Non-negative Matrix Factorization Decomposition Research Articles

Heat-induced changes in soil water-extractable organic matter characterized using fluorescence and FTIR spectroscopies coupled with dimensionality reduction methods

Water extractable organic matter (WEOM) is a very mobile and reactive soil OM fraction, critical in the translocation of carbon (C) from soils to other environmental compartments. Transformations of WEOM due to soil heating can have implications not only at a local scale, but in places far away from the location of the event. However, their accurate characterization is costly when analyzing a large number of samples. The objectives of this work were to identify common patterns for the changes in WEOM caused by the heating of various soil types using a combination of spectroscopic and dimensionality reduction techniques. Six soils from Spain, Kenya and Israel were collected at depths 0–10 cm and analysed before and after heating in air to temperatures of 300 and 600 °C. Fluorescence EEMs were measured in soil–water extracts containing WEOM, and decomposed using parallel factor (PARAFAC) analysis. The FTIR spectra were measured in freeze-dried extracts and further analysed using non-negative matrix factorization (NMF). Total organic C and SUVA254 values of the extracts experienced changes with the heating treatments that were soil dependant. Four PARAFAC and three NMF components were sufficient to characterize WEOM changes in all soils, which showed common thermal transformation patterns irrespective of their origin and properties. Thermal transformation of fluorescent WEOM led to the increase in the proportion of a component with an emission maximum at Ex 300/Em 392 nm, and to a lower extent one with the emission maximum at Ex 300/Em 426 nm. Concomitantly, the proportion of components with emission maxima at longer excitation wavelengths was reduced. These changes occurred at the lowest heating temperature and were maintained at 600 °C, and they seem to indicate a depletion of fluorescent components more conjugated, bigger in size, and an enrichment in smaller ones. The NMF components obtained from FTIR spectra showed an increase of the proportion of compounds with CO bonds, more oxidized. No correlations were found between the components obtained with each method, thus indicating that the information obtained from the fluorescence EEMs-PARAFAC analysis and the NMF decomposition of FTIR spectra is complementary. It can be concluded that there is a common pattern of WEOM changes induced by thermal soil transformations irrespective of the origin and properties of the soils studied, and that the combination of different spectroscopic techniques coupled with dimensionality reduction methods can be used as a simple and low-cost method to fingerprint changes in WEOM composition, in general, and those caused by soil heating, in particular.

Two subtypes of cutaneous melanoma with distinct mutational signatures and clinico-genomic characteristics.

Background: To decipher mutational signatures and their associations with biological implications in cutaneous melanomas (CMs), including those with a low ultraviolet (UV) signature. Materials and Methods: We applied non-negative matrix factorization (NMF) and unsupervised clustering to the 96-class mutational context of The Cancer Genome Atlas (TCGA) cohort (N = 466) as well as other publicly available datasets (N = 527). To explore the feasibility of mutational signature-based classification using panel sequencing data, independent panel sequencing data were analyzed. Results: NMF decomposition of the TCGA cohort and other publicly available datasets consistently found two mutational signatures: UV (SBS7a/7b dominant) and non-UV (SBS1/5 dominant) signatures. Based on mutational signatures, TCGA CMs were classified into two clusters: UV-high and UV-low. CMs belonging to the UV-low cluster showed significantly worse overall survival and landmark survival at 1-year than those in the UV-high cluster; low or high UV signature remained the most significant prognostic factor in multivariate analysis. The UV-low cluster showed distinct genomic and functional characteristic patterns: low mutation counts, increased proportion of triple wild-type and KIT mutations, high burden of copy number alteration, expression of genes related to keratinocyte differentiation, and low activation of tumor immunity. We verified that UV-high and UV-low clusters can be distinguished by panel sequencing. Conclusion: Our study revealed two mutational signatures of CMs that divide CMs into two clusters with distinct clinico-genomic characteristics. Our results will be helpful for the clinical application of mutational signature-based classification of CMs.

