Application Of Non-negative Matrix Factorization Research Articles

Metabotypes Related to Meat and Vegetable Intake Reflect Microbial, Lipid and Amino Acid Metabolism in Healthy People.

The objective of this study is to develop a new methodology to identify the relationship between dietary patterns and metabolites indicative of food intake and metabolism. Plasma and urine samples from healthy Swiss subjects (n = 89) collected over two time points are analyzed for a panel of host-microbial metabolites using GC- and LC-MS. Dietary intake is evaluated using a validated food frequency questionnaire. Dietary pattern clusters and relationships with metabolites are determined using Non-Negative Matrix Factorization (NNMF) and Sparse Generalized Canonical Correlation Analysis (SGCCA). Use of NNMF allows detection of latent diet clusters in this population, which describes a high intake of meat or vegetables. SGCCA associates these clusters to i) diet-host microbial and lipid associated bile acid metabolism, and ii) essential amino acid metabolism. This novel application of NNMF and SGCCA allows detection of distinct metabotypes for meat and vegetable dietary patterns in a heterogeneous population. As many of the metabolites associated with meat or vegetable intake are the result of host-microbiota interactions, the findings support a role for microbiota mediating the metabolic imprinting of different dietary choices.

An Endmember Initialization Scheme for Nonnegative Matrix Factorization and Its Application in Hyperspectral Unmixing

Nonnegative matrix factorization (NMF) is a blind source separation (BSS) method often used in hyperspectral unmixing. However, it tends to converge to a local optimum. To overcome this limitation, we present a simple, but effective endmember initialization scheme for NMF, which is realized by improving initial values through the application of the automatic target generation process (ATGP) algorithm. The initial spectra and abundances of target endmembers are first obtained using the ATGP algorithm and nonnegative least squares (NNLS) method, respectively. The preliminary results are then optimized through iterative application of NMF. To validate the applicability and effectiveness of the proposed method, we analyzed the improvement of NMF by the ATGP algorithm, using the synthetic hyperspectral data and real hyperspectral images. The results from the proposed method are compared with those of the vertex component analysis (VCA)-NMF algorithm, which uses the VCA algorithm to perform initialization for NMF, the minimum volume constrained NMF (MVC-NMF) algorithm, the traditional two-step VCA-fully-constrained least squares (FCLS) algorithm, which uses the VCA to extract the endmember matrix, and the FCLS algorithm to estimate the abundance matrix. The comparison results prove that proper endmember initialization can help the NMF algorithm yield better estimation results. Through the optimization of target endmembers’ initial values, the proposed ATGP-NMF algorithm can consistently produce good results at a lower computational cost, especially in the case of a real hyperspectral image for which pure pixels do not exist and there is little prior knowledge. With its high applicability and effectiveness, the ATGP-NMF algorithm has a great potential to solve hyperspectral unmixing problems.

A novel approach for data-driven process and condition monitoring systems on the example of mill-turn centers

Implementing condition monitoring functionality in production machinery often proves to be a difficult task. Device- and process-specific algorithms must be created while inhomogeneous industrial communication networks hinder the aggregation of control signals and process variables. Further challenges arise from the advance of flexible cyber-physical systems (CPS) and the industrial internet of things (IIoT). They demand a service-oriented condition monitoring architecture, which seamlessly adapts to quickly changing production topologies. In this context, data-driven systems which are capable of unsupervised learning are promising approaches. The aim is the autonomous identification of significant process variables and patterns. This paper describes a machine learning approach for a condition and process monitoring system on the basis of pattern recognition within structure-borne noise of rotating cutting machinery. Process states are defined under application of non-negative matrix factorization (NMF). A production model is learned and deployed on the basis of Gaussian mixture models (GMM) and hidden Markov models (HMM) in a two stage process. Additionally a generic framework to ease the implementation of decentralized condition monitoring functionalities is given. A decentralized component, the monitoring module, constitutes a part of a holistic condition monitoring architecture managed by a central server. The approach is evaluated on the example of mill-turn centers.

Joint Linear Regression and Nonnegative Matrix Factorization Based on Self-Organized Graph for Image Clustering and Classification

Nonnegative matrix factorization (NMF) technique has been developed successfully to represent the intuitively meaningful feature of data. A suitable representation can faithfully preserve the intrinsic structure of data. Due to the fact that it introduces the label information, semi-supervised NMF has been demonstrated more advantageous in image representation than original NMF. However, previous semi-supervised NMF variants construct a label indicator matrix only for tagging the labeled data and not being optimized together with the matrix factorization. It is short of label propagation and fails to work for predicting the attribution of data. Moreover, the transductive semi-supervised NMF variants cannot dispose the prediction of unseen data, restricting the application of NMF. In this paper, a joint optimization framework of linear regression and NMF (LR-NMF) based on the self-organized graph is proposed for a completed task which simultaneously takes into account image representation and attribution prediction. By minimizing the proposed objective, three interactive threads are running: decomposing the data into nonnegative basis matrix and the corresponding representation, linear regression using the nonnegative representation, and label propagation based on the self-organized graph which is defined in the feature space. The products of LR-NMF can be viewed as extracting nonnegative feature for clustering, meanwhile, they can be used to solve the out-of-sample problem for classification. Extensive clustering and classification experiments on the digit, face, and object challenging data sets are presented to show the efficacy of the proposed LR-NMF algorithm.

Bird sound spectrogram decomposition through Non-Negative Matrix Factorization for the acoustic classification of bird species.

Feature extraction for Acoustic Bird Species Classification (ABSC) tasks has traditionally been based on parametric representations that were specifically developed for speech signals, such as Mel Frequency Cepstral Coefficients (MFCC). However, the discrimination capabilities of these features for ABSC could be enhanced by accounting for the vocal production mechanisms of birds, and, in particular, the spectro-temporal structure of bird sounds. In this paper, a new front-end for ABSC is proposed that incorporates this specific information through the non-negative decomposition of bird sound spectrograms. It consists of the following two different stages: short-time feature extraction and temporal feature integration. In the first stage, which aims at providing a better spectral representation of bird sounds on a frame-by-frame basis, two methods are evaluated. In the first method, cepstral-like features (NMF_CC) are extracted by using a filter bank that is automatically learned by means of the application of Non-Negative Matrix Factorization (NMF) on bird audio spectrograms. In the second method, the features are directly derived from the activation coefficients of the spectrogram decomposition as performed through NMF (H_CC). The second stage summarizes the most relevant information contained in the short-time features by computing several statistical measures over long segments. The experiments show that the use of NMF_CC and H_CC in conjunction with temporal integration significantly improves the performance of a Support Vector Machine (SVM)-based ABSC system with respect to conventional MFCC.

Enhancing social collaborative filtering through the application of non-negative matrix factorization and exponential random graph models

Social collaborative filtering recommender systems extend the traditional user-to-item interaction with explicit user-to-user relationships, thereby allowing for a wider exploration of correlations among users and items, that potentially lead to better recommendations. A number of methods have been proposed in the direction of exploring the social network, either locally (i.e. the vicinity of each user) or globally. In this paper, we propose a novel methodology for collaborative filtering social recommendation that tries to combine the merits of both the aforementioned approaches, based on the soft-clustering of the Friend-of-a-Friend (FoaF) network of each user. This task is accomplished by the non-negative factorization of the adjacency matrix of the FoaF graph, while the edge-centric logic of the factorization algorithm is ameliorated by incorporating more general structural properties of the graph, such as the number of edges and stars, through the introduction of the exponential random graph models. The preliminary results obtained reveal the potential of this idea.

Regularized Non-Negative Matrix Factorization for Identifying Differentially Expressed Genes and Clustering Samples: A Survey.

Non-negative Matrix Factorization (NMF), a classical method for dimensionality reduction, has been applied in many fields. It is based on the idea that negative numbers are physically meaningless in various data-processing tasks. Apart from its contribution to conventional data analysis, the recent overwhelming interest in NMF is due to its newly discovered ability to solve challenging data mining and machine learning problems, especially in relation to gene expression data. This survey paper mainly focuses on research examining the application of NMF to identify differentially expressed genes and to cluster samples, and the main NMF models, properties, principles, and algorithms with its various generalizations, extensions, and modifications are summarized. The experimental results demonstrate the performance of the various NMF algorithms in identifying differentially expressed genes and clustering samples.

Nonnegative Matrix Factorization with Integrated Graph and Feature Learning

Matrix factorization is a useful technique for data representation in many data mining and machine learning tasks. Particularly, for data sets with all nonnegative entries, matrix factorization often requires that factor matrices be nonnegative, leading to nonnegative matrix factorization (NMF). One important application of NMF is for clustering with reduced dimensions of the data represented in the new feature space. In this paper, we propose a new graph regularized NMF method capable of feature learning and apply it to clustering. Unlike existing NMF methods that treat all features in the original feature space equally, our method distinguishes features by incorporating a feature-wise sparse approximation error matrix in the formulation. It enables important features to be more closely approximated by the factor matrices. Meanwhile, the graph of the data is constructed using cleaner features in the feature learning process, which integrates feature learning and manifold learning procedures into a unified NMF model. This distinctly differs from applying the existing graph-based NMF models after feature selection in that, when these two procedures are independently used, they often fail to align themselves toward obtaining a compact and most expressive data representation. Comprehensive experimental results demonstrate the effectiveness of the proposed method, which outperforms state-of-the-art algorithms when applied to clustering.

Accelerated anti-lopsided algorithm for nonnegative least squares

Nonnegative least squares (NNLS) problem has been widely used in scientific computation and data modeling, especially for low-rank representation such as nonnegative matrix and tensor factorization. When applied to large-scale datasets, first-order methods are preferred to provide fast flexible computation for regularized NNLS variants, but they still have the limitations of performance and convergence as key challenges. In this paper, we propose an accelerated anti-lopsided algorithm for NNLS with linear over-bounded convergence rate $$\left[ \left( 1 - \frac{\mu }{L}\right) \left( 1-\frac{\mu }{nL}\right) ^{2n}\right] ^k$$ in the subspace of passive variables where $$\mu $$ and L are always bounded as $$\frac{1}{2} \le \mu \le L \le n$$ , and n is the dimension size of solutions, which is highly competitive with current advanced methods such as accelerated gradient methods having sub-linear convergence $$\frac{L}{k^2}$$ , and greedy coordinate descent methods having convergence $$\left( 1 - \frac{\mu }{nL}\right) ^k$$ , where $$\mu $$ and L are unbounded. The proposed algorithm transforms the variable x into the new space satisfying the second derivative equals constant $$\frac{\partial ^2 f}{\partial x_i^2} = 1$$ for all variables $$x_i$$ to implicitly exploit the second-order derivative, and to guarantee that $$\mu $$ and L are always bounded in order to achieve over-bounded convergence of the algorithm, and to enhance the performance of internal processes based on exact line search, greedy coordinate descent methods, and accelerated search. The experiments on large matrices and real applications of nonnegative matrix factorization clearly show the higher performance of the proposed algorithm in comparison with the state-of-the-art algorithms.

Multiparametric Non-Negative Matrix Factorization for Longitudinal Variations Detection in White-Matter Fiber Bundles.

Processing of longitudinal diffusion tensor imaging (DTI) data is a crucial challenge to better understand pathological mechanisms of complex brain diseases such as multiple sclerosis (MS) where white-matter (WM) fiber bundles are variably altered by inflammatory events. In this study, we propose a new fully automated method to detect longitudinal changes in diffusivity metrics along WM fiber bundles. The proposed method is divided in three main parts: 1) preprocessing of longitudinal diffusion acquisitions, 2) WM fiber-bundle extraction, and 3) application of nonnegative matrix factorization and density-based local outliers algorithms to detect and delineate longitudinal variations appearing in the cross section of the WM fiber bundle. In order to validate our method, we introduce a new model to simulate real longitudinal changes based on a generalized Gaussian probability density function. Moreover, we applied our method on longitudinal data. High level of performances were obtained for the detection of small longitudinal changes along the WM fiber bundles in MS patients.

Using semi-nonnegative matrix underapproximation for statistical process monitoring

In this paper, we explore the application of nonnegative matrix factorization (NMF) in statistical process monitoring. NMF has become a famous dimension reduction and feature extraction method due to its ability to produce highly localized, sparse and parts-based representation. However, NMF and all kinds of its variants have to suffer their failure to obtain some kind of statistical property of data. In this paper, semi-NMF, a variant of NMF, is first improved to reduce the correlation of the obtained low-dimensional data using an underapproximation technique called semi-nonnegative matrix underapproximation (semi-NMU). As a result, semi-NMU can extract latent variables with lower correlation and additionally obtain base matrix with higher sparsity and orthogonality. Then semi-NMU is used for fault detection. The monitoring performance of semi-NMU is evaluated by three case studies.

Application of non-negative matrix factorization to LC/MS data

Liquid Chromatography-Mass Spectrometry (LC/MS) provides large datasets from which one needs to extract the relevant information. Since these data are made of non-negative mixtures of non-negative mass spectra, non-negative matrix factorization (NMF) is well suited for their processing. These data are however very difficult to deal with since they are usually contaminated with non-Gaussian noise and the intensities vary on several orders of magnitude. In this paper, we propose an adaptation of a state-of-the-art NMF algorithms so as to specifically be able to deal with LC/MS data, by using a non-stationary noise model and a stochastic term. We finally perform experiments and compare standard NMF algorithms on both simulated data and an annotated LC/MS dataset. The results of these experiments highlight the significant improvement obtained by our adaptation over other NMF algorithms.

Acoustic Event Classification using spectral band selection and Non-Negative Matrix Factorization-based features

Feature extraction methods for sound events have been traditionally based on parametric representations specifically developed for speech signals, such as the well-known Mel Frequency Cepstrum Coefficients (MFCC). However, the discrimination capabilities of these features for Acoustic Event Classification (AEC) tasks could be enhanced by taking into account the spectro-temporal structure of acoustic event signals. In this paper, a new front-end for AEC which incorporates this specific information is proposed. It consists of two different stages: short-time feature extraction and temporal feature integration. The first module aims at providing a better spectral representation of the different acoustic events on a frame-by-frame basis, by means of the automatic selection of the optimal set of frequency bands from which cepstral-like features are extracted. The second stage is designed for capturing the most relevant temporal information in the short-time features, through the application of Non-Negative Matrix Factorization (NMF) on their periodograms computed over long audio segments. The whole front-end has been evaluated in clean and noisy conditions. Experiments show that the removal of certain frequency bands (which are mainly located in the medium region of the spectrum for clean conditions and in low frequencies for noisy environments) in the short-time feature computation process in conjunction with the NMF technique for temporal feature integration improves significantly the performance of a Support Vector Machine (SVM) based AEC system with respect to the use of conventional MFCCs.

Intermuscular coherence contributions in synergistic muscles during pedaling.

The execution of rhythmical motor tasks requires the control of multiple skeletal muscles by the Central Nervous System (CNS), and the neural mechanisms according to which the CNS manages their coordination are not completely clear yet. In this study, we analyze the distribution of the neural drive shared across muscles that work synergistically during the execution of a free pedaling task. Electromyographic (EMG) activity was recorded from eight lower limb muscles of eleven healthy untrained participants during an unconstrained pedaling exercise. The coordinated activity of the lower limb muscles was described within the framework of muscle synergies, extracted through the application of nonnegative matrix factorization. Intermuscular synchronization was assessed by calculating intermuscular coherence between pairs of EMG signals from co-active, both synergistic and non-synergistic muscles within their periods of co-activation. The spatiotemporal structure of muscle coordination during pedaling was well represented by four muscle synergies for all the subjects. Significant coherence values within the gamma band (30-60 Hz) were identified only for one out of the four extracted muscle synergies. This synergy is mainly composed of the activity of knee extensor muscles, and its function is related to the power production and crank propelling during the pedaling cycle. In addition, a significant coherence peak was found in the lower frequencies for the GAM/SOL muscle pair, possibly related to the ankle stabilizing function of these two muscles during the pedaling task. No synchronization was found either for the other extracted muscle synergies or for pairs of co-active but non-synergistic muscles. The obtained results seem to suggest the presence of intermuscular synchronization only when a functional force production is required, with the observed gamma band contribution possibly reflecting a cortical drive to synergistic muscles during pedaling.

