Component Non-negative Matrix Factorization Research Articles

Interpretable dimensionality reduction and classification of mass spectrometry imaging data in a visceral pain model via non-negative matrix factorization.

Mass spectrometry imaging (MSI) is a powerful scientific tool for understanding the spatial distribution of biochemical compounds in tissue structures. In this paper, we introduce three novel approaches in MSI data processing to perform the tasks of data augmentation, feature ranking, and image registration. We use these approaches in conjunction with non-negative matrix factorization (NMF) to resolve two of the biggest challenges in MSI data analysis, namely: 1) the large file sizes and associated computational resource requirements and 2) the complexity of interpreting the very high dimensional raw spectral data. There are many dimensionality reduction techniques that address the first challenge but do not necessarily result in readily interpretable features, leaving the second challenge unaddressed. We demonstrate that NMF is an effective dimensionality reduction algorithm that reduces the size of MSI datasets by three orders of magnitude with limited loss of information, yielding spatial and spectral components with meaningful correlation to tissue structure that may be used directly for subsequent data analysis without the need for additional clustering steps. This analysis is demonstrated on an MSI dataset from female Sprague-Dawley rats for an animal model of comorbid visceral pain hypersensitivity (CPH). We find that high-dimensional MSI data (∼ 100,000 ions per pixel) can be reduced to 20 spectral NMF components with < 20% loss in reconstruction accuracy. The resulting spatial NMF components are reproducible and correlate well with H&E-stained tissue images. These components may also be used to generate images with enhanced specificity for different tissue types. Small patches of NMF data (i.e., 20 spatial NMF components over 20 × 20 pixels) provide an accuracy of ∼ 87% in classifying CPH vs naïve control subjects. This paper presents the novel data processing methodologies that were used to produce these results, encompassing novel data processing pipelines for data augmentation to support training for classification, ranking of features according to their contribution to classification, and image registration to enhance tissue-specific imaging.

Factorizer: A scalable interpretable approach to context modeling for medical image segmentation.

Convolutional Neural Networks (CNNs) with U-shaped architectures have dominated medical image segmentation, which is crucial for various clinical purposes. However, the inherent locality of convolution makes CNNs fail to fully exploit global context, essential for better recognition of some structures, e.g., brain lesions. Transformers have recently proven promising performance on vision tasks, including semantic segmentation, mainly due to their capability of modeling long-range dependencies. Nevertheless, the quadratic complexity of attention makes existing Transformer-based models use self-attention layers only after somehow reducing the image resolution, which limits the ability to capture global contexts present at higher resolutions. Therefore, this work introduces a family of models, dubbed Factorizer, which leverages the power of low-rank matrix factorization for constructing an end-to-end segmentation model. Specifically, we propose a linearly scalable approach to context modeling, formulating Nonnegative Matrix Factorization (NMF) as a differentiable layer integrated into a U-shaped architecture. The shifted window technique is also utilized in combination with NMF to effectively aggregate local information. Factorizers compete favorably with CNNs and Transformers in terms of accuracy, scalability, and interpretability, achieving state-of-the-art results on the BraTS dataset for brain tumor segmentation and ISLES'22 dataset for stroke lesion segmentation. Highly meaningful NMF components give an additional interpretability advantage to Factorizers over CNNs and Transformers. Moreover, our ablation studies reveal a distinctive feature of Factorizers that enables a significant speed-up in inference for a trained Factorizer without any extra steps and without sacrificing much accuracy. The code and models are publicly available at https://github.com/pashtari/factorizer.

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.

Unsupervised detection of fragment length signatures of circulating tumor DNA using non-negative matrix factorization.

Sequencing of cell-free DNA (cfDNA) is currently being used to detect cancer by searching both for mutational and non-mutational alterations. Recent work has shown that the length distribution of cfDNA fragments from a cancer patient can inform tumor load and type. Here, we propose non-negative matrix factorization (NMF) of fragment length distributions as a novel and completely unsupervised method for studying fragment length patterns in cfDNA. Using shallow whole-genome sequencing (sWGS) of cfDNA from a cohort of patients with metastatic castration-resistant prostate cancer (mCRPC), we demonstrate how NMF accurately infers the true tumor fragment length distribution as an NMF component - and that the sample weights of this component correlate with ctDNA levels (r=0.75). We further demonstrate how using several NMF components enables accurate cancer detection on data from various early stage cancers (AUC = 0.96). Finally, we show that NMF, when applied across genomic regions, can be used to discover fragment length signatures associated with open chromatin.

Prospective association between dietary pesticide exposure profiles and type 2 diabetes risk in the NutriNet-Santé cohort

BackgroundStudies focusing on dietary pesticides in population-based samples are scarce and little is known about potential mixture effects. We aimed to assess associations between dietary pesticide exposure profiles and Type 2 Diabetes (T2D) among NutriNet-Santé cohort participants.MethodsParticipants completed a Food Frequency Questionnaire at baseline, assessing conventional and organic food consumption. Exposures to 25 active substances used in European Union pesticides were estimated using the Chemisches und Veterinäruntersuchungsamt Stuttgart residue database accounting for farming practices. T2D were identified through several sources.Exposure profiles were established using Non-Negative Matrix Factorization (NMF), adapted for sparse data. Cox models adjusted for known confounders were used to estimate hazard ratios (HR) and 95% confidence interval (95% CI), for the associations between four NMF components, divided into quintiles (Q) and T2D risk.ResultsThe sample comprised 33,013 participants aged 53 years old on average, including 76% of women. During follow-up (median: 5.95 years), 340 incident T2D cases were diagnosed.Positive associations were detected between NMF component 1 (reflecting highest exposure to several synthetic pesticides) and T2D risk on the whole sample: HRQ5vsQ1 = 1.47, 95% CI (1.00, 2.18). NMF Component 3 (reflecting low exposure to several synthetic pesticides) was associated with a decrease in T2D risk, among those with high dietary quality only (high adherence to French dietary guidelines, including high plant foods consumption): HRQ5vsQ1 = 0.31, 95% CI (0.10, 0.94).ConclusionsThese findings suggest a role of dietary pesticide exposure in T2D risk, with different effects depending on which types of pesticide mixture participants are exposed to. These associations need to be confirmed in other types of studies and settings, and could have important implications for developing prevention strategies (regulation, dietary guidelines).Trial RegistrationThis study is registered in ClinicalTrials.gov (NCT03335644).

Label-free analytic histology of carotid atherosclerosis by mid-infrared optoacoustic microscopy

Background and aimsAnalysis of atherosclerotic plaque composition is a vital tool for unraveling the pathological metabolic processes that contribute to plaque growth. MethodsWe visualize the constitution of human carotid plaques by mid-infrared optoacoustic microscopy (MiROM), a method for label-free analytic histology that requires minimal tissue preparation, rapidly yielding large field-of-view en-face images with a resolution of a few micrometers. We imaged endarterectomy specimens (n = 3, 12 sections total) at specific vibrational modes, targeting carbohydrates, lipids and proteins. Additionally, we recorded spectra at selected tissue locations. We identified correlations in the variability in this high-dimensional data set using non-negative matrix factorization (NMF). ResultsWe visualized high-risk plaque features with molecular assignment. Consistent NMF components relate to different dominant tissue constituents, dominated by lipids, proteins, and cholesterol and carbohydrates respectively. ConclusionsThese results introduce MiROM as an innovative, stain-free, analytic histology technology for the biochemical characterization of complex human vascular pathology.

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.

Prospective association between dietary pesticide exposure profiles and Type 2 Diabetes risk

Abstract Background Many modifiable risk factors have been identified for type 2 diabetes. However, emerging risk factors such as food contaminants could also play a role and studies are lacking on the subject. We aimed to assess the prospective associations between dietary pesticide exposure profiles and Type 2 Diabetes (T2D) risk among NutriNet-Santé cohort participants. Methods In 2014, participants completed a Food Frequency Questionnaire, assessing conventional and organic food consumption. Exposures to 25 active substances were estimated using a residue database accounting for farming practices from Chemisches und Veterinäruntersuchungsamt Stuttgart, Germany. Exposure profiles were established using Non-Negative Matrix Factorization (NMF), adapted for sparse data. Cox models adjusted for confounding factors were used to estimate hazard ratios (HR) and 95% confidence interval (95% CI), for the association between the four obtained NMF components and T2D risk. Results The sample comprised 33,013 participants aged 53 years old on average, among which 76% of women. During follow-up (median: 5.95 years), 340 incident T2D cases were diagnosed. Positive associations were detected between NMF component 1 (reflecting high exposure to azoxystrobin, chlorpyriphos, imazalil, malathion, profenofos, thiabendazole) and T2D risk: HRQ5 vs Q1=1.47, 95% CI(1.00, 2.18). NMF Component 3 (reflecting low exposure to several synthetic pesticides) was associated with a decrease in T2D risk, among those with high dietary quality only (high adherence to French dietary guidelines): HRQ5vsQ1=0.31, 95%CI(0.10, 0.94). No associations were found for NMF Components 2 and 4. Conclusions These associations between some pesticide mixtures and T2D diabetes risk need to be confirmed in other types of studies and settings. These results could have important implications for developing prevention strategies, through regulations or dietary guidelines. Key messages Specific pesticide mixtures could play a role in increased type 2 Diabetes risk. Organic eaters were less exposed to most synthetic pesticides.

Prospective association between dietary pesticide exposure profiles and postmenopausal breast-cancer risk in the NutriNet-Santé cohort.

Some pesticides, used in large quantities in current agricultural practices all over Europe, are suspected of adverse effects on human reproductive health (breast and prostate cancers), through mechanisms of endocrine disruption and possible carcinogenic properties, as observed in agricultural settings. However, evidence on dietary pesticide exposure and breast cancer (BC) is lacking for the general population. We aimed to assess the associations between dietary exposure to pesticides and BC risk among postmenopausal women of the NutriNet-Santé cohort. In 2014, participants completed a self-administered semi-quantitative food-frequency questionnaire distinguishing conventional and organic foods. Exposures to 25 active substances used in EU plant-protection products were estimated using a pesticide-residue database accounting for farming practices, from Chemisches und Veterinäruntersuchungsamt Stuttgart, Germany. Non-negative matrix factorization (NMF), adapted for data with excess zeros, was used to establish exposure profiles. The four extracted NMF components' quintiles were introduced into Cox models estimating hazard ratio (HR) and 95% confidence interval (95% CI), adjusted for known confounding factors. A total of 13 149 postmenopausal women were included in the analysis (169 BC cases, median follow-up = 4.83 years). Negative associations between Component 3, reflecting low exposure to synthetic pesticides, and postmenopausal BC risk were found [HRQ5 = 0.57; 95% CI (0.34; 0.93), p-trend = 0.006]. Positive association between Component 1 score (highly correlated to chlorpyrifos, imazalil, malathion, thiabendazole) and postmenopausal BC risk was found specifically among overweight and obese women [HRQ5 = 4.13; 95% CI (1.50; 11.44), p-trend = 0.006]. No associations were detected for the other components. These associations suggest a potential role of dietary pesticide exposure on BC risk. Further research is needed to investigate the mechanisms and confirm these results in other populations.

Non-Negative Matrix Factorization of Simulated High Density Surface Electromyograms Reflects Both Muscle Excitation and Muscle Shortening

We analyzed muscle excitation estimation systematically by Non-negative matrix factorization (NMF) from surface electromyograms (EMG) during dynamic contractions of biceps brachii (BB) muscles. We used motor unit action potentials (MUAPs) estimated experimentally from surface EMGs during slow dynamic contractions of BB muscles in healthy young males, and convolved them by simulated motor unit firing patterns. Different uncorrelated muscle excitation and muscle shortening profiles were combined when generating the EMG signals from left and right BBs (64 channels per muscle). EMG signals were rectified, low-passed filtered and decomposed by NMF into 2, 3, 4 or 6 components. The identified NMF components demonstrated good separation of left and right BB activity, but relatively large sensitivity of NMF components to muscle shortening, especially at high levels of muscle excitation. When averaged across different numbers of identified NMF components at excitation levels ranging from 40 to 80%, the average correlation coefficient between the NMF components and muscle shortening profiles was 0.45 ± 0.15. At excitation levels between 0 and 40 % these correlations decreased to 0.15 ± 0.09. Therefore, NMF components reflect both muscle excitation and muscle shortening profiles.

A NMF-based extraction of physically meaningful components from sensory data of metal casting processes

The paper introduces a novel approach for the extraction of physically meaningful thermal component time series during the manufacturing of casting parts. We treat their extraction as Blind Source Separation (BSS) problem by exploiting process-related prior knowledge. Our proposed method arranges temperature time series into a data matrix, which is then decomposed by Non-negative Matrix Factorization (NMF). The latter is guided by a knowledge-based strategy, which initializes the NMF component matrix with time curves designed according to basic physical processes. The temperature time series encompass exclusively non-negative data. Hence NMF lends itself a natural choice as it does not impose mathematical constraints that lack any immediate physical interpretation. We show how to extract components linked to physical phenomena that typically occur during production and cannot be monitored directly. We apply our method to real world data, collected in a foundry during the series production of casting parts for the automobile industry and demonstrate its efficiency.

