Non-negative Matrix Factorization Algorithm Research Articles

Influence of α-Stable Noise on the Effectiveness of Non-Negative Matrix Factorization—Simulations and Real Data Analysis

Non-negative matrix factorization (NMF) has been used in various applications, including local damage detection in rotating machines. Recent studies highlight the limitations of diagnostic techniques in the presence of non-Gaussian noise. The authors examine the impact of non-Gaussianity levels on the extraction of the signal of interest (SOI). The simple additive model of the signal is proposed: SOI and non-Gaussian noise. As a model of the random component, i.e., noise, a heavy-tailed α-stable distribution with two important parameters (σ and α) was proposed. If SOI is masked by noise (controlled by σ), the influence of non-Gaussianity level (controlled by α) is more critical. We performed an empirical analysis of how these parameters affect SOI extraction effectiveness using NMF. Finally, we applied two NMF algorithms to several (both vibration and acoustic) signals from a machine with faulty bearings at different levels of non-Gaussian disturbances and the obtained results align with the simulations. The main conclusion of this study is that NMF is a very powerful tool for analyzing non-Gaussian data and can provide satisfactory results in a wide range of a non-Gaussian noise levels.

Whole leg compression garments influence lower limb kinematics and associated muscle synergies during running.

The utilization of compression garments (CGs) has demonstrated the potential to improve athletic performance; however, the specific mechanisms underlying this enhancement remain a subject of further investigation. This study aimed to examine the impact of CGs on running mechanics and muscle synergies from a neuromuscular control perspective. Twelve adult males ran on a treadmill at 12km/h, while data pertaining to lower limb kinematics, kinetics, and electromyography were collected under two clothing conditions: whole leg compression garments and control. The Non-negative matrix factorization algorithm was employed to extract muscle synergy during running, subsequently followed by cluster analysis and correlation analysis. The findings revealed that the CGs increased knee extension and reduced hip flexion at foot strike compared with the control condition. Moreover, CGs were found to enhance stance-phase peak knee extension, while diminishing hip flexion and maximal hip extension during the stance-phase, and the ankle kinematics remained unaltered. We extracted and classified six synergies (SYN1-6) during running and found that only five SYNs were observed after wearing CGs. CGs altered the structure of the synergies and changed muscle activation weights and durations. The current study is the first to apply muscle synergy to discuss the effect of CGs on running biomechanics. Our findings provide neuromuscular evidence for the idea of previous studies that CGs alter the coordination of muscle groups, thereby affecting kinematic characteristics during running.

Anoikis-related genes as potential prognostic biomarkers in gastric cancer: A multilevel integrative analysis and predictive therapeutic value.

Gastric cancer (GC) is a frequent malignancy of the gastrointestinal tract. Exploring the potential anoikis mechanisms and pathways might facilitate GC research. The authors aim to determine the significance of anoikis-related genes (ARGs) in GC prognosis and explore the regulatory mechanisms in epigenetics. After describing the genetic and transcriptional alterations of ARGs, we searched differentially expressed genes (DEGs) from the cancer genome atlasand gene expression omnibusdatabases to identify major cancer marker pathways. The non-negative matrix factorisation algorithm, Lasso, and Cox regression analysis were used to construct a risk model, and we validated and assessed the nomogram. Based on multiple levels and online platforms, this research evaluated the regulatory relationship of ARGs with GC. Overexpression of ARGs is associated with poor prognosis, which modulates immune signalling and promotes anti-anoikis. The consistency of the DEGs clustering with weighted gene co-expression network analysisresults and the nomogram containing 10 variable genes improved the clinical applicability of ARGs. In anti-anoikis mode, cytology, histology, and epigenetics could facilitate the analysis of immunophenotypes, tumour immune microenvironment (TIME), and treatment prognosis. A novel anoikis-related prognostic model for GC is constructed, and the significance of anoikis-related prognostic genes in the TIME and the metabolic pathways of tumours is initially explored.

Revealing the Distribution of Lithium Compounds in Lithium Dendrites by Four-Dimensional Electron Microscopy Analysis.

Characterizing the microstructure of radiation- and chemical-sensitive lithium dendrites and its solid electrolyte interphase (SEI) is an important task when investigating the performance and reliability of lithium-ion batteries. Widely used methods, such as cryogenic high-resolution transmission electron microscopy as well as related spectroscopy, are able to reveal the local structure at nanometer and atomic scale; however, these methods are unable to show the distribution of various crystal phases along the dendrite in a large field of view. In this work, two types of four-dimensional electron microscopy diffractive imaging methods, i.e., scanning electron nanodiffraction (SEND) and scanning convergent beam electron diffraction (SCBED), are employed to show a new pathway on characterizing the sensitive lithium dendrite samples at room temperature and in a large field of view. Combining with the non-negative matrix factorization (NMF) algorithm, orientations of different lithium metal grains along the lithium dendrite as well as different lithium compounds in the SEI layer are clearly identified.

A Robust Method for the Unsupervised Scoring of Immunohistochemical Staining.

Immunohistochemistry is a powerful technique that is widely used in biomedical research and clinics; it allows one to determine the expression levels of some proteins of interest in tissue samples using color intensity due to the expression of biomarkers with specific antibodies. As such, immunohistochemical images are complex and their features are difficult to quantify. Recently, we proposed a novel method, including a first separation stage based on non-negative matrix factorization (NMF), that achieved good results. However, this method was highly dependent on the parameters that control sparseness and non-negativity, as well as on algorithm initialization. Furthermore, the previously proposed method required a reference image as a starting point for the NMF algorithm. In the present work, we propose a new, simpler and more robust method for the automated, unsupervised scoring of immunohistochemical images based on bright field. Our work is focused on images from tumor tissues marked with blue (nuclei) and brown (protein of interest) stains. The new proposed method represents a simpler approach that, on the one hand, avoids the use of NMF in the separation stage and, on the other hand, circumvents the need for a control image. This new approach determines the subspace spanned by the two colors of interest using principal component analysis (PCA) with dimension reduction. This subspace is a two-dimensional space, allowing for color vector determination by considering the point density peaks. A new scoring stage is also developed in our method that, again, avoids reference images, making the procedure more robust and less dependent on parameters. Semi-quantitative image scoring experiments using five categories exhibit promising and consistent results when compared to manual scoring carried out by experts.

Abnormal interlimb coordination of motor developmental delay during infant crawling based on kinematic synergy analysis

BackgroundPrevious studies have reported that abnormal interlimb coordination is a typical characteristic of motor developmental delay (MDD) during human movement, which can be visually manifested as abnormal motor postures. Clinically, the scale assessments are usually used to evaluate interlimb coordination, but they rely heavily on the subjective judgements of therapists and lack quantitative analysis. In addition, although abnormal interlimb coordination of MDD have been studied, it is still unclear how this abnormality is manifested in physiology-related kinematic features.ObjectivesThis study aimed to evaluate how abnormal interlimb coordination of MDD during infant crawling was manifested in the stability of joints and limbs, activation levels of synergies and intrasubject consistency from the kinematic synergies of tangential velocities of joints perspective.MethodsTangential velocities of bilateral shoulder, elbow, wrist, hip, knee and ankle over time were computed from recorded three-dimensional joint trajectories in 40 infants with MDD [16 infants at risk of developmental delay, 11 infants at high risk of developmental delay, 13 infants with confirmed developmental delay (CDD group)] and 20 typically developing infants during hands-and-knees crawling. Kinematic synergies and corresponding activation coefficients were derived from those joint velocities using the non-negative matrix factorization algorithm. The variability accounted for yielded by those synergies and activation coefficients, and the synergy weightings in those synergies were used to measure the stability of joints and limbs. To quantify the activation levels of those synergies, the full width at half maximum and center of activity of activation coefficients were calculated. In addition, the intrasubject consistency was measured by the cosine similarity of those synergies and activation coefficients.ResultsInterlimb coordination patterns during infant crawling were the combinations of four types of single-limb movements, which represent the dominance of each of the four limbs. MDD mainly reduced the stability of joints and limbs, and induced the abnormal activation levels of those synergies. Meanwhile, MDD generally reduced the intrasubject consistency, especially in CDD group.ConclusionsThese features have the potential for quantitatively evaluating abnormal interlimb coordination in assisting the clinical diagnosis and motor rehabilitation of MDD.

Identifying molecular subtypes and tumor microenvironment infiltration signatures in kidney renal clear cell carcinoma based on stemness-associated disulfidptosis genes by integrating machine learning, single-cell analyses and experimental validation