Heart-lung sound separation by nonnegative matrix factorization and deep learning

Auscultation is an ordinary way to diagnose cardiovascular and respiratory diseases. The heart-lung sound (HLS) from the stethoscope is a mixture of heart sound (HS) and lung sound (LS). The first and most crucial step is to differentiate between HS and LS from the mixture signal. This paper proposes an unsupervised single-channel blind source separation (BSS) algorithm based on nonnegative matrix factorization (NMF) and deep learning (DL). Firstly, HS signals are extracted by the multi-constrained NMF (MCNMF) decomposition algorithm and K-means & SVM (KS) clustering method proposed in this paper, and different types of HS signals are classified by a convolutional neural network (CNN). Then, the HLS is separated by the embedding space centroid network (ECNet) proposed in our study. The method outperforms the known state-of-the-art techniques in all evaluation metrics SNR, SDR, SIR, SAR, and correlation coefficient. Our algorithm has two advantages: 1) this study is the first to combine NMF and DL for the HLS separation. MCNMF with selected constraints can have a more substantial sparsity effect that improves the decomposition accuracy. KS clustering algorithm can distinguish the HS component from the LS component in two clustering results. By mapping classified HLS into an embedding space, the ECNet demonstrates excellent separation results. 2) HS extraction and classification first, then HLS separation. Because our method exploits more detailed information from HS types in HLS before BSS, the ECNet can outperform other HLS separation methods.

Constrained non-negative matrix factorization enabling real-time insights of in situ and high-throughput experiments

Non-negative matrix factorization (NMF) is an appealing class of methods for performing unsupervised learning on streaming spectral data, particularly in time-sensitive applications such as in situ characterization of materials. These methods seek to decompose a dataset into a small number of components and weights that can compactly represent the underlying signal while effectively reconstructing the observations with minimal error. However, canonical NMF methods have no underlying requirement that the reconstruction uses components or weights that are representative of the true physical processes. In this work, we demonstrate how constraining a subset of the NMF weights or components as rigid priors, provided as known or assumed values, can provide significant improvement in revealing true underlying phenomena. We present a PyTorch-based method for efficiently applying constrained NMF and demonstrate its application to several synthetic examples. Our implementation allows an expert researcher-in-the-loop to provide and dynamically adjust the constraints during a live experiment involving streaming spectral data. Such interactive priors allow researchers to specify known or identified independent components, as well as functional expectations about the mixing or transitions between the components. We further demonstrate the application of this method to measured synchrotron x-ray total scattering data from in situ beamline experiments. In such a context, constrained NMF can result in a more interpretive and scientifically relevant decomposition than canonical NMF or other decomposition techniques. The details of the method are provided, along with general guidance for employing constrained NMF in the extraction of critical information and insights during time-sensitive experimental applications.

Improved SVD-based initialization for nonnegative matrix factorization using low-rank correction

Due to the iterative nature of the most nonnegative matrix factorization (NMF) algorithms, initialization is a key aspect as it significantly influences both the convergence and the final solution obtained. Many initialization schemes have been proposed for NMF, among which one of the most popular class of methods are based on the singular value decomposition (SVD) and clustering. However, these SVD-based initializations as well as clustering based initializations (if they dense their right factor H), do not satisfy a rather natural condition, namely that the error should decrease as the rank of factorization increases. In this paper, we propose a novel SVD-based NMF initialization to specifically address this shortcoming by taking into account the SVD factors that were discarded to obtain a nonnegative initialization. This method, referred to as nonnegative SVD with low-rank correction (NNSVD-LRC), allows us to significantly reduce the initial error at a negligible additional computational cost using the low-rank structure of the discarded SVD factors. NNSVD-LRC has two other advantages compared to other NMF initializations: (1) it provably generates sparse initial factors, and (2) it is faster as it only requires to compute a truncated SVD of rank ⌊r2+1⌋ where r is the factorization rank of the sought NMF decomposition (as opposed to a rank-r truncated SVD for other methods). We show on several standard dense and sparse data sets that our new method competes favorably with state-of-the-art SVD-based and clustering based initializations for NMF.