DNA methylation identifies genetically and prognostically distinct subtypes of myelodysplastic syndromes

AbstractRecurrent mutations implicate several epigenetic regulators in the early molecular pathobiology of myelodysplastic syndromes (MDS). We hypothesized that MDS subtypes defined by DNA methylation (DNAm) patterns could enhance our understanding of MDS disease biology and identify patients with convergent epigenetic profiles. Bisulfite padlock probe sequencing was used to measure DNAm of ∼500 000 unique cytosine guanine dinucleotides covering 140 749 nonoverlapping regulatory regions across the genome in bone marrow DNA samples from 141 patients with MDS. Application of a nonnegative matrix factorization (NMF)–based decomposition of DNAm profiles identified 5 consensus clusters described by 5 NMF components as the most stable grouping solution. Each of the 5 NMF components identified by this approach correlated with specific genetic abnormalities and categorized patients into 5 distinct methylation clusters, each largely defined by a single NMF component. Methylation clusters displayed unique differentially methylated regulatory loci enriched for active and bivalent promoters and enhancers. Two clusters were enriched for samples with complex karyotypes, although only one had an increased number of TP53 mutations. Each of the 3 most frequently mutated splicing factors, SF3B1, U2AF1, and SRSF2, was enriched in different clusters. Mutations of ASXL1, EZH2, and RUNX1 were coenriched in the SRSF2-containing cluster. In multivariate analysis, methylation cluster membership remained independently associated with overall survival. Targeted DNAm profiles identify clinically relevant subtypes of MDS not otherwise distinguished by mutations or clinical features. Patients with diverse genetic lesions can converge on common DNAm states with shared pathogenic mechanisms and clinical outcomes.

DNA Methylation Identifies Genetically and Prognostically Distinct Subtypes of MDS

Background: Recurrent somatic mutations in patients with myelodysplastic syndromes (MDS) implicate several epigenetic regulators in the molecular pathobiology of these disorders. We hypothesized that identification of MDS subtypes defined by DNA methylation patterns could improve prognostication and enhance our understanding of MDS disease biology. Methylation assays that investigate regions of the genome beyond promoters may better inform which regulatory regions possess biologic importance in the development and progression of MDS. Additionally, computational methods that agnostically approach large methylation datasets are needed when attempting to classify clinically and genetically heterogeneous disease populations such as MDS.Methods: To measure DNA methylation, we used bisulfite padlock probes (BSPP), a targeted enrichment technique that captures approximately 500,000 unique CpGs in regions known to contain differentially methylated regulatory regions. BSPP was performed on bone marrow mononuclear DNA from 141 treatment-naïve patients with MDS that were genetically and clinically annotated in prior studies (Bejar et al. N Engl J Med 2011 and J Clin Oncol 2012). We used Onco-GPS, a computational method that identifies shared underlying cellular states among heterogeneous sample populations in an unsupervised manner, to identify DNA methylation subtypes of MDS (Kim et al. Cell Systems 2017). This method uses non-negative matrix factorization (NMF) followed by consensus clustering of the resulting NMF components. The optimal number of NMF components and consensus clusters were chosen to maximize the cophenetic correlation coefficient. A Fisher's Exact test was used to test for enrichment of genetic lesions in specific clusters. Univariate and multivariable models of overall survival (OS) were constructed using cox proportional hazards regression. Variables with univariate p-values <0.2 were evaluated for inclusion in the final multivariable model and the final model was constructed using a forward and backward stepwise procedure based on the Aikake Information Criterion.Results: We found that 5 NMF components and 5 consensus clusters maximized the cophenetic correlation coefficient, indicating the most stable partitioning of our dataset (Figures 1A-1B). The samples making up each cluster were enriched largely in a single NMF component, indicating that the underlying DNA methylation loci contributing to each cluster are distinct. Specific genetic and cytogenetic abnormalities were significantly enriched in different clusters, including enrichment of mutations in TP53 and U2AF1 in cluster 2; EZH2, ASXL1, RUNX1, SRSF2 in cluster 3; TET2 in cluster 4; SF3B1 in cluster 5; and abnormal and complex karyotypes enriched in clusters 1 and 2 (Figure 1C-1D). Kaplan-Meier curves revealed two major patterns of survival with clusters 2 and 3 displaying inferior OS when compared with clusters 1, 4, and 5. We combined clusters with similar median OS into “High Risk” and “Low Risk” cluster groups. In univariate Cox proportional hazards regression, High Risk and Low Risk cluster groups had significant differences in OS (HR, 1.95; 95% CI,1.24-3.08; p=0.003). In a multivariable model including elements of the IPSS-R, cluster risk group remained a significant predictor of OS (HR, 2.02; 95% CI, 1.25-3.27, p=0.004). We determined cluster-specific differentially methylated regions (DMRs) and found divergent patterns of methylation among clusters with the majority of DMRs located at non-promoter regulatory regions with high enrichment at both active and bivalent enhancers (as defined in a reference epigenome from mobilized CD34+ cells).Conclusion: Using BSPP and novel computational methods, we found that DNA methylation of MDS patients identifies clinically relevant subtypes not otherwise distinguished by current prognostic models. Our analysis also shows that while genetic abnormalities can be associated with specific DNA methylation changes, patients with diverse genetic lesions can converge on common DNA methylation states, reflecting shared pathogenic mechanisms and clinical outcomes. Ongoing work to annotate the biological differences between the DNA methylation subgroups identified will enhance our understanding of the role of DNAm in prognosis and the underlying biology of MDS. [Display omitted] DisclosuresZhang:Singlera Genomics: Consultancy, Equity Ownership, Membership on an entity's Board of Directors or advisory committees. Bejar:AbbVie/Genentech: Consultancy, Honoraria; Modus Outcomes: Consultancy; Takeda: Research Funding; Celgene: Consultancy, Honoraria; Astex/Otsuka: Consultancy, Honoraria; Genoptix: Consultancy; Foundation Medicine: Consultancy.