Clear cell renal cell carcinoma (ccRCC) is an aggressive malignant tumor. Disulfidptosis is a new programmed cell death mechanism, which is characterized by the abnormal accumulation of intracellular disulfides that are highly toxic to cells. However, the contribution of disulfidptosis to ccRCC progression has not been fully clarified. In this study, two different molecular subtypes related to disulfidptosis were identified in ccRCC patients by the non-negative matrix factorization (NMF) algorithm. The cluster 1 was characterized by a worse prognosis and higher mRNAsi levels. Then, difference analysis and weighted gene co-expression network analysis (WGCNA) were conducted to search modular genes that are highly associated with tumor stemness and tumor microenvironment. Subsequently, a SADG signature containing nine genes was constructed stepwise by WGCNA and least absolute shrinkage and selection operator (LASSO) Cox regression analysis. The high-risk score group had a worse outcome, and immune regulation and metabolic signatures might be responsible for cancer progression in the high-risk group. After that, a predictive nomogram was constructed, and the predicting power of the risk model was verified using inter and three independent external validation datasets. Nine SADGs were shown to significantly correlate with immune infiltration, tumor mutation burden (TMB), microsatellite instability (MSI) and immune checkpoint. In addition, based on the single-cell RNA sequencing dataset (GSE139555), the distribution and expression of nine hub genes in various types of immune cells were analyzed. Finally, the expression level of the nine genes was verified in clinical samples by qRT-PCR.

Prediction of Actively Exerted Torque From Ankle Joint Complex Based on Muscle Synergy

Prediction of actively exerted torque from the ankle joint complex (AJC) is critical for human-robot interaction because this is the real torque that the patient exerts. In this work, we develop a prediction framework to predict the actively exerted torque from the surface electromyography (sEMG) signal. The modified non-negative matrix factorization (mNMF) algorithm is used to extract muscle activation information (MAI) and muscle synergy information (MSI); the pseudo-siamese network (PSN) is used to fit the MAI and MSI to actively exerted torque. The prediction accuracy is compared under different ankle attitudes, synergistic feature extraction algorithms, and prediction algorithms, and the results show that the prediction accuracy of the proposed framework is 94.15%, and the variance of prediction accuracy is just 3.56% under different ankle attitudes. The proposed framework can provide the real actively exerted torque for the active rehabilitation training of ankle joint, so as to improve the enthusiasm and initiative of patients during rehabilitation training.

Disentangling Multiple Emitting Components in Molecular Observations with Nonnegative Matrix Factorization

Molecular emission from the galactic and extragalactic interstellar medium (ISM) is often used to determine the physical conditions of the dense gas. However, even from spatially resolved regions, the observed molecules do not necessarily arise from a single component. Disentangling multiple gas components is often a degenerate problem in radiative transfer studies. In this paper, we investigate the use of the nonnegative matrix factorization (NMF) approach as a means to recover gas components from a set of blended line intensity maps of molecular transitions that may trace different physical conditions. We run a series of experiments on synthetic data sets designed to replicate conditions in two very different environments: galactic pre-stellar cores and the ISM in high-redshift galaxies. We find that the NMF algorithm often recovers the multiple components resembling those used in the data-generating process, provided that the different components have similar column densities. When NMF fails to recover all the individual components it does however group together the most similarly emitting ones. We further found that initialization and regularisation are key factors in the efficiency of the NMF algorithm.

Two-Dimensional SERS Sensor Array for Identifying and Visualizing the Gas Spatial Distributions of Two Distinct Odor Sources

The spatial distribution of gas emitted from an odor source provides valuable information regarding the composition, size, and localization of the odor source. Surface-enhanced Raman scattering (SERS) gas sensors exhibit ultra-high sensitivity, molecular specificity, rapid response, and large-area detection. In this paper, a SERS gas sensor array was developed for visualizing the spatial distribution of gas evaporated from benzaldehyde and 4-ethylbenzaldehyde odor sources. The SERS spectra of the gas were collected by scanning the sensor array using an automatic detection system. The non-negative matrix factorization algorithm was employed to extract feature and concentration information at each spot on the sensor array. A heatmap image was generated for visualizing the gas spatial distribution using concentration information. Gaussian fitting was applied to process the image for localizing the odor source. The size of the odor source was estimated using the processed image. Moreover, the spectra of benzaldehyde, 4-ethylbenzaldehyde, and their gas mixture were simultaneously detected using one SERS sensor array. The feature information was recognized using a convolutional neural network with an accuracy of 98.21%. As a result, the benzaldehyde and 4-ethylbenzaldehyde odor sources were identified and visualized. Our research findings have various potential applications, including odor source localization, environmental monitoring, and healthcare.

Privacy-Preserving Identification of Cancer Subtype-Specific Driver Genes Based on Multigenomics Data with Privatedriver.

Identifying cancer subtype-specific driver genes from a large number of irrelevant passengers is crucial for targeted therapy in cancer treatment. Recently, the rapid accumulation of large-scale cancer genomics data from multiple institutions has presented remarkable opportunities for identification of cancer subtype-specific driver genes. However, the insufficient subtype samples, privacy issues, and heterogenous of aberration events pose great challenges in precisely identifying cancer subtype-specific driver genes. To address this, we introduce privatedriver, the first model for identifying subtype-specific driver genes that integrates genomics data from multiple institutions in a data privacy-preserving collaboration manner. The process of identifying subtype-specific cancer driver genes using privatedriver involves the following two steps: genomics data integration and collaborative training. In the integration process, the aberration events from multiple genomics data sources are combined for each institution using the forward and backward propagation method of NetICS. In the collaborative training process, each institution utilizes the federated learning framework to upload encrypted model parameters instead of raw data of all institutions to train a global model by using the non-negative matrix factorization algorithm. We applied privatedriver on head and neck squamous cell and colon cancer from The Cancer Genome Atlas website and evaluated it with two benchmarks using macro-Fscore. The comparison analysis demonstrates that privatedriver achieves comparable results to centralized learning models and outperforms most other nonprivacy preserving models, all while ensuring the confidentiality of patient information. We also demonstrate that, for varying predicted driver gene distributions in subtype, our model fully considers the heterogeneity of subtype and identifies subtype-specific driver genes corresponding to the given prognosis and therapeutic effect. The success of privatedriver reveals the feasibility and effectiveness of identifying cancer subtype-specific driver genes in a data protection manner, providing new insights for future privacy-preserving driver gene identification studies.

Real-Time Movie Recommendation: Integrating Persona-Based User Modeling with NMF and Deep Neural Networks

The proliferation of uncategorized information on the Internet has intensified the need for effective recommender systems. Recommender systems have evolved from content-based filtering to collaborative filtering and, most recently, to deep learning-based and hybrid models. However, they often face challenges such as high computational costs, reduced reliability, and the Cold Start problem. We introduce a persona-based user modeling approach for real-time movie recommendations. Our system employs Non-negative Matrix Factorization (NMF) and Deep Learning algorithms to manage complex and sparse data types and to mitigate the Cold Start issue. Experimental results, based on criteria involving 50 topics and 35 personas, indicate a significant performance gain. Specifically, with 500 users, the precision@K for NMF was 86.01%, and for the Deep Neural Network (DNN), it was 92.67%. Tested with 900 users, the precision@K for NMF increased to 97.04%, and for DNN, it was 95.55%. These results represent an approximate 10% and 5% improvement in performance, respectively. The system not only delivers fast and accurate recommendations but also reduces computational overhead by updating the model only when user personas change. The generated user personas can be adapted for other recommendation services or large-scale data mining.

Privacy-Preserving Non-Negative Matrix Factorization with Outliers

Non-negative matrix factorization is a popular unsupervised machine learning algorithm for extracting meaningful features from inherently non-negative data. Such data often contain privacy-sensitive user information. Additionally, the dataset can contain outliers, which may lead to extracting sub-optimal features from the data. It is, therefore, necessary to address these two issues while analyzing privacy-sensitive data that may contain outliers. In this work, we develop a non-negative matrix factorization algorithm in the privacy-preserving framework that (i) considers the presence of outliers in the data, and (ii) can achieve results comparable to those of the non-private algorithm. We design our method in such a way that one has the control to select the degree of privacy grantee based on the required utility gap. We show the effectiveness of our proposed algorithm’s performance on six real and diverse datasets. The experimental results show that our proposed method can achieve a performance that closely approximates the performance of the non-private algorithm under some parameter choices, while ensuring strict privacy guarantees.

Convergence of a Fast Hierarchical Alternating Least Squares Algorithm for Nonnegative Matrix Factorization

The hierarchical alternating least squares (HALS) algorithms are powerful tools for nonnegative matrix factorization (NMF), among which the Fast-HALS, proposed in [A. Cichocki and A.-H. Phan, 2009], is one of the most efficient. This paper investigates the convergence of Fast-HALS. First, a more general weak convergence (converged subsequences exist and converge to the stationary point set) is established without any assumption, while most existing results assume all the columns of iterates are strictly away from the origin. Then, a simplified strong convergence (the entire sequence converges to a stationary point) proof is provided. The existing strong convergence is attributed to the block prox-linear (BPL) method, which is a more general framework including Fast-HALS as a special case. So, the convergence proof under BPL is quite complex. Our simplified proof explores the structure of Fast-HALS and can be regarded as a complement to the results under BPL. In addition, some numerical verifications are presented.

Algorithms for Non-Negative Matrix Factorization on Noisy Data With Negative Values

Algorithms for Non-Negative Matrix Factorization on Noisy Data With Negative Values

Muscle Coordination During Maximal Butterfly Stroke Swimming: Comparison Between Competitive and Recreational Swimmers.

