Non-negative Matrix Factorization Algorithm Research Articles

Prognostic Stratification of Epithelioid Pleural Mesothelioma Based on the Hippo-TEADs Network

Background. The Hippo pathway is the most frequently altered signaling in pleural mesothelioma (PM). Epithelioid PM (ePM) is associated with better outcome than non-epithelioid subtypes, but its prognosis can be heterogeneous. Here, we tried to stratify ePM using the expression levels of the Hippo-TEAD network. Methods. Thirty patients with ePM were included in this study. Tumors were stratified using the expression levels of 74 genes belonging to the Hippo-TEAD network and using the non-negative matrix factorization algorithm. Results were validated using ePM cases from the TCGA cohort. Alterations associated with the molecular subgroups were investigated using mutation and copy number alteration data from TCGA. Results. Two groups of ePM (i.e., HP1 and HP2) were identified and validated using TCGA data. HP2 comprises about one-third of tumors. These tumors are frequently high-grade (73% vs. 35%), have higher levels of downstream Hippo effectors (i.e., YAP1, WWTR1 and TEADs), lower levels of VSIR—which encodes for VISTA—and poorer PFS and OS. HP2 tumors commonly harbor homodeletions in Hippo core suppressors (25% vs. 3%), while no specific gene mutation or copy number alterations of Hippo genes was associated with the two groups. Conclusions. ePM can be stratified in prognostic subtypes based on the expression levels of the Hippo-TEAD network. Higher levels of downstream Hippo effectors are associated with poor response to platinum-pemetrexed doublet and worse OS. The stratification of ePM based on the activation of the YAP/TAZ-TEAD axis is an intriguing approach in the light of the inhibitors of this signaling that are currently under investigation.

Exploring Brain Imaging and Genetic Risk Factors in Different Progression States of Alzheimer's Disease Through OSnetNMF-Based Methods.

Alzheimer's disease (AD) is a neurodegenerative disease with no effective treatment, often preceded by mild cognitive impairment (MCI). Multimodal imaging genetics integrates imaging and genetic data to gain a deeper understanding of disease progression and individual variations. This study focuses on exploring the mechanisms that drive the transition from normal cognition to MCI and ultimately to AD. As an effective joint feature extraction and dimensionality reduction method, non-negative matrix factorization (NMF) and its improved variants, particularly the network-based non-negative matrix factorization (netNMF), have been widely used in multimodal analysis to mine brain imaging and genetic data by considering the interactions between different features. However, many of these methods overlook the importance of the coefficient matrix and do not address issues related to data accuracy and feature redundancy. To address these limitations, we propose an orthogonal sparse network non-negative matrix factorization (OSnetNMF) algorithm, which introduces orthogonal and sparse constraints based on netNMF. By establishing linear relationships between structural magnetic resonance imaging (sMRI) and corresponding gene expression data, OSnetNMF reduces feature redundancy and decreases correlation between data, resulting in more accurate and reliable biomarker extraction. Experiments demonstrate that the OSnetNMF algorithm can accurately identify risk regions of interest (ROIs) and key genes that characterize AD progression, revealing significant trends in ROI pairs such as l4thVen-HIF1A, rBst-MPO, and rBst-PTK2B. Comparative experiments show that the improved algorithm outperforms traditional methods, identifying more disease-related biomarkers and achieving better reconstruction performance.

Optimal Number of Topics in Topic Modeling Using Deep Auto Encoder Graph Regularized Non-Negative Matrix Factorization Algorithm

Optimal Number of Topics in Topic Modeling Using Deep Auto Encoder Graph Regularized Non-Negative Matrix Factorization Algorithm

Multispectral imaging through scattering media and around corners via spectral component separation.

