A novel trilinear decomposition algorithm： Three-dimension non-negative matrix factorization

Non-negative matrix factorization(NMF)is a technique for dimensionality reduction by placing non-negativity constraints onthe matrix.Based on the PARAFAC model,NMF was extended for three-dimension data decomposition.The three-dimension non-negative matrix factorization(NMF3)algorithm,which was concise and easy to implement,was given in this paper.The NMF3algorithm implementation was based on elements but not on vectors.It could decompose a data array directly without unfolding,which was not similar to that the traditional algorithms do.It has been applied to the simulated data array decomposition andobtained reasonable results.It showed that NMF3 could be introduced for curve resolution in chemometrics.     

Blind separation of fluorescence spectra using sparse non‐negative matrix factorization on right hand factor

Sparse non‐negative matrix factorization on right side factor (SNMF/R) has better performance in feature extraction than non‐negative matrix factorization. In this work, SNMF/R was first used to separate the overlapped three‐dimensional fluorescence spectra of polycyclic aromatic hydrocarbons mixtures in pure water, lake water, and river water, respectively. It is found that the similarity coefficients between the acquired three‐dimensional spectra and the corresponding reference spectra with random initials are all above 0.80; the recognition rate of SNMF/R is higher than that of PARAFAC and non‐negative matrix factorization algorithms, especially in the case of lake water and river water samples. In addition, SNMF/R does not need any initialization scheme designing during spectra separation. These results demonstrate that SNMF/R is an appropriate algorithm to separate the overlapped fluorescence spectra of polycyclic aromatic hydrocarbons in aquatic environment accurately and effectively. Copyright © 2015 John Wiley & Sons, Ltd.     

非负矩阵因子分解法分析苍术的气相色谱-质谱重叠峰

非负矩阵因子分解（non-negative matrix factorization，NMF）是对非负数据处理的一种多元统计分析方法。NMF分解结果没有“负值”，易于理解和解释，具有比较明确的物理化学意义。由于其多解的特征，文献介绍的NMF算法并不能直接用于化学混合信号解析。作者根据化学波谱的基本特征（化学波谱的平滑性、色谱的单峰性以及质谱的稀疏性）对NMF算法进行了改进，缩小了其多解范围。应用改进的NMF进行模拟HPLC-DAD型两维数据（其中色谱严重重叠和完全重叠）和苍术GC／MS实验数据解析，得到了比较理想的结果。实验表明，改进后的NMF是一个可用于复杂样品化学信号分析的化学计量学新方法。     

Direct decomposition of three-way arrays using a non-negative approximation

Non-negative matrix approximation (NNMA) has been used in diverse scientific fields, but it still has some major limitations. In the present study a novel trilinear decomposition method, termed three-way NNMA (TWNNMA), was developed. The method decomposes three-way arrays directly without unfolding and overcomes the restriction of locking zero elements in the deduced multiplicative update rules by adding a positive symmetric matrix. Direct trilinear decomposition was used as the TWNNMA initialization method and experimental results confirm that this greatly accelerated the convergence. An obvious advantage of TWNNMA is the uniqueness of the non-negative solution, which facilitates a better understanding of the underlying physical realities of complex data. TWNNMA was applied in complex systems such as chemical kinetics, second-order calibration and analysis of GC-MS data. The results demonstrate that TWNNMA, differing from previous trilinear decomposition methods, is comparable to existing second-order calibration methods and represents a promising resolution method for complex systems.     

Integrative graph regularized matrix factorization for drug-pathway associations analysis

Pathway-based drug discovery can give full consideration to the efficacy of compounds in the systemic physiological environment. The recently emerged drug-pathway association identification approaches gain popularity due to its potential to decipher the mechanism of action and the targets of compounds. In this study, we propose a novel drug-pathway association identification method: Integrative Graph regularized Matrix Factorization (IGMF). It employs graph regularization to encode data geometrical information and prevent possible overfitting in prediction. Furthermore, it achieves parts-based and sparse data representation by imposing L₁-norm regularization on the objective function.Empirical studies demonstrate that IGMF has strong advantages in identifying more new drug-pathway associations compared to its peer methods. It further shows a good capability to unveil the intrinsic structures of data. As an effective drug-pathway discovery method, it will inspire new analytics methods in this subfield.     

Component recognition with three‐dimensional fluorescence spectra based on non‐negative matrix factorization

Non‐negative matrix factorization (NMF) is a widely used approach in signal processing. In this work, we apply it to the component recognition of mixtures with multicomponent three‐dimensional fluorescence spectra. Compared with the popular PARAFAC for component recognition, NMF has the following advantages: on one hand, the decomposed spectra are three dimensional, and thus, more information can be obtained, which is beneficial for component recognition; on the other hand, the decomposed spectra are non‐negative and thus have a certain physical significance. More importantly, we propose a type of integrated similarity indices for the three‐dimensional fluorescence spectra, which, by construction, is good at component recognition from overlapping fluorescence spectra. Experiment results demonstrate that NMF combined with integrated similarity index provides an effective method for component recognition of multicomponent three‐dimensional overlapping fluorescence spectra. Copyright © 2011 John Wiley & Sons, Ltd.     

A multiresolution approach for the convergence acceleration of multivariate curve resolution methods

Modern computerized spectroscopic instrumentation can result in high volumes of spectroscopic data. Such accurate measurements rise special computational challenges for multivariate curve resolution techniques since pure component factorizations are often solved via constrained minimization problems. The computational costs for these calculations rapidly grow with an increased time or frequency resolution of the spectral measurements.     

Accurate grading of brain gliomas by soft independent modeling of class analogy based on non‐negative matrix factorization of proton magnetic resonance spectra

Hydrogen magnetic resonance spectroscopy (¹H‐MRS) is a non‐invasive technique which provides a ‘frequency‐signal intensity’ spectrum of biochemical compounds of tissues in the body. Although this method is currently used in human brain studies, accurate classification of in‐vivo ¹H‐MRS is a challenging task in the diagnosis of brain tumors. Problems such as overlapping metabolite peaks, incomplete information on background component and low signal‐to‐noise ratio disturb classification results of this spectroscopic method. This study presents an alternative approach to the soft independent modeling of class analogy (SIMCA) technique, using non‐negative matrix factorization (NMF) for dimensionality reduction. In the adopted strategy, the performance of SIMCA was improved by application of a robust algorithm for classification in the presence of noisy measurements. Total of 219 spectra from two databases were taken by water‐suppressed short echo‐time ¹H‐MRS, acquired from different subjects with different stages of glial brain tumors (Grade II (26 cases), grade III (24 cases), grade IV (41 cases), as well as 25 healthy cases). The SIMCA was performed using two approaches: (i) principal component analysis (PCA) and (ii) non‐negative matrix factorization (NMF), as a modified approach. Square prediction error was considered to assess the class membership of the external validation set. Finally, several figures of merit such as the correct classification rate (CCR), sensitivity and specificity were calculated. Results of SIMCA based on NMF showed significant improvement in percentage of correctly classified samples, 91.4% versus 83.5% for PCA‐based model in an independent test set. Copyright © 2015 John Wiley & Sons, Ltd.     

The application and comparison of several chemometric methods of excitation-emission matrix spectra in studying the interactions of metal complexes with DNA

The interactions of fs DNA and two metal complexes [Cu(phen)SO₄]·2H₂O and [Ni(phen)SO₄]·2H₂O were explored by several chemometric methods, including parallel factor (PARAFAC), singular value decomposition-least squares (SVD-LS), and singular value decomposition-nonnegative least squares (SVD-NNLS) of excitation-emission matrix spectra (EEMs). The applications of SVD-LS and SVD-NNLS in this domain have been discussed. Rayleigh scatter part is avoided by ordered zero and reconstructed by linear interpolation. The importance of avoiding Rayleigh scatter has also been discussed. All the three methods do well in qualitative analysis. SVD-LS does best in present small changes of ethidium bromide (EB). In order to get accurate results, PARAFAC and SVD-NNLS can be utilized together in quantitative analysis. All the three chemometric methods indicate that the DNA binding modes of [Cu(phen)SO₄]·2H₂O are hydrogen bond effect and intercalation, while intercalation is the only DNA binding mode for [Ni(phen)SO₄]·2H₂O. These results are verified by the electronic absorption and emission fluorescence spectra. Just like PARAFAC, both SVD-LS and SVD-NNLS are proven to be convenient and convincing in studying the interactions between nucleic acids and complexes.     

Decomposition of mixtures' spectra by multivariate curve resolution of rapidly acquired TOCSY experiments

A method is presented that allows for retrieving 1D spectra of the individual components of a mixture from a sparsely acquired 2D‐TOCSY spectrum. The decomposition of the 2D‐TOCSY data into pure 1D traces is achieved using a non‐negative matrix factorization algorithm, also known as multivariate curve resolution analysis. Here, we show that the algorithm can be applied to data processed in the direct dimension only. Thus, our method can be applied to non‐linearly sampled experiments or data acquired with few indirect points. An example is shown for the spectra of a mixture of six amino acids, acquired in 15 min. Copyright © 2010 John Wiley & Sons, Ltd.     

Novel matrix strategies for improved ionization and spatial resolution using IR-MALDESI mass spectrometry imaging

In mass spectrometry imaging (MSI) applications of infrared matrix-assisted laser desorption electrospray ionization (IR-MALDESI), an exogenous ice layer is the gold standard for an energy-absorbing matrix. However, the formation of the ice matrix requires additional time and instrument hardware, so glycerol was investigated herein as an alternative to the ice matrix to potentially improve spatial resolution and ionization, while decreasing experiment time. Glycerol solutions of varying concentrations were sprayed over top of rat liver tissue sections for analysis by IR-MALDESI and compared to the typical ice matrix condition. Additionally, we tested if combining the ice matrix and glycerol matrix would further improve analyses. Matrix conditions were evaluated by comparing ion abundance of six lipid species, the laser ablation spot diameter, and number of METASPACE annotations. The ion abundances were also normalized to the volume of tissue ablated to correct for lower abundance values due to less ablated tissue. It was observed that utilizing a 50% glycerol matrix without ice provides improved spatial resolution with lipid abundances and annotations comparable to the ice matrix standard, while decreasing the time required to complete an IR-MALDESI tissue imaging experiment.     

Multi‐component analysis: blind extraction of pure components mass spectra using sparse component analysis

The paper presents sparse component analysis (SCA)‐based blind decomposition of the mixtures of mass spectra into pure components, wherein the number of mixtures is less than number of pure components. Standard solutions of the related blind source separation (BSS) problem that are published in the open literature require the number of mixtures to be greater than or equal to the unknown number of pure components. Specifically, we have demonstrated experimentally the capability of the SCA to blindly extract five pure components mass spectra from two mixtures only. Two approaches to SCA are tested: the first one based on ?₁ norm minimization implemented through linear programming and the second one implemented through multilayer hierarchical alternating least square nonnegative matrix factorization with sparseness constraints imposed on pure components spectra. In contrast to many existing blind decomposition methods no a priori information about the number of pure components is required. It is estimated from the mixtures using robust data clustering algorithm together with pure components concentration matrix. Proposed methodology can be implemented as a part of software packages used for the analysis of mass spectra and identification of chemical compounds. Copyright © 2009 John Wiley & Sons, Ltd.     

Resolution of multicomponent overlapped peaks A comparison of several curve resolution methods

Several curve resolution methods were compared in their performance of identification and quantification of overlapping peaks. These resolution methods are heuristic evolving latent projections (HELP), sub-window factor analysis (SFA), and orthogonal projection resolution (OPR). In this paper, HELP, SFA and OPR with the rank map produced by evolving factor analysis (EFA) or fixed size moving window-evolving factor analysis (FSMW-EFA) were applied to the simulated and experimental data. The resolved results were compared qualitatively and quantitatively. In addition, the further comparison was carried out with the results obtained from multivariate curve resolution-alternate least square (MCR-ALS) by using the initial estimates provided by EFA.     

Rapid analysis of multicomponent pesticide mixture by GC-MS with the aid of chemometric resolution

Applications of hyphenated chromatographic techniques, especially GC-MS technique, have been reported in chemical, biological, environmental, agricultural and medical analysis. The complexity of the samples in these fields is still an obstacle for the technique to be practical and the overlapping of the multicomponent signals induces chemometric methods widely employed. In this work, taking the rapid analysis of pesticide mixture as an example, a chemometric approach was proposed for resolution of multicomponent overlapping GC-MS signal. In the method, a mass spectral library of pesticides was organized at first, then target factor analysis (TFA) was employed for testing the existence of a specific pesticide in the multicomponent overlapping GC-MS signal, and finally the chromatographic information of the pesticide was extracted by a non-negative immune algorithm (IA). A GC-MS signal of a 40-component pesticide mixture eluted within 9 min was analyzed by the method. It was found that the mass spectra and chromatographic profiles of almost all the pesticides can be obtained.     

Pressure drop effects on selectivity and resolution in packed column supercritical fluid chromatography

The influence of pressure drop on retention, selectivity, plate height and resolution was investigated systematically in packed supercritical fluid chromatography (SFC) using pure carbon dioxide as the mobile phase. Numerical methods developed previously which enabled the prediction of pressure gradients, diffusivities, capacity factors, plate heights and resolutions along the length of the column were used for the model calculations. The effects of inlet pressure and supercritical fluid flow rate on selectivity and resolution are studied. In packed column SFC with pure carbon dioxide as the mobile phase, the pressure drop can have a significant effect on resolution. The flow rate is shown to have a larger effect than generally realized. The calculated data are shown to be in good agreement with the experimental results. Finally, the variation of the chromatographic parameters along a 5.5 meter long model SFC column is illustrated. The possibilities and limitations of using long packed columns in SFC are discussed. It is demonstrated that long columns with large plate numbers do not necessarily yield better separations.     

Comparative qualitative analysis of nonylphenol isomers by gas chromatography-mass spectrometry combined with chemometric resolution

The relationship between nonylphenol (NP) isomers' structures and their estrogenic potencies has been evaluated previously. However, due to their similarities in both chemical and physical properties, complete separation and identification remain strikingly difficult. In the present study, gas chromatography-mass spectrometry (GC-MS) is employed to separate commercial NP isomers. Both extracted ion chromatograms (EIC) based on selected ions known to be definitive for the suite of isomers, and the heuristic evolving latent projection (HELP) chemometric resolution method have been applied for the analysis and identification of the NP isomers. This method corrected the wrong identification of one isomer which was suspected based on the EIC data, and also was able to be applied for the determination of an additional isomer with low abundance. Overall, 15 NP isomers have been proposed by the HELP interpretation method. Pure component chromatograms and mass spectra have been extracted with the aid of chemometric resolution. The applicability of the commercial deconvolution software package automated mass spectral deconvolution and identification system (AMDIS) has also been tested against the HELP method for comparative presentation of pure component mass spectra.     

基质固相分散-超高效液相色谱-质谱检测器测定牛奶中9种类固醇激素残留

利用基质固相分散技术(MSPD),建立了超高效液相色谱-质谱检测器(MSD)同时分析牛奶中9种类固醇激素残留的方法。便携式MSD的灵敏度和准确度优于紫外检测器;相比传统的质谱仪,MSD不需质谱参数优化,操作简便,开机抽真空时间短(只要5 min),即开即用。分别考察了流动相比例、萃取溶剂和固相萃取小柱净化对MSD灵敏度和牛奶样品基质效应的影响。结果表明,MSD正离子模式对吸电子基团化合物的灵敏度更高,受外界条件影响大。经MSPD净化后,9种类固醇激素的基质效应由84%~160%降低为80%~121%。方法学研究结果表明,9种类固醇激素的日内精密度和日间精密度分别为0.87%~1.78%和1.82%~3.79%,加标回收率为68.7%~94.7%,相对标准偏差(RSD)小于10%,方法检出限(LOD)为0.5~10 μ g/kg,定量限(LOQ)为2~20 μ g/kg。该方法适合日常大批量样品的检测。     