This study aimed to clarify the differences in muscular coordination during butterfly swimming between high- and low-performance swimmers using muscle synergy analysis. Eight female competitive swimmers and 8 female recreational swimmers participated in this study. The participants swam a 25-m butterfly stroke with maximum effort. Surface electromyography was measured from 12 muscles and muscle synergy analysis was performed from the data using nonnegative matrix factorization algorithms. From the results of the muscle synergy analysis, 4 synergies were extracted from both groups. Synergies 1 and 2 were characterized by coactivation of the upper and lower limb muscles in the recreational swimmers, whereas only synergy 1 was characterized by this in the competitive swimmers. Synergy 3 was involved in arm recovery in both groups. Synergy 4 was only involved in the downward kick in the competitive swimmers. From these results, it can be concluded that muscle synergies with combined coordination of upper and lower limb muscles were extracted more in the recreational swimmers and that the competitive swimmers controlled the downward kick with an independent synergy and that the adjustment of the timing of the downward kick may be an important factor for the efficient performance of butterfly swimming.

Trans-Stilbene aggregates and crystallites in polystyrene films: microscopy and spectroscopy studies.

Solid and liquid stilbene forms were characterized using a range of techniques, including atomic force microscopy, coherent anti-Stokes Raman scattering microspectroscopy and optical spectroscopy. The obtained experimental results were analyzed by means of quantum chemical calculations and using a non-negative matrix factorization algorithm. It was confirmed that pure cis-stilbene formed a homogeneous fluid film on a glass substrate, whereas pure trans-stilbene formed crystals. Mixtures of trans-stilbene and polystyrene were shown to form stable solid films, which were non-homogeneous on the microscopic scale: stilbene molecules self-organized into microcrystals, which floated on the surface of polystyrene glass.

Investigating the feature extraction capabilities of non-negative matrix factorisation algorithms for black-and-white images

Investigating the feature extraction capabilities of non-negative matrix factorisation algorithms for black-and-white images

Advancing Auditory Processing by Detecting Frequency-Following Responses Through a Specialized Machine Learning Model.

In this study, we explore the feasibility and performance of detecting scalp-recorded frequency-following responses (FFRs) with a specialized machine learning (ML) model. By leveraging the strengths of feature extraction of the source separation non-negative matrix factorization (SSNMF) algorithm and its adeptness in handling limited training data, we adapted the SSNMF algorithm into a specialized ML model with a hybrid architecture to enhance FFR detection amidst background noise. We recruited 40 adults with normal hearing and evoked their scalp recorded FFRs using the English vowel/i/with a rising pitch contour. The model was trained on FFR-present and FFR-absent conditions, and its performance was evaluated using sensitivity, specificity, efficiency, false-positive rate, and false-negative rate metrics. This study revealed that the specialized SSNMF model achieved heightened sensitivity, specificity, and efficiency in detecting FFRs as the number of recording sweeps increased. Sensitivity exceeded 80% at 500 sweeps and maintained over 89% from 1000 sweeps onwards. Similarly, specificity and efficiency also improved rapidly with increasing sweeps. The progressively enhanced sensitivity, specificity, and efficiency of this specialized ML model underscore its practicality and potential for broader applications. These findings have immediate implications for FFR research and clinical use, while paving the way for further advancements in the assessment of auditory processing.

Mapping emission heterogeneity in layered halide perovskites using cathodoluminescence

Recent advancements in the fabrication of layered halide perovskites and their subsequent modification for optoelectronic applications have ushered in a need for innovative characterisation techniques. In particular, heterostructures containing multiple phases and consequently featuring spatially defined optoelectronic properties are very challenging to study. Here, we adopt an approach centered on cathodoluminescence, complemented by scanning electron microscopy coupled with energy-dispersive x-ray spectroscopy analysis. Cathodoluminescence enables assessment of local emission variations by injecting charges with a nanometer-scale electron probe, which we use to investigate emission changes in three different systems: PEA2PbBr4, PEA2PbI4 and lateral heterostructures of the two, fabricated via halide substitution. We identify and map different emission bands that can be correlated with local chemical composition and geometry. One emission band is characteristic of bromine-based halide perovskite, while the other originates from iodine-based perovskite. The coexistence of these emissions bands in the halide-substituted sample confirms the formation of lateral heterostructures. To improve the signal quality of the acquired data, we employed multivariate analysis, specifically the non-negative matrix factorization algorithm, on both cathodoluminescence and compositional datasets. The resulting understanding of the halide replacement process and identification of potential synergies in the optical properties will lead to optimised architectures for optoelectronic applications.