Interactive visualization for NILM in large buildings using non-negative matrix factorization

Non-intrusive load monitoring (NILM) techniques have recently attracted much interest, since they allow to obtain latent patterns from power demand data in buildings, revealing useful information to the expert user. Unsupervised methods are specially attractive, since they do not require labeled datasets. Particularly, non-negative matrix factorization (NMF) methods decompose a single power demand measurement over a certain time period into a set of components or “parts” that are sparse, non-negative and sum up the original measured quantity. Such components reveal hidden temporal patterns which may be difficult to interpret in complex systems such as large buildings. We suggest to integrate the knowledge of the user into the analysis in order to recognize the real events inside the electric network behind the learnt patterns. In this paper, we integrate the available domain knowledge of the user by means of a visual analytics web application in which an expert user can interact in a fluid way with the NMF outcome through visual approaches such as barcharts, heatmaps or calendars. Our approach is tested with real electric power demand data from a hospital complex, showing how the interpretation of the decomposition is improved by means of interactive data cube visualizations, in which the user can insightfully relate the NMF components to characteristic demand patterns of the hospital such as those derived from human activity, as well as to inefficient behaviors of the largest systems in the hospital.

On the Impact of Muscle Shortening on Non-Negative Matrix Factorization of Dynamic Surface Electromyograms.

We analyzed the sensitivity of Non-negative Matrix Factorization (NMF) of dynamic surface electromyograms (EMG) to muscle shortening. We first identified Motor unit action potentials (MUAPs) by decomposing experimentally recorded EMG signals during slow shortening of biceps brachii muscle in five young healthy males. We then used these MUAPs to generate different synthetic EMG signals with different muscle shortening and excitation profiles. Afterwards, we applied NMF to the synthetic EMG signals and calculated Pearson correlation coefficient (CC) between the extracted NMF components and a) muscle shortening and b) muscle excitation profiles. The results demonstrated good match between NMF components and muscle excitation profiles, but only when the muscle excitation level changed for at least 10 % during the muscle shortening. During constant muscle excitation, the resulting NMF components correlated significantly with the muscle shortening profiles. These results demonstrate that NMF components reflect not only the muscle excitation profiles but also muscle shortening profiles. Therefore, the results of NMF analysis of dynamic EMG signals need to be interpreted with caution.

Non-negative Matrix Factorization: Robust Extraction of Extended Structures

Abstract We apply the vectorized non-negative matrix factorization (NMF) method to the post-processing of the direct imaging data of exoplanetary systems such as circumstellar disks. NMF is an iterative approach, which first creates a nonorthogonal and non-negative basis of components using the given reference images and then models a target with the components. The constructed model is then rescaled with a factor to compensate for the contribution from the disks. We compare NMF with existing methods (classical reference differential imaging method, and the Karhunen–Loève image projection algorithm) using synthetic circumstellar disks and demonstrate the superiority of NMF: with no need of prior selection of references, NMF not only can detect fainter circumstellar disks but also better preserves their morphology and does not require forward modeling. As an application to a well-known disk example, we process the archival Hubble Space Telescope STIS coronagraphic observations of HD 181327 with different methods and compare them, and NMF is able to extract some circumstellar materials inside the primary ring for the first time. In an appendix, we mathematically investigate the stability of NMF components during the iteration and the linearity of NMF modeling.

Discriminative non-negative matrix factorization (DNMF) and its application to the fault diagnosis of diesel engine

Diesel engines, widely used in engineering, are very important for the running of equipments and their fault diagnosis have attracted much attention. In the past several decades, the image based fault diagnosis methods have provided efficient ways for the diesel engine fault diagnosis. By introducing the class information into the traditional non-negative matrix factorization (NMF), an improved NMF algorithm named as discriminative NMF (DNMF) was developed and a novel imaged based fault diagnosis method was proposed by the combination of the DNMF and the KNN classifier. Experiments performed on the fault diagnosis of diesel engine were used to validate the efficacy of the proposed method. It is shown that the fault conditions of diesel engine can be efficiently classified by the proposed method using the coefficient matrix obtained by DNMF. Compared with the original NMF (ONMF) and principle component analysis (PCA), the DNMF can represent the class information more efficiently because the class characters of basis matrices obtained by the DNMF are more visible than those in the basis matrices obtained by the ONMF and PCA.

Functional connectivity changes during a working memory task in rat via NMF analysis.

Working memory (WM) is necessary in higher cognition. The brain as a complex network is formed by interconnections among neurons. Connectivity results in neural dynamics to support cognition. The first aim is to investigate connectivity dynamics in medial prefrontal cortex (mPFC) networks during WM. As brain neural activity is sparse, the second aim is to find the intrinsic connectivity property in a feature space. Using multi-channel electrode recording techniques, spikes were simultaneously obtained from mPFC of rats that performed a Y-maze WM task. Continuous time series converted from spikes were embedded in a low-dimensional space by non-negative matrix factorization (NMF). mPFC network in original space was constructed by measuring connections among neurons. And the same network in NMF space was constructed by computing connectivity values between the extracted NMF components. Causal density (Cd) and global efficiency (E) were estimated to present the network property. The results showed that Cd and E significantly peaked in the interval right before the maze choice point in correct trials. However, the increase did not emerge in error trials. Additionally, Cd and E in two spaces displayed similar trends in correct trials. The difference was that the measures in NMF space were significantly greater than those in original space. Our findings indicated that the anticipatory changes in mPFC networks may have an effect on future WM behavioral choices. Moreover, the NMF analysis achieves a better characterization for a brain network.

A stable approach for model order selection in nonnegative matrix factorization

In order to find the correct model order in non-negative matrix factorization (NMF), an algorithm called automatic relevance determination (ARD) is proposed in Tan and Fevotte (2013). The algorithm explores the similarities of the NMF components and removes redundant ones iteratively. However, the algorithm can yield over-parsimonious representations where ground truth patterns can be grouped into one single component to cause superposition. In this paper, mixed entropy regularized NMF (MER-NMF) is proposed to overcome the above problem. In MER-NMF, the objective function of NMF is regularized by minimizing a mixed entropy of the coefficient matrix which is a weighted sum of two parts: the entropy of all the entries and the entropy of the row sums of the coefficient matrix. With the mixed entropy regularization, the algorithm tends to yield sharper activations of the components for each sample. By combining MER-NMF and ARD-NMF, correct number of components can always be selected according to our experiments.

Multi-Stage Non-Negative Matrix Factorization for Monaural Singing Voice Separation

Separating singing voice from music accompaniment can be of interest for many applications such as melody extraction, singer identification, lyrics alignment and recognition, and content-based music retrieval. In this paper, a novel algorithm for singing voice separation in monaural mixtures is proposed. The algorithm consists of two stages, where non-negative matrix factorization (NMF) is applied to decompose the mixture spectrograms with long and short windows respectively. A spectral discontinuity thresholding method is devised for the long-window NMF to select out NMF components originating from pitched instrumental sounds, and a temporal discontinuity thresholding method is designed for the short-window NMF to pick out NMF components that are from percussive sounds. By eliminating the selected components, most pitched and percussive elements of the music accompaniment are filtered out from the input sound mixture, with little effect on the singing voice. Extensive testing on the MIR-1K public dataset of 1000 short audio clips and the Beach-Boys dataset of 14 full-track real-world songs showed that the proposed algorithm is both effective and efficient.