolysis improved the detection of conjugated phenolics.

On the performance of multiway methods for simultaneous quantification of two fluoroquinolones in urine samples by fluorescence spectroscopy and second-order calibration strategies

In the present work, the analytical performance of three multi-way algorithms has been evaluated. The proposed analytical problem was the simultaneous determination of moxifloxacin and ciprofloxacin in human urine samples using fluorescence spectroscopy. Parallel factor analysis (PARAFAC), self-weighted alternating trilinear decomposition (SWATLD) and unfolded partial least squares combined with the residual bilinearization procedure (U-PLS/RBL) have been compared, regarding their ability to solve the proposed problem. In this study, “second-order advantage” was also exploited for the mentioned algorithms through different calibration strategies. The three-way data was obtained via fluorescence spectroscopy, so that excitation–emission matrices (EEM) of the samples were recorded as the analytical signals. The accuracy and precision of each individual algorithm for analyzing the drugs in urine samples were compared using root mean square error of prediction (RMSEP), recovery and elliptical joint confidence region (EJCR) plots. The results revealed that each of the three algorithms could be applied for determination of moxifloxacin and ciprofloxacin, despite different EEM subsets and calibration strategies. However, better analytical performances were observed through PARAFAC and U-PLS/RBL modeling for MOX and CIP, respectively. So, by coupling the multi-way decomposition algorithms with fluorescence spectroscopy, a main part of preliminary sample preparation steps can be eliminated and experimental procedure might be significantly simplified, while achieving desirable analytical performance.

Reductive enhanced multivariance product representation for multi-way arrays

The main purpose of this work is to develop a new multi-way decomposition technique by considering statistical structure of target multi-way array. To this end enhanced multivariance products representation (EMPR), which is an expansion extended from high dimensional model representation (HDMR), is used. EMPR provides quite successful results on representation and approximation of multivariate functions when they have high level multiplicativity. Hence this urges us to reconstruct EMPR as a multi-way array decomposer. This paper presents this decomposition technique with all reconstruction formulations and numerical experiments on synthetic and real-life data sets to denote EMPR’s efficiency as a decomposer and also presents a combined method Reductive-EMPR (R-EMPR) as a multi-way array decomposition technique.

Noninvasive diagnosis of melanoma with tensor decomposition-based feature extraction from clinical color image

We propose a method for feature extraction from clinical color images, with application in classification of skin lesions. Proposed feature extraction method is based on tensor decomposition of the clinical color image of skin lesion. Since color image is naturally represented as a three-way tensor, it is reasonable to use multi-way techniques to capture the underlying information contained in the image. Extracted features are elements of the core tensor in the corresponding multi-way decomposition, and represent spatial-spectral profile of the lesion. In contrast to common methods that exploit either texture or spectral diversity of the tumor only, the proposed approach simultaneously captures spatial and spectral characteristics. The procedure is tested on a problem of noninvasive diagnosis of melanoma from the clinical color images of skin lesions, with overall sensitivity 82.1% and specificity 86.9%. Our method compares favorably with the state of the art results reported in the literature and provides an interesting alternative to the existing approaches.

Plant metabolomics: Resolution and quantification of elusive peaks in liquid chromatography–mass spectrometry profiles of complex plant extracts using multi-way decomposition methods

Previous studies on LC–MS metabolomic profiling of 127 F2 Barbarea vulgaris plants derived from a cross of parental glabrous (G) and pubescent (P) type, revealed four triterpenoid saponins (hederagenin cellobioside, oleanolic acid cellobioside, epihederagenin cellobioside, and gypsogenin cellobioside) that correlated with resistance of plants against the insect herbivore, Phyllotreta nemorum. In this study, for the first time, we demonstrate the efficiency of the multi-way decomposition method PARAllel FACtor analysis 2 (PARAFAC2) for exploring complex LC–MS data. PARAFAC2 enabled automated resolution and quantification of several elusive chromatographic peaks (e.g. overlapped, elution time shifted and low s/n ratio), which could not be detected and quantified by conventional chromatographic data analysis. Raw LC–MS data of 127 F2 B. vulgaris plants were arranged in a three-way array (elution time point×mass spectra×samples), divided into 17 different chromatographic intervals and each interval were individually modeled by PARAFAC2. Three main outputs of the PARAFAC2 models described: (1) elution time profile, (2) relative abundance, and (3) pure mass spectra of the resolved peaks modeled from each interval of the chromatographic data. PARAFAC2 scores corresponding to relative abundances of the resolved peaks were extracted and further used for correlation and partial least squares (PLS) analysis. A total of 71 PARAFAC2 components (which correspond to actual peaks, baselines and tails of neighboring peaks) were modeled from 17 different chromatographic retention time intervals of the LC–MS data. In addition to four previously known saponins, correlation- and PLS-analysis resolved five unknown saponin-like compounds that were significantly correlated with insect resistance. The method also enabled a good separation between resistant and susceptible F2 plants. PARAFAC2 spectral loadings corresponding to the pure mass spectra of chromatographic peaks matched well with experimentally recorded mass spectra (correlation based similarity >95%). This enabled to extract pure mass spectra of highly overlapped and low s/n ratio peaks.

ChemInform Abstract: Rapid Multidimensional NMR: Decomposition Methods and Their Applications

AbstractReview: 30 refs.

Applications of tensor (multiway array) factorizations and decompositions in data mining

AbstractTensor (multiway array) factorization and decomposition has become an important tool for data mining. Fueled by the computational power of modern computer researchers can now analyze large‐scale tensorial structured data that only a few years ago would have been impossible. Tensor factorizations have several advantages over two‐way matrix factorizations including uniqueness of the optimal solution and component identification even when most of the data is missing. Furthermore, multiway decomposition techniques explicitly exploit the multiway structure that is lost when collapsing some of the modes of the tensor in order to analyze the data by regular matrix factorization approaches. Multiway decomposition is being applied to new fields every year and there is no doubt that the future will bring many exciting new applications. The aim of this overview is to introduce the basic concepts of tensor decompositions and demonstrate some of the many benefits and challenges of modeling data multiway for a wide variety of data and problem domains. © 2011 John Wiley & Sons, Inc.WIREs Data Mining Knowl Discov2011 1 24‐40 DOI: 10.1002/widm.1This article is categorized under:Algorithmic Development > Scalable Statistical MethodsTechnologies > ClassificationTechnologies > Machine LearningTechnologies > Structure Discovery and Clustering

Parallel factor analysis of EEM of the fluorescence of carbon dots nanoparticles

AbstractThe effect of experimental factors [pH and Hg(II)] on the fluorescence excitation emission matrices (EEMs) of nanosensor carbon dots (CDs) was analyzed by multiway decomposition methods based on parallel factor (PARAFAC) analysis. PARAFAC analysis of the EEM structures identifies three components corresponding to two different‐sized CDs with the Hg(II) and pH profiles highly correlated plus a background. Parallel profiles with Linear Dependences (PARALIND) model with three components in the excitation–emission spectral modes and two components in the Hg(II) or pH mode gave similar results as PARAFAC, but is more useful from a theoretical point of view because PARALIND shows that the two different‐sized CDs have similar chemical reactivity toward Hg(II) and pH. PARAFAC2 was used as a trilinear confirmatory test of the data structures under analysis. Copyright © 2010 John Wiley & Sons, Ltd.

A classification tool for N-way array based on SIMCA methodology

In the literature there are only few papers concerned with classification methods for multi-way arrays. The most common procedure, by far, is to unfold the multi-way data array into an ordinary matrix and then to apply the traditional multivariate tools for classification. As opposed to unfolding the data several possibilities exist for building classification models more directly based on the multi-way structure of the data. As an example, multi-way partial least squares discriminant analysis has been used as a supervised classification method, another alternative that has been investigated is to perform classification using Fisher's LDA or SIMCA on the score matrix from e.g. a PARAFAC or a Tucker model. Despite a few attempts of applying such multi-way classification approaches, no-one has looked into how such models are best built and implemented. In this work, the SIMCA method is extended to three-way arrays. Included in this work is also actual code that will work on general multi-way arrays rather than just three-way arrays. In analogy with two-way SIMCA, a decomposition model is separately built for the multi-way data for each class, using multi-way decomposition method such as PARAFAC or Tucker3. In the choice of the best class dimensionality, i.e. number of latent factors, both the results of cross-validation but mainly the sensitivity/specificity values are evaluated. In order to estimate the class limits for each class model, orthogonal and score distances are considered, and different statistics are implemented and tested to set confidence limits for these two parameters. Classification performance using different definitions of class boundaries and classification rules, including the use of cross-validated residuals and scores is compared. The proposed N-SIMCA methodology and code, besides simulated data sets of varying dimensionality, has been tested on two case studies, concerning food authentication tasks for typical food products.

Multiway chemometric decomposition of EEM of fluorescence of CdTe quantum dots obtained as function of pH

The effect of the pH (from 3 to 10) on the excitation emission matrices (EEMs) of fluorescence of CdTe quantum dots (QDs), capped with mercaptopropionic acid (MPA), were analyzed by multiway decomposition methods of parallel factor analysis (PARAFAC), a variant of the parallel factor analysis method (PARAFAC2) and multivariate curve resolution alternating least squares (MCR-ALS). Three different sized CdTe QDs with emission maximum at 555 nm (QDa), 594 nm (QDb) and 628 nm (QDc) were selected for analysis. The three-way data structures composed of sets of EEMs obtained as function of the pH (EEMs, pH) do not have a trilinear structure. A marked deviation to the trilinearity is observed in the emission wavelength order—the emission spectra suffers wavelength shift as the pH is varied. The pH-induced variation of the fluorescence properties of QDs is described with only one-component PARAFAC2 or MCR-ALS models—other components are necessary to model scattering and/or other background signals in (EEMs, pH) data structures. Bigger sized QDs are more suitable tools for analytical methodologies because they show higher Stokes shifts (resulting in simpler models) and higher pH range sensitivity. The pH dependence of the maximum wavelength of the emission spectra is particularly suitable for the development of QDs/EEMs wavelength-encoded pH sensor bioimaging or biological label methodologies when coupled to multiway chemometric decomposition.

Assignment of protein NMR spectra based on projections, multi-way decomposition and a fast correlation approach

We present an approach for the assignment of protein NMR resonances that combines established and new concepts: (a) Based on published reduced dimensionality methods, two 5-dimensional experiments are proposed. (b) Multi-way decomposition (PRODECOMP) applied simultaneously to all acquired NMR spectra provides the assignment of resonance frequencies under conditions of very low signal-to-noise. (c) Each resulting component characterizes all spin (1/2) nuclei in a (doubly-labeled) CbetaH(n)-CalphaH-C'-NH-CalphaH-CbetaH(n) fragment in an unambiguous manner, such that sequentially neighboring components have about four atoms in common. (d) A new routine (SHABBA) determines correlations for all component pairs based on the common nuclei; high correlation values yield sequential chains of a dozen or more components. (e) The potentially error-prone peak picking is delayed to the last step, where it helps to place the component chains within the protein sequence, and thus to achieve the final backbone assignment. The approach was validated by achieving complete backbone resonance assignments for ubiquitin.

PRODECOMPv3: decompositions of NMR projections for protein backbone and side-chain assignments and structural studies

PRODECOMP (projection decomposition) is an implementation of a multi-way decomposition algorithm for the analysis of two-dimensional projections of high-dimensional nuclear magnetic resonance spectra. The newest version, PRODECOMPv3, features a dramatic speedup, more reliable decompositions, a substantial reduction in memory demands, a new graphical user interface and integration into third-party software. These improvements extend the applicability of decompositions to novel types of NMR data on proteins, yielding backbone and side-chain assignments as well as structural information, and therewith enabling complete characterizations of proteins. Program, short manual and an example calculation are freely available at www2.chem.gu.se/bcbp/nmr/prodecomp.html.

460 パラレルファクター解析法を用いた梁の振動解析

This paper proposes to utilize the multi-way decomposition method PARAFAC for analysis on lateral vibration of a simply supported beam. First we use wavelet transform to pre-process the data series measured by five sensors, then the coefficients of the wavelet transform are decomposed by PARAFAC to trilinear components, which represent frequency, temporal, and spatial profiles. We easily obtain natural frequencies and modal shapes. Results of numerical calculations show the validity of this method.

On the distribution of UV-blue fluorescent organic matter in the Southern Ocean

The purpose of the work presented in this paper was to study the components of fluorescent organic matter (FOM) resulting from multi-way decomposition of excitation-emission matrices (EEMs) and to find out how their relative distributions and amounts were affected by the changing hydrography and productivity in the Southern Ocean. Data were collected during the austral summer 97/98 along the 6°E meridian covering the area between the spring ice edge and the Subtropical Front. By multiway PARAllel FACtor (PARAFAC) analysis, fluorescence EEMs could be decomposed into components that could be used for relative quantification. It is shown that three components suffice to model the fluorescence in this specific region. Two of the components obtained were protein-like and directly related to in-situ production/degradation; they were correlated with chlorophyll a, and were found to mix down to the core of the Antarctic intermediate water (AAIW) in the Subtropical Front. One component was classified as UV/Visible humic-like and showed a distribution that was very closely related to the qsu-calibrated fluorescence, i.e. indicative of terrestrial input, and of long term processes in the ocean. We suggest that the UV/Visible humic-like component consists of refractory material that is not produced or degraded significantly. It is concluded that a small number of components from PARAFAC analysis were satisfactory representatives of the major types of UV-blue fluorescent structural units present. The qualitative and quantitative results from the PARAFAC model also correlated well with other chemical and physical parameters.