Hybrid Projective Nonnegative Matrix Factorization With Drum Dictionaries for Harmonic/Percussive Source Separation

One of the most general models of music signals considers that such signals can be represented as a sum of two distinct components: a tonal part that is sparse in frequency and temporally stable and a transient (or percussive) part that is composed of short-term broadband sounds. In this paper, we propose a novel hybrid method built upon nonnegative matrix factorization (NMF) that decomposes the time frequency representation of an audio signal into such two components. The tonal part is estimated by a sparse and orthogonal nonnegative decomposition, and the transient part is estimated by a straightforward NMF decomposition constrained by a pre-learned dictionary of smooth spectra. The optimization problem at the heart of our method remains simple with very few hyperparameters and can be solved thanks to simple multiplicative update rules. The extensive benchmark on a large and varied music database against four state of the art harmonic/percussive source separation algorithms demonstrate the merit of the proposed approach.

Determined Blind Source Separation Unifying Independent Vector Analysis and Nonnegative Matrix Factorization

This paper addresses the determined blind source separation problem and proposes a new effective method unifying independent vector analysis (IVA) and nonnegative matrix factorization (NMF). IVA is a state-of-the-art technique that utilizes the statistical independence between sources in a mixture signal, and an efficient optimization scheme has been proposed for IVA. However, since the source model in IVA is based on a spherical multivariate distribution, IVA cannot utilize specific spectral structures such as the harmonic structures of pitched instrumental sounds. To solve this problem, we introduce NMF decomposition as the source model in IVA to capture the spectral structures. The formulation of the proposed method is derived from conventional multichannel NMF (MNMF), which reveals the relationship between MNMF and IVA. The proposed method can be optimized by the update rules of IVA and single-channel NMF. Experimental results show the efficacy of the proposed method compared with IVA and MNMF in terms of separation accuracy and convergence speed.

Sleep-spindle identification on EEG signals from polysomnographie recordings using correntropy.

Sleep spindles (SSs) are characteristic electroencephalographic (EEG) waveforms of sleep stages N2 and N3. One of the main problems associated with SS detection is the high number of false positives. In this paper we propose a new periodogram based on correntropy to detect SSs and enhance their characterization. Correntropy is a generalized correlation, under the information theoretic learning framework. A non-negative matrix factorization decomposition of correntropy allows us to obtain a new periodogram, which shows an improved resolution capability compared to the conventional power spectrum density. Preliminary results show that the proposed method obtained a sensitivity rate of 0.868 with a false positive rate of 0.121.

A Modified Adaptive GMM Approach Based GMM Supervector and I-vector Using NMF Decomposition for Robust Speaker Verification

We propose a new method to enhance performance of speaker verification by investigating a novel modification of adaptive Gaussian Mixture Model (GMM) training. This model is trained using a modified Expectation Maximization (EM) algorithm, combined with a modified Maximum A Posteriori (MAP) estimation based weight factor of observation probabilities, called the observation confidence. The observation confidence is calculated based on the SNR estimation. Based on this modified adaptive GMM training algorithm, we propose to construct GMM supervectors and i-vectors, which are considered as input feature vectors for SVM. Besides, the discriminant features for speaker verification are also exploited by using non-negative matrix factorization (NMF) in the GMM-supervector and i-vector space. Experiment results on utterances from Korean drama (“You came from the stars”) show that our proposed methods significantly outperform the baseline GMM-UBM, GMM-supervector and i-vector based SVM under various noisy conditions.

Joint source separation and dereverberation using constrained spectral divergence optimization

A novel method of joint source separation and dereverberation that minimizes the divergence between the observed and true spectral subband envelopes is discussed in this paper. This divergence minimization is carried out within the non-negative matrix factorization (NMF) framework by imposing certain non-negative constraints on the subband envelopes. Additionally, the joint source separation and dereverberation framework described herein utilizes the spectral subband envelope obtained from group delay spectral magnitude (GDSM). In order to obtain the spectral subband envelope from the GDSM, the equivalence of the magnitude and the group delay spectrum via the weighted cepstrum is used. Since the subband envelope of the group delay spectral magnitude is robust and has a high spectral resolution, less error is noted in the NMF decomposition. Late reverberation components present in the separated signals are then removed using a modified spectral subtraction technique. The quality of separated and dereverberated speech signal is evaluated using several objective and subjective criteria. Experiments on distant speech recognition are then conducted at various direct-to-reverberant ratios (DRR) on the GRID corpus. Experimental results indicate significant improvements over existing methods in the literature.