Improved spectra for MALDI MSI of peptides using ammonium phosphate monobasic in MALDI matrix

MALDI mass spectrometry imaging (MSI) enables analysis of peptides along with histology. However, there are several critical steps in MALDI MSI of peptides, 1 of which is spectral quality. Suppression of MALDI matrix clusters by the aid of ammonium salts in MALDI experiments is well known. It is asserted that addition of ammonium salts dissociates potential matrix adducts and thereafter decreases matrix cluster formation. Consequently, MALDI MS sensitivity and mass accuracy increase. Up to our knowledge, a limited number of MALDI MSI studies used ammonium salts as matrix additives to suppress matrix clusters and enhance peptide signals. In this work, we investigated the effect of ammonium phosphate monobasic (AmP) as alpha‐cyano‐4‐hydroxycinnamic acid (α‐CHCA) matrix additive in MALDI MSI of peptides. Prior to MALDI MSI, the effect of varying concentrations of AmP in α‐CHCA was assessed in bovine serum albumin tryptic digests and compared with the control (α‐CHCA without AmP). Based on our data, the addition of AmP as matrix additive decreased matrix cluster formation regardless of its concentration, and specifically, 8 mM AmP and 10 mM AmP increased bovine serum albumin peptide signal intensities. In MALDI MSI of peptides, both 8 and 10 mM AmP in α‐CHCA improved peptide signals especially in the mass range of m/z 2000 to 3000. In particular, 9 peptide signals were found to have differential intensities within the tissues deposited with AmP in α‐CHCA (AUC > 0.60). To the best of our knowledge, this is the first MALDI MSI of peptides work investigating different concentrations of AmP as α‐CHCA matrix additive to enhance peptide signals in formalin‐fixed paraffin‐embedded (FFPE) tissues. Further, AmP as part of α‐CHCA matrix could enhance protein identifications and support MALDI MSI‐based proteomic approaches.     

All-valence-electron and transition density matrix calculations of the electronic spectra of [2.2]paracyclophanequinones

The combined CNDO/S and transition density matrix methods reproduced well the UV-VIS spectra of the intramolecular charge-transfer complexes of double- and triple-layered [2.2]paracyclophanequinones in which benzene and p-benzoquinone represent the donor and acceptor layers: DA, DDA and DAD. Calculations pointed to the already known experimental bathochromic shifts of the longest wavelength absorption band for the DADDADAD transformations. The electronic transitions corresponding to this band are for DA and DDA the CT transitions of the ^* type; however, for DAD the band represents the n ^* transition localized on the acceptor ring.     

Sources and source regions effecting the aerosol composition of the Eastern Mediterranean

Positive matrix factorization (PMF) was used to deduce the aerosol sources at a rural site on the Mediterranean coast of Turkey, using sample collected between February 1992 and December 1993. Approximately 600 daily aerosol samples were collected and 40 elements and compounds were analyzed by atomic absorption spectrometry, instrumental neutron activation analysis, ion chromatography and colorimetry.Seven factors were identified with PMF, namely local dust, Saharan dust, sea salt, long range transport, smelter, arsenic and fertilizer factors. The non-parametric bootstrapped potential source contribution function (PSCF) was then used to help identify likely locations of the regional sources of pollution. Besides, explained variance, enrichment factors, seasonal variation of G-score values and back trajectories were used to define the source regions of the factors. Results demonstrated that there are major potential source areas, for the pollution-derived component in aerosol mass, on the Aegean coast, Northwest Turkey, Balkan countries, Ukraine and regions located northern part of Ukraine.