The application of principal component analysis and non-negative matrix factorization to analyze time-resolved optical waveguide absorption spectroscopy data

Time-resolved optical waveguide absorption spectroscopy (OWAS) makes use of an evanescent field to detect the polarized absorption spectra of sub-monomolecular adlayers. This technique is suitable for the investigation of kinetics at the solid–liquid interface of dyes, pigments, fluorescent molecules, quantum dots, metallic nanoparticles, and proteins with chromophores. In this work, we demonstrate for the first time the application of non-negative matrix factorization (NMF) to the analysis of time-resolved OWAS data, because NMF prevents the negative factors from occurring, avoids contradicting physical reality, and makes factors more easily interpretable. Meanwhile, principal component analysis (PCA) is researched for the comparison of NMF. Two-factor loadings and scores derived by PCA and NMF are consistent with the results analyzed by the function of time/wavelength-absorbance. Moreover, NMF avoids contradicting physical reality, and makes factors more easily interpretable. We believe that NMF will provide a valuable analysis route to allow processing of increasingly large and complex data sets.

Application of non-negative matrix factorization to multispectral FLIM data analysis

Existing methods of interpreting fluorescence lifetime imaging microscopy (FLIM) images are based on comparing the intensity and lifetime values at each pixel with those of known fluorophores. This method becomes unwieldy and subjective in many practical applications where there are several fluorescing species contributing to the bulk fluorescence signal, and even more so in the case of multispectral FLIM. Non-negative matrix factorization (NMF) is a multivariate data analysis technique aimed at extracting non-negative signatures of pure components and their non-negative abundances from an additive mixture of those components. In this paper, we present the application of NMF to multispectral time-domain FLIM data to obtain a new set of FLIM features (relative abundance of constituent fluorophores). These features are more intuitive and easier to interpret than the standard fluorescence intensity and lifetime values. The proposed approach, unlike several FLIM data analysis methods, is not limited by the number of constituent fluorescing species or their possibly complex decay dynamics. Moreover, the new set of FLIM features can be obtained by processing raw multispectral FLIM intensity data, thereby rendering time deconvolution unnecessary and resulting in lesser computational time and relaxed SNR requirements. The performance of the NMF method was validated on simulated and experimental multispectral time-domain FLIM data. The NMF features were also compared against the standard intensity and lifetime features, in terms of their ability to discriminate between different types of atherosclerotic plaques.

Abstract 2995: Identifying subtypes of colorectal cancer tumors and cell lines with treatment relevance using iterative clustering (iNMF)

Abstract Genetic and epigenetic features such as KRAS mutation status have been used to define colorectal cancer (CRC) subtypes and to take treatment decisions. In order to develop new targeted drugs, however, it is necessary to gain a better understanding of the molecular differences of CRC subtypes. We developed a new unsupervised approach for stratifying tumor samples using genome-wide mRNA expression data. Our method is based on the iterative application of non-negative matrix factorization (iNMF) on randomly selected sets of genes. In a sample set consisting of 63 CRC tumors, we identified two dominant subtypes. These subtypes were highly concordant with the epithelial-mesenchymal-transition (EMT) gene expression signatures consistent with recent publications. However further stratification of the tumor samples revealed five subtypes. These subtypes exhibit distinct differences, most notably differential activation of specific signaling pathways. Importantly, assessment of this method and derived subtype gene signatures stratified several independent, published datasets, suggesting that the signatures capture disease-relevant intrinsic features of CRC. Furthermore, application of the gene signatures to expression data obtained from three independent colon cell line panels revealed that the tumor subtypes were represented in all these different panels. Additional integration of pharmacological response data allowed us to identify several targeted compounds showing differential response across the subtypes. The CRC stratification obtained with our new method, iNMF, offers valuable insight into the differences between CRC subtypes at a functional level. Most importantly, it captures features of the disease that are highly relevant for the development of new targeted drugs in defined CRC patient sub-populations. Citation Format: {Authors}. {Abstract title} [abstract]. In: Proceedings of the 103rd Annual Meeting of the American Association for Cancer Research; 2012 Mar 31-Apr 4; Chicago, IL. Philadelphia (PA): AACR; Cancer Res 2012;72(8 Suppl):Abstract nr 2995. doi:1538-7445.AM2012-2995

An insect-inspired bionic sensor for tactile localization and material classification with state-dependent modulation

Insects carry a pair of antennae on their head: multimodal sensory organs that serve a wide range of sensory-guided behaviors. During locomotion, antennae are involved in near-range orientation, for example in detecting, localizing, probing, and negotiating obstacles. Here we present a bionic, active tactile sensing system inspired by insect antennae. It comprises an actuated elastic rod equipped with a terminal acceleration sensor. The measurement principle is based on the analysis of damped harmonic oscillations registered upon contact with an object. The dominant frequency of the oscillation is extracted to determine the distance of the contact point along the probe and basal angular encoders allow tactile localization in a polar coordinate system. Finally, the damping behavior of the registered signal is exploited to determine the most likely material. The tactile sensor is tested in four approaches with increasing neural plausibility: first, we show that peak extraction from the Fourier spectrum is sufficient for tactile localization with position errors below 1%. Also, the damping property of the extracted frequency is used for material classification. Second, we show that the Fourier spectrum can be analysed by an Artificial Neural Network (ANN) which can be trained to decode contact distance and to classify contact materials. Thirdly, we show how efficiency can be improved by band-pass filtering the Fourier spectrum by application of non-negative matrix factorization. This reduces the input dimension by 95% while reducing classification performance by 8% only. Finally, we replace the FFT by an array of spiking neurons with gradually differing resonance properties, such that their spike rate is a function of the input frequency. We show that this network can be applied to detect tactile contact events of a wheeled robot, and how detrimental effects of robot velocity on antennal dynamics can be suppressed by state-dependent modulation of the input signals.

A flexible R package for nonnegative matrix factorization

BackgroundNonnegative Matrix Factorization (NMF) is an unsupervised learning technique that has been applied successfully in several fields, including signal processing, face recognition and text mining. Recent applications of NMF in bioinformatics have demonstrated its ability to extract meaningful information from high-dimensional data such as gene expression microarrays. Developments in NMF theory and applications have resulted in a variety of algorithms and methods. However, most NMF implementations have been on commercial platforms, while those that are freely available typically require programming skills. This limits their use by the wider research community.ResultsOur objective is to provide the bioinformatics community with an open-source, easy-to-use and unified interface to standard NMF algorithms, as well as with a simple framework to help implement and test new NMF methods. For that purpose, we have developed a package for the R/BioConductor platform. The package ports public code to R, and is structured to enable users to easily modify and/or add algorithms. It includes a number of published NMF algorithms and initialization methods and facilitates the combination of these to produce new NMF strategies. Commonly used benchmark data and visualization methods are provided to help in the comparison and interpretation of the results.ConclusionsThe NMF package helps realize the potential of Nonnegative Matrix Factorization, especially in bioinformatics, providing easy access to methods that have already yielded new insights in many applications. Documentation, source code and sample data are available from CRAN.

Nonnegative Matrix Factorization of Laboratory Astrophysical Ice Mixtures

We present an application of nonnegative matrix factorization (NMF) in astrophysics. It consists of the study of ice mixtures obtained in the laboratory. They simulate real astrophysical ices. The goal is to identify the molecules that are present in the ice mixtures. The data correspond to the infrared absorption spectra of ices formed by different combinations of molecules. The spectra and abundances are nonnegative, allowing the application of NMF. In addition, the statistics of the spectra correspond to supergaussian signals, so a sparseness restriction can be added. We review some NMF algorithms imposing sparseness in a Bayesian framework. We perform several simulations with artificial mixtures of ices in order to compare the algorithms and with real mixtures to show the usefulness of the approach. NMF is revealed as a powerful technique to analyze large databases in order to determine the compounds present in every ice.