Projected Gradients for Subclass Discriminant Nonnegative Subspace Learning

Current discriminant nonnegative matrix factorization (NMF) methods either do not guarantee convergence to a stationary limit point or assume a compact data distribution inside classes, thus ignoring intra class variance in extracting discriminant data samples representations. To address both limitations, we regard that data inside each class has a multimodal distribution, forming various subclasses and perform optimization using a projected gradients framework to ensure limit point stationarity. The proposed method combines appropriate clustering-based discriminant criteria in the NMF decomposition cost function, in order to find discriminant projections that enhance class separability in the reduced dimensional projection space, thus improving classification performance. The developed algorithms have been applied to facial expression, face and object recognition, and experimental results verified that they successfully identified discriminant parts, thus enhancing recognition performance.

Nonnegative Matrix Factorization Based Adaptive Noise Sensing over Wireless Sensor Networks

An adaptive noise sensing method is proposed to improve the speech sensing performance of speech-based applications operated over wireless sensor networks. The proposed method is based on nonnegative matrix factorization (NMF), which consists of adaptive noise sensing and noise reduction. In other words, adaptive noise sensing is performed by adapting a priori noise basis matrix of the NMF, which is estimated from the noise signal, resulting in an adapted noise basis matrix. Subsequently, the adapted noise basis matrix is used for the NMF decomposition of noisy speech into clean speech and background noise. The estimated clean speech signal is then applied to a front-end of the speech-based applications. The performance of the proposed NMF-based noise sensing and reduction method is first evaluated by measuring the source to distortion ratio (SDR), the source to interferences ratio (SIR), and the source to artifacts ratio (SAR). In addition, the proposed method is applied to an automatic speech recognition (ASR) system, which is a typical speech-based application, and then the average word error rate (WER) of the ASR is compared with that employing either a Wiener filter, or a conventional NMF-based noise reduction method using only a priori noise basis matrix.

Source separation using regularized NMF with MMSE estimates under GMM priors with online learning for the uncertainties

We propose a new method to incorporate priors on the solution of nonnegative matrix factorization (NMF). The NMF solution is guided to follow the minimum mean square error (MMSE) estimates of the weight combinations under a Gaussian mixture model (GMM) prior. The proposed algorithm can be used for denoising or single-channel source separation (SCSS) applications. NMF is used in SCSS in two main stages, the training stage and the separation stage. In the training stage, NMF is used to decompose the training data spectrogram for each source into a multiplication of a trained basis and gains matrices. In the separation stage, the mixed signal spectrogram is decomposed as a weighted linear combination of the trained basis matrices for the source signals. In this work, to improve the separation performance of NMF, the trained gains matrices are used to guide the solution of the NMF weights during the separation stage. The trained gains matrix is used to train a prior GMM that captures the statistics of the valid weight combinations that the columns of the basis matrix can receive for a given source signal. In the separation stage, the prior GMMs are used to guide the NMF solution of the gains/weights matrices using MMSE estimation. The NMF decomposition weights matrix is treated as a distorted image by a distortion operator, which is learned directly from the observed signals. The MMSE estimate of the weights matrix under the trained GMM prior and log-normal distribution for the distortion is then found to improve the NMF decomposition results. The MMSE estimate is embedded within the optimization objective to form a novel regularized NMF cost function. The corresponding update rules for the new objectives are derived in this paper. The proposed MMSE estimates based regularization avoids the problem of computing the hyper-parameters and the regularization parameters. MMSE also provides a better estimate for the valid gains matrix. Experimental results show that the proposed regularized NMF algorithm improves the source separation performance compared with using NMF without a prior or with other prior models.

Subclass discriminant Nonnegative Matrix Factorization for facial image analysis

Nonnegative Matrix Factorization (NMF) is among the most popular subspace methods, widely used in a variety of image processing problems. Recently, a discriminant NMF method that incorporates Linear Discriminant Analysis inspired criteria has been proposed, which achieves an efficient decomposition of the provided data to its discriminant parts, thus enhancing classification performance. However, this approach possesses certain limitations, since it assumes that the underlying data distribution is unimodal, which is often unrealistic. To remedy this limitation, we regard that data inside each class have a multimodal distribution, thus forming clusters and use criteria inspired by Clustering based Discriminant Analysis. The proposed method incorporates appropriate discriminant constraints in the NMF decomposition cost function in order to address the problem of finding discriminant projections that enhance class separability in the reduced dimensional projection space, while taking into account subclass information. The developed algorithm has been applied for both facial expression and face recognition on three popular databases. Experimental results verified that it successfully identified discriminant facial parts, thus enhancing recognition performance.

Symmetric Nonnegative Matrix Factorization: Algorithms and Applications to Probabilistic Clustering

Nonnegative matrix factorization (NMF) is an unsupervised learning method useful in various applications including image processing and semantic analysis of documents. This paper focuses on symmetric NMF (SNMF), which is a special case of NMF decomposition. Three parallel multiplicative update algorithms using level 3 basic linear algebra subprograms directly are developed for this problem. First, by minimizing the Euclidean distance, a multiplicative update algorithm is proposed, and its convergence under mild conditions is proved. Based on it, we further propose another two fast parallel methods: α-SNMF and β -SNMF algorithms. All of them are easy to implement. These algorithms are applied to probabilistic clustering. We demonstrate their effectiveness for facial image clustering, document categorization, and pattern clustering in gene expression.

A non-negative matrix factorization framework for identifying modular patterns in metagenomic profile data

Metagenomic studies sequence DNA directly from environmental samples to explore the structure and function of complex microbial and viral communities. Individual, short pieces of sequenced DNA ("reads") are classified into (putative) taxonomic or metabolic groups which are analyzed for patterns across samples. Analysis of such read matrices is at the core of using metagenomic data to make inferences about ecosystem structure and function. Non-negative matrix factorization (NMF) is a numerical technique for approximating high-dimensional data points as positive linear combinations of positive components. It is thus well suited to interpretation of observed samples as combinations of different components. We develop, test and apply an NMF-based framework to analyze metagenomic read matrices. In particular, we introduce a method for choosing NMF degree in the presence of overlap, and apply spectral-reordering techniques to NMF-based similarity matrices to aid visualization. We show that our method can robustly identify the appropriate degree and disentangle overlapping contributions using synthetic data sets. We then examine and discuss the NMF decomposition of a metabolic profile matrix extracted from 39 publicly available metagenomic samples, and identify canonical sample types, including one associated with coral ecosystems, one associated with highly saline ecosystems and others. We also identify specific associations between pathways and canonical environments, and explore how alternative choices of decompositions facilitate analysis of read matrices at a finer scale.

Exploiting discriminant information in nonnegative matrix factorization with application to frontal face verification

In this paper, two supervised methods for enhancing the classification accuracy of the Nonnegative Matrix Factorization (NMF) algorithm are presented. The idea is to extend the NMF algorithm in order to extract features that enforce not only the spatial locality, but also the separability between classes in a discriminant manner. The first method employs discriminant analysis in the features derived from NMF. In this way, a two-phase discriminant feature extraction procedure is implemented, namely NMF plus Linear Discriminant Analysis (LDA). The second method incorporates the discriminant constraints inside the NMF decomposition. Thus, a decomposition of a face to its discriminant parts is obtained and new update rules for both the weights and the basis images are derived. The introduced methods have been applied to the problem of frontal face verification using the well-known XM2VTS database. Both methods greatly enhance the performance of NMF for frontal face verification.