Existing methods for imaging through scattering media prioritize grayscale and often falter in resolving multispectral speckles, leading to inadequate spectral recovery. We propose a method that establishes a spectral component separation model for high-quality multispectral imaging through scattering media and around corners. By leveraging the uncorrelation among speckles of different wavelengths and the superposition essence of multispectral speckles, a multispectral speckle simplex with speckles of different wavelengths as vertices is constructed. To resolve these vertices, spectral intensity modulation and a joint-solving mechanism are designed for mutual cooperation. This mechanism employs the Harsanyi-Farrand-Chang method for wavelength number estimation, enhances vertex component analysis with a standby rule for initial solutions, and implements an improved non-negative matrix factorization algorithm for accurate separation. Our method successfully recovers multispectral objects from separated speckles, as confirmed by experiments across six wavelength channels. It is also validated for imaging hidden objects around corners, enhancing surround view functionality. This technique holds significant promise for multispectral imaging in various scattering environments.

Collaborative filtering recommendation based on K-nearest neighbor and non-negative matrix factorization algorithm

Collaborative filtering recommendation based on K-nearest neighbor and non-negative matrix factorization algorithm

Effect of foot type on electromyography characteristics and synergy of lower limb muscles during running

The foot structure is associated with different running mechanics. The central nervous system is responsible for using the muscles through synergies during locomotion. The purpose of the present study was to examine the effect of foot structure on the electromyography factors and the synergy of the selected muscles of the lower extremity. Tibialis anterior, extensor digitorum longus, peroneus longus, soleus, biceps femoris, vastus lateralis, gastrocnemius lateralis and medialis muscles activity of 60 barefoot recreational runners with different foot structures was recorded while running at a speed of 3.3 m/s. Muscle activity was measured in the running cycle. Besides, muscle synergies were extracted using non-negative matrix factorization algorithm. The results showed that there were differences between groups with different foot type in muscle activity under different phases of running in some muscles. Furthermore, the findings indicated that the number of synergies was similar in different groups and the relative weight of muscles was not different across groups. In conclusion, despite the difference in muscle activity under different phases of the running cycle, muscle synergies are similar among the groups. This can indicate similar control by the central nervous system in runners with different arch structures while running and the observed changes in muscle activity can be attributed to the type of forces exerted on the body, the length-tension relationship, and changes in the direction of the lower limbs in people with different arch structures.

Non-Negative Matrix Factorization with Averaged Kurtosis and Manifold Constraints for Blind Hyperspectral Unmixing

The Nonnegative Matrix Factorization (NMF) algorithm and its variants have gained widespread popularity across various domains, including neural networks, text clustering, image processing, and signal analysis. In the context of hyperspectral unmixing (HU), an important task involving the accurate extraction of endmembers from mixed spectra, researchers have been actively exploring different regularization techniques within the traditional NMF framework. These techniques aim to improve the precision and reliability of the endmember extraction process in HU. In this study, we propose a novel HU algorithm called KMBNMF, which introduces an average kurtosis regularization term based on endmember spectra to enhance endmember extraction, additionally, it integrates a manifold regularization term into the average kurtosis-constrained NMF by constructing a symmetric weight matrix. This combination of these two regularization techniques not only optimizes the extraction process of independent endmembers but also improves the part-based representation capability of hyperspectral data. Experimental results obtained from simulated and real-world hyperspectral datasets demonstrate the competitive performance of the proposed KMBNMF algorithm when compared to state-of-the-art algorithms.

An Improved Nonnegative Matrix Factorization Algorithm Combined with K-Means for Audio Noise Reduction

Clustering algorithms have the characteristics of being simple and efficient and can complete calculations without a large number of datasets, making them suitable for application in noise reduction processing for audio module mass production testing. In order to solve the problems of the NMF algorithm easily getting stuck in local optimal solutions and difficult feature signal extraction, an improved NMF audio denoising algorithm combined with K-means initialization was designed. Firstly, the Euclidean distance formula of K-means has been improved to extract audio signal features from multiple dimensions. Combined with the initialization strategy of K-means decomposition, the initialization dictionary matrix of the NMF algorithm has been optimized to avoid getting stuck in local optimal solutions and effectively improve the robustness of the algorithm. Secondly, in the sparse coding part of the NMF algorithm, feature extraction expressions are added to solve the problem of noise residue and partial spectral signal loss in audio signals during the operation process. At the same time, the size of the coefficient matrix is limited to reduce operation time and improve the accuracy of feature extraction in high-precision audio signals. Then, comparative experiments were conducted using the NOIZEUS and NOISEX-92 datasets, as well as random noise audio signals. This algorithm improved the signal-to-noise ratio by 10–20 dB and reduced harmonic distortion by approximately −10 dB. Finally, a high-precision audio acquisition unit based on FPGA was designed, and practical applications have shown that it can effectively improve the signal-to-noise ratio of audio signals and reduce harmonic distortion.

Hierarchical Biclustering of Mouse Pancreas Mass Spectrometry Imaging Data Using Recursive Rank-2 Non-negative Matrix Factorization.

One of the main challenges in mass spectrometry imaging data analysis remains the analysis of m/z-spectra displaying a low signal-to-noise ratio caused by their low abundance, sample preparation, matrix effects, fragmentation, and other artifacts. Additionally, we observe that molecules with a high abundance suppress those with lower intensities and misdirect classical tools for MSI data analysis, such as principal component analysis. As a result, the observed significance of a molecule may not always be directly related to its abundance. In this work, we present a recursive rank-2 non-negative matrix factorization (rr2-NMF) algorithm that automatically returns spectral and spatial visualization of colocalized molecules, both highly and lowly abundant. Using this hierarchical decomposition, our method finds spatial and spectral correlations on different levels of abundances. The quality of the analysis is evaluated on MALDI-TOF data of healthy mouse pancreatic tissue for the annotation of molecules of interest in the lower abundances. The results show interesting findings regarding the functioning and colocalization of certain molecules.

Revolutionizing prognostic predictions in colorectal cancer: Macrophage‑driven transcriptional insights from single‑cell RNA sequencing and gene co‑expression network analysis.

Tumor-associated macrophages have become important biomarkers for cancer diagnosis, prognosis and therapy. The dynamic changes in macrophage subpopulations significantly impact the outcomes of cancer immunotherapy. Hence, identifying additional macrophage-related biomarkers is essential for enhancing prognostic predictions in colorectal cancer (CRC) immunotherapy. CRC single-cell RNA sequencing (scRNA-seq) data was obtained from the Gene Expression Omnibus (GEO) database. The data were processed, normalized and clustered using the 'Seurat' package. Cell types within each cluster were annotated using the 'SingleR' package. Weighted gene co-expression network analysis identified modules corresponding to specific cell types. A non-negative matrix factorization algorithm was employed to segregate different clusters based on the selected module. Differentially expressed genes (DEGs) were identified across various clusters and a prognostic model was constructed using lasso regression and Cox regression analyses. The robustness of the model was validated using The Cancer Genome Atlas (TCGA) database and GEO microarrays. Additionally, the prognosis, immune characteristics and response to immune checkpoint inhibitor (ICI) therapy were individually analyzed. The scRNA-seq data from GSE200997, consisting of 23 samples, were analyzed. Dimensionality reduction and cluster identification allowed the isolation of the primary myeloid cell subpopulations. The macrophage-related brown module was identified, which was further divided into two clusters. Using the DEGs from these clusters, a prognostic model was developed, comprising five macrophage-related genes. The robustness of the model was confirmed using microarray datasets GSE17536, GSE38832 and GSE39582, as well as TCGA cohort. Patients classified as high-risk by the present model exhibited poorer survival rates, lower tumor mutation burden, reduced microsatellite instability, lower tumor purity, more severe tumor immune dysfunction and exclusion, and less benefit from ICIs therapy compared with low-risk patients. The present prognostic model shows promise as a biomarker for risk stratification and predicting therapeutic efficacy in patients with CRC. However, further well-designed prospective studies are necessary to validate the findings.

Binning Metagenomic Contigs Using Contig Embedding and Decomposed Tetranucleotide Frequency.

Metagenomic binning is a crucial step in metagenomic research. It can aggregate the genome sequences belonging to the same microbial species into independent bins. Most existing methods ignore the semantic information of contigs and lack effective processing of tetranucleotide frequency, resulting in insufficient and complex feature information extracted for binning and poor binning results. To address the above problems, we propose CedtBin, a metagenomic binning method based on contig embedding and decomposed tetranucleotide frequency. First, the improved BERT model is used to learn the contigs to obtain their embedding representation. Secondly, the tetranucleotide frequencies are decomposed using a non-negative matrix factorization (NMF) algorithm. After that, the two features are spliced and input into the clustering algorithm for binning. Considering the sensitivity of the DBSCAN clustering algorithm to input parameters, in order to solve the drawbacks of manual parameter input, we also propose an Annoy-DBSCAN algorithm that can adaptively determine the parameters of the DBSCAN algorithm. This algorithm uses Approximate Nearest Neighbors Oh Yeah (Annoy) and combines it with a grid search strategy to find the optimal parameters of the DBSCAN algorithm. On simulated and real datasets, CedtBin achieves better binning results than mainstream methods and can reconstruct more genomes, indicating that the proposed method is effective.

Progression from cardiomyopathy to heart failure with reduced ejection fraction: A CORIN deficient course

Cardiomyopathies, encompassing hypertrophic cardiomyopathy (HCM) and dilated cardiomyopathy (DCM), constitute a diverse spectrum of heart muscle diseases that often culminating in heart failure (HF). The inherent molecular heterogeneity of these conditions has implications for prognosis and therapeutic strategies.Publicly available microarray and RNA sequencing (RNA-seq) data sets of HCM (n = 106 from GSE36961) and DCM (n = 18 from GSE135055 and 166 from GSE141910) patients were employed for our analysis. The Non-negative Matrix Factorization (NMF) algorithm was applied to explore the molecular stratification within HCM and DCM, and enrichment analysis was performed to delineate their biological characteristics. By integrating bulk and single-nucleus RNA-seq (snRNA-seq) data, we identified a potential biomarker for HCM progression and cardiac fibrosis, which was subsequently validated using mendelian randomization and in vitro.Our application of NMF identified two distinct molecular clusters. Particularly, a profibrotic, heart failure with reduced ejection fraction (HFrEF)-resembling Cluster 1 emerged, characterized by diminished expression of CORIN and a high degree of fibroblast activation. This cluster also exhibited lower left ventricular ejection fraction (LVEF) and worse prognostic outcomes, establishing the significance of this molecular subclassification. We further found that overexpression of CORIN could mitigate TGFβ1-induced expression of col1a1 and α-SMA in neonatal rat cardiac fibroblasts.Our results indicated the heterogeneity of HCM population, and further evidenced the participation of corin in the progression of HCM, DCM and HFrEF. Nevertheless, our study is constrained by the lack of corresponding clinical data and experimental validation of the identified subtypes. Therefore, further studies are warranted to elucidate the downstream pathways of corin and to validate these findings in independent patient cohorts.

A disulfidptosis-associated long noncoding RNA signature to predict low-grade glioma classification, prognosis, tumor microenvironment, and therapy regimens: Observational study.

This study aimed to investigate the function of disulfidptosis-associated long noncoding RNAs (DAlncRNAs) in low-grade gliomas (LGG) through bioinformatics analysis and construct a signature to predict the classification, prognosis, tumor microenvironment, and selection of immunotherapy and chemotherapy in LGG. Genomic, clinical, and mutational information of 526 patients with LGG was retrieved from The Cancer Genome Atlas repository. A nonnegative matrix factorization algorithm was applied to classify patients with LGG. Univariate, LASSO regression, and multivariate Cox regression analyses were performed to determine prognostic DAlncRNAs. Following the median risk score, we defined the sample as a high-risk (HR) or low-risk group. Finally, survival, receiver operating characteristic curve, risk curve, principal component, independent prognosis, risk difference, functional enrichment, tumor microenvironment, immune cell infiltration, mutation, and drug sensitivity analyses were performed. Patients were classified into C1 and C2 subtypes associated with disulfidptosis. Eight prognostic DAlncRNAs (AC003035.2, AC010157.2, AC010273.3, AC011444.3, AC092667.1, AL450270.1, AL645608.2, and LINC01571) were identified, and a prognostic signature of LGG was developed. The DAlncRNA-based signature was found to be an independent prognostic factor in patients with LGG, thereby constructing a nomogram. In addition, in the HR group, immune function was more active and the tumor mutation burden was higher. The patients were mainly composed of subtype C2, and their prognosis was worse. Immunotherapy and chemotherapy were predicted in the HR and low-risk groups, respectively. Our study, based on DAlncRNAs, highlights 2 disulfidptosis-associated LGG subtypes with different prognostic and immune characteristics and creates a novel disulfidptosis-associated prognostic signature, which may inform the classification, prognosis, molecular pathogenesis, and therapeutic strategies for patients with LGG.

A unified framework of semi-supervised community detection integrating network topology and node content

Detecting the community structure within networks is important because it aids in the analysis of complex networks. However, the existence of diverse complex structures in the network topology can limit the topological information’s ability to represent communities. For instance, the accuracy of many traditional methods based on topology alone decreases sharply when a link is missing or noisy. To solve the above-mentioned issues simultaneously, we propose a unified framework of semi-supervised community detection integrating content information. Three models are proposed, instead of a special model-handling problem. The framework used performs the same interpretation for a target problem. The inputs contain the adjacent and node content matrix. The proposed models describe the network topology using a non-negative matrix factorization (NMF) algorithm–based generative model or modularity maximization algorithm. Additionally, we use the equivalence theory of the pLSI, and NMF models the content information based on NMF. Community membership is also used as the relationship between communities and node contents. The models uniformly integrate content information and network topology. Further, a constraint matrix that depicts must-links is built by calculating the similarity of neighbors between any two nodes. Must-link pairs can represent the network topology’s prior information. The models’ community memberships are adjusted by using a strong constraint based on the connected component of this matrix. The models also introduce prior information into the topological and content information in the mentioned models. We compared the proposed models with the state-of-the-art community detection models on artificial networks and five real networks. The experimental results show that the proposed models outperformed the models combining topology and content and semi-supervised models. Fusing the topology with the content and the prior information in the models was also effective for community detection. Thus, the models under the framework are more advantageous than other semi-supervised models when incorporating the same amount of prior information into the models. The semi-supervised framework used also has a certain level of competitiveness in detecting communities.

Robust fatigue markers obtained from muscle synergy analysis.

This study aimed to utilize the nonnegative matrix factorization (NNMF) algorithm for muscle synergy analysis, extracting synergy structures and muscle weightings and mining biomarkers reflecting changes in muscle fatigue from these synergy structures. A leg press exercise to induce fatigue was performed by 11 participants. Surface electromyography (sEMG) data from seven muscles, electrocardiography (ECG) data, Borg CR-10 scale scores, and the z-axis acceleration of the weight block were simultaneously collected. Three indices were derived from the synergy structures: activation phase difference, coactivation area, and coactivation time. The indicators were further validated for single-leg landing. Differences in heart rate (HR) and heart rate variability (HRV) were observed across different fatigue levels, with varying degrees of disparity. The median frequency (MDF) exhibited a consistent decline in the primary working muscle groups. Significant differences were noted in activation phase difference, coactivation area, and coactivation time before and after fatigue onset. Moreover, a significant correlation was found between the activation phase difference and the coactivation area with fatigue intensity. The further application of single-leg landing demonstrated the effectiveness of the coactivation area. These indices can serve as biomarkers reflecting simultaneous alterations in the central nervous system and muscle activity post-exertion.

Integrating Multi-omics to Identify Age-Related Macular Degeneration Subtypes and Biomarkers

Age-related macular degeneration (AMD) is one of the most common causes of irreversible vision loss in the elderly. Its pathogenesis is likely multifactorial, involving a complex interaction of metabolic and environmental factors, and remains poorly understood. Previous studies have shown that mitochondrial dysfunction and oxidative stress play a crucial role in the development of AMD. Oxidative damage to the retinal pigment epithelium (RPE) has been identified as one of the major mediators in the pathogenesis of age-related macular degeneration (AMD). Therefore, this article combines transcriptome sequencing (RNA-seq) and single-cell sequencing (scRNA-seq) data to explore the role of mitochondria-related genes (MRGs) in AMD. Firstly, differential expression analysis was performed on the raw RNA-seq data. The intersection of differentially expressed genes (DEGs) and MRGs was performed. This paper proposes a deep subspace nonnegative matrix factorization (DS-NMF) algorithm to perform a multi-layer nonlinear transformation on the intersection of gene expression profiles corresponding to AMD samples. The age of AMD patients is used as prior information at the network’s top level to change the data distribution. The classification is based on reconstructed data with altered distribution. The types obtained significantly differ in scores of multiple immune-related pathways and immune cell infiltration abundance. Secondly, an optimal AMD diagnosis model was constructed using multiple machine learning algorithms for external and qRT-PCR verification. Finally, ten potential therapeutic drugs for AMD were identified based on cMAP analysis. The AMD subtypes identified in this article and the diagnostic model constructed can provide a reference for treating AMD and discovering new drug targets.

Graph-Regularized Non-Negative Matrix Factorization for Single-Cell Clustering in scRNA-Seq Data.

The advent of single-cell RNA sequencing (scRNA-seq) has brought forth fresh perspectives on intricate biological processes, revealing the nuances and divergences present among distinct cells. Accurate single-cell analysis is a crucial prerequisite for in-depth investigation into the underlying mechanisms of heterogeneity. Due to various technical noises, like the impact of dropout values, scRNA-seq data remains challenging to interpret. In this work, we propose an unsupervised learning framework for scRNA-seq data analysis (aka Sc-GNNMF). Based on the non-negativity and sparsity of scRNA-seq data, we propose employing graph-regularized non-negative matrix factorization (GNNMF) algorithm for the analysis of scRNA-seq data, which involves estimating cell-cell sparse similarity and gene-gene sparse similarity through Laplacian kernels and p-nearest neighbor graphs ( p-NNG). By assuming intrinsic geometric local invariance, we use a weighted p-nearest known neighbors ( p-NKN) to optimize the scRNA-seq data. The optimized scRNA-seq data then participates in the matrix decomposition process, promoting the closeness of cells with similar types in cell-gene data space and determining a more suitable embedding space for clustering. Sc-GNNMF demonstrates superior performance compared to other methods and maintains satisfactory compatibility and robustness, as evidenced by experiments on 11 real scRNA-seq datasets. Furthermore, Sc-GNNMF yields excellent results in clustering tasks, extracting useful gene markers, and pseudo-temporal analysis.

Construction and validation of a ubiquitination-related prognostic risk score signature in breast cancer

BackgroundBreast cancer (BC) is a highly common form of cancer that occurs in many parts of the world. However, early -stage BC is curable. Many patients with BC have poor prognostic outcomes owing to ineffective diagnostic and therapeutic tools. The ubiquitination system and associated proteins were found influencing the outcome of individuals with cancer. Therefore, developing a biomarker associated with ubiquitination genes to forecast BC patient outcomes is a feasible strategy. ObjectiveThe primary goal of this work was to develop a novel risk score signature capable of accurately estimate the future outcome of patients with BC by targeting ubiquitinated genes. MethodsUnivariate Cox regression analysis was conducted utilizing the E1, E2, and E3 ubiquitination-related genes in the GSE20685 dataset. Genes with p < 0.01 were screened again using the Non-negative Matrix Factorization (NMF) algorithm, and the resulting hub genes were composed of a risk score signature. Patients were categorized into two risk groups, and the predictive effect was tested using Kaplan-Meier (KM) and Receiver Operating Characteristic (ROC) curves. This risk score signature was later validated using multiple external datasets, namely TCGA-BRAC, GSE1456, GSE16446, GSE20711, GSE58812 and GSE96058. Immuno-microenvironmental, single-cell, and microbial analyses were also performed. ResultsThe selected gene signature comprising six ubiquitination-related genes (ATG5, FBXL20, DTX4, BIRC3, TRIM45, and WDR78) showed good prognostic power in patients with BC. It was validated using multiple externally validated datasets, with KM curves showing significant differences in survival (p < 0.05). The KM curves also demonstrated superior predictive ability compared to traditional clinical indicators. Single-cell analysis revealed that Vd2 gd T cells were less abundantin the low-risk group, whereas patients in the high-risk group lacked myeloid dendritic cells. Tumor microbiological analysis revealed a notable variation in microorganism diversity between the high- and low-risk groups. ConclusionThis study established an risk score signature consisting of six ubiquitination genes, that can accurately forecast the outcome of patients with BC using multiple datasets. It can provide personalized and targeted assistance to provide the evaluation and therapy of individuals having BC.

Demixing fluorescence time traces transmitted by multimode fibers

Optical methods based on thin multimode fibers (MMFs) are promising tools for measuring neuronal activity in deep brain regions of freely moving mice thanks to their small diameter. However, current methods are limited: while fiber photometry provides only ensemble activity, imaging techniques using of long multimode fibers are very sensitive to bending and have not been applied to unrestrained rodents yet. Here, we demonstrate the fundamentals of a new approach using a short MMF coupled to a miniscope. In proof-of-principle in vitro experiments, we disentangled spatio-temporal fluorescence signals from multiple fluorescent sources transmitted by a thin (200 µm) and short (8 mm) MMF, using a general unconstrained non-negative matrix factorization algorithm directly on the raw video data. Furthermore, we show that low-cost open-source miniscopes have sufficient sensitivity to image the same fluorescence patterns seen in our proof-of-principle experiment, suggesting a new avenue for novel minimally invasive deep brain studies using multimode fibers in freely behaving mice.

Separation and Extraction of Compound-Fault Signal Based on Multi-Constraint Non-Negative Matrix Factorization.

To solve the separation of multi-source signals and detect their features from a single channel, a signal separation method using multi-constraint non-negative matrix factorization (NMF) is proposed. In view of the existing NMF algorithm not performing well in the underdetermined blind source separation, the β-divergence constraints and determinant constraints are introduced in the NMF algorithm, which can enhance local feature information and reduce redundant components by constraining the objective function. In addition, the Sine-bell window function is selected as the processing method for short-time Fourier transform (STFT), and it can preserve the overall feature distribution of the original signal. The original vibration signal is first transformed into time-frequency domain with the STFT, which describes the local characteristic of the signal from the time-frequency distribution. Then, the multi-constraint NMF is applied to reduce the dimensionality of the data and separate feature components in the low dimensional space. Meanwhile, the parameter WK is constructed to filter the reconstructed signal that recombined with the feature component in the time domain. Ultimately, the separated signals will be subjected to envelope spectrum analysis to detect fault features. The simulated and experimental results indicate the effectiveness of the proposed approach, which can realize the separation of multi-source signals and their fault diagnosis of bearings. In addition, it is also confirmed that the proposed method, juxtaposed with the NMF algorithm of the traditional objective function, is more applicable for compound fault diagnosis of the rotating machinery.