Motor patterns of patients with spinal muscular atrophy suggestive of sensory and corticospinal contributions to the development of locomotor muscle synergies

Complex locomotor patterns are generated by combination of muscle synergies. How genetic processes, early sensorimotor experiences, and the developmental dynamics of neuronal circuits contribute to the expression of muscle synergies remains elusive. We shed light on the factors that influence development of muscle synergies by studying subjects with spinal muscular atrophy (SMA, types II/IIIa), a disorder associated with degeneration and deafferentation of motoneurons and possibly motor cortical and cerebellar abnormalities, from which the afflicted would have atypical sensorimotor histories around typical walking onset. Muscle synergies of children with SMA were identified from electromyographic signals recorded during active-assisted leg motions or walking, and compared with those of age-matched controls. We found that the earlier the SMA onset age, the more different the SMA synergies were from the normative. These alterations could not just be explained by the different degrees of uneven motoneuronal losses across muscles. The SMA-specific synergies had activations in muscles from multiple limb compartments, a finding reminiscent of the neonatal synergies of typically developing infants. Overall, while the synergies shared between SMA and control subjects may reflect components of a core modular infrastructure determined early in life, the SMA-specific synergies may be developmentally immature synergies that arise from inadequate activity-dependent interneuronal sculpting due to abnormal sensorimotor experience and other factors. Other mechanisms including SMA-induced intraspinal changes and altered cortical-spinal interactions may also contribute to synergy changes. Our interpretation highlights the roles of the sensory and descending systems to the typical and abnormal development of locomotor modules.NEW & NOTEWORTHY This is likely the first report of locomotor muscle synergies of children with spinal muscular atrophy (SMA), a subject group with atypical developmental sensorimotor experience. We found that the earlier the SMA onset age, the more the subjects' synergies deviated from those of age-matched controls. This result suggests contributions of the sensory/corticospinal activities to the typical expression of locomotor modules, and how their disruptions during a critical period of development may lead to abnormal motor modules.

A weakly supervised NMF method to decipher molecular subtype-related dynamic patterns in breast DCE-MR images

Objective. Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is an important imaging modality for breast cancer diagnosis. Intratumoral heterogeneity causes a major challenge in the interpretation of breast DCE-MRI. Previous studies have introduced decomposition methods on DCE-MRI to reveal intratumoral heterogeneity by analyzing distinct dynamic patterns within each tumor. However, these methods estimated the dynamic patterns and their corresponding component coefficients in an unsupervised manner, without considering any clinically relevant information.Approach. To decipher molecular subtype-related dynamic patterns, we propose a weakly supervised nonnegative matrix factorization method (WSNMF), which is able to decompose the pixel kinetics of DCE-MRI with image-level subtype labels. The WSNMF is developed based on a discriminant nonnegative matrix factorization (NMF) to utilize coarse-grained subtype information, in which between- and within-class scatters are defined on the mean vector of component coefficients over all pixels in each tumor, rather than directly on the vector of component coefficients of each pixel.Main results. Experiments demonstrated that the dynamic patterns identified by WSNMF had superior performance in distinguishing between luminal A and the other subtype tumors. The classification performance was evaluated using the area under the receiver operating characteristic curve (AUC). WSNMF yielded better classification performance (AUC = 0.822) than other heterogeneity analysis methods, including two partitioning-based methods (KPC with AUC = 0.697 and TTP with AUC = 0.760) and two unsupervised decomposition-based methods (PCA with AUC = 0.774 and NMF with AUC = 0.797).Significance. Our method adds a valuable new perspective into DCE-MRI decomposition-based heterogeneity analysis by taking advantage of intrinsic tumor characteristics to improve the diagnosis of breast cancer.

UNMF: a unified nonnegative matrix factorization for multi-dimensional omics data

Factor analysis, ranging from principal component analysis to nonnegative matrix factorization, represents a foremost approach in analyzing multi-dimensional data to extract valuable patterns, and is increasingly being applied in the context of multi-dimensional omics datasets represented in tensor form. However, traditional analytical methods are heavily dependent on the format and structure of the data itself, and if these change even slightly, the analyst must change their data analysis strategy and techniques and spend a considerable amount of time on data preprocessing. Additionally, many traditional methods cannot be applied as-is in the presence of missing values in the data. We present a new statistical framework, unified nonnegative matrix factorization (UNMF), for finding informative patterns in messy biological data sets. UNMF is designed for tidy data format and structure, making data analysis easier and simplifying the development of data analysis tools. UNMF can handle a wide range of data structures and formats, and works seamlessly with tensor data including missing observations and repeated measurements. The usefulness of UNMF is demonstrated through its application to several multi-dimensional omics data, offering user-friendly and unified features for analysis and integration. Its application holds great potential for the life science community. UNMF is implemented with R and is available from GitHub (https://github.com/abikoushi/moltenNMF).

Evaluation of the default mode network using nonnegative matrix factorization in patients with cognitive impairment induced by occupational aluminum exposure

Aluminum (Al) is an important environmental pathogenic factor for neurodegenerative diseases, especially mild cognitive impairment (MCI). The aim of this study was to evaluate the gray matter volume of structural covariance network alterations in patients with Al-induced MCI. Male subjects who had been exposed to Al for >10 years were included in the present study. The plasma Al concentration, Montreal cognitive assessment (MoCA) score, and verbal memory assessed by the Rey auditory verbal learning test (AVLT) score were collected from each participant. Nonnegative matrix factorization was used to identify the structural covariance network. The neural structural basis for patients with Al-induced MCI was investigated using correlation analysis and group comparison. Plasma Al concentration was inversely related to MoCA scores, particularly AVLT scores. In patients with Al-induced MCI, the gray matter volume of the default mode network (DMN) was considerably lower than that in controls. Positive correlations were discovered between the DMN and MoCA scores as well as between the DMN and AVLT scores. In sum, long-term occupational Al exposure has a negative impact on cognition, primarily by affecting delayed recognition. The reduced gray matter volume of the DMN may be the neural mechanism of Al-induced MCI.

Impaired cardiac glycolysis and glycogen depletion are linked to poor myocardial outcomes in juvenile male swine with metabolic syndrome and ischemia

Obesity continues to rise in the juveniles and obese children are more likely to develop metabolic syndrome (MetS) and related cardiovascular disease. Unfortunately, effective prevention and long-term treatment options remain limited. We determined the juvenile cardiac response to MetS in a swine model. Juvenile male swine were fed either an obesogenic diet, to induce MetS, or a lean diet, as a control (LD). Myocardial ischemia was induced with surgically placed ameroid constrictor on the left circumflex artery. Physiological data were recorded and at 22 weeks of age the animals underwent a terminal harvest procedure and myocardial tissue was extracted for total metabolic and proteomic LC/MS-MS, RNA-seq analysis, and data underwent nonnegative matrix factorization for metabolic signatures. Significantly altered in MetS versus. LD were the glycolysis-related metabolites and enzymes. In MetS compared with LD Glycogen synthase 1 (GYS1)-glycogen phosphorylases (PYGM/PYGL) expression disbalance resulted in a loss of myocardial glycogen. Our findings are consistent with the concept that transcriptionally driven myocardial changes in glycogen and glucose metabolism-related enzymes lead to a deficiency of their metabolite products in MetS. This abnormal energy metabolism provides insight into the pathogenesis of the juvenile heart in MetS. This study reveals that MetS and ischemia diminishes ATP availability in the myocardium via altering the glucose-G6P-pyruvate axis at the level of metabolites and gene expression of related enzymes. The observed severe glycogen depletion in MetS coincides with disbalance in expression of GYS1 and both PYGM and PYGL. This altered energy substrate metabolism is a potential target of pharmacological agents for improving juvenile myocardial function in MetS and ischemia.

Local and long-distance organization of prefrontal cortex circuits in the marmoset brain

The prefrontal cortex (PFC) has dramatically expanded in primates, but its organization and interactions with other brain regions are only partially understood. We performed high-resolution connectomic mapping of the marmoset PFC and found two contrasting corticocortical and corticostriatal projection patterns: "patchy" projections that formed many columns of submillimeter scale in nearby and distant regions and "diffuse" projections that spread widely across the cortex and striatum. Parcellation-free analyses revealed representations of PFC gradients in these projections' local and global distribution patterns. We also demonstrated column-scale precision of reciprocal corticocortical connectivity, suggesting that PFC contains a mosaic of discrete columns. Diffuse projections showed considerable diversity in the laminar patterns of axonal spread. Altogether, these fine-grained analyses reveal important principles of local and long-distance PFC circuits in marmosets and provide insights into the functional organization of the primate brain.

Computational chromatography: A machine learning strategy for demixing individual chemical components in complex mixtures

Surface-enhanced Raman spectroscopy (SERS) holds exceptional promise as a streamlined chemical detection strategy for biological and environmental contaminants compared with current laboratory methods. Priority pollutants such as polycyclic aromatic hydrocarbons (PAHs), detectable in water and soil worldwide and known to induce multiple adverse health effects upon human exposure, are typically found in multicomponent mixtures. By combining the molecular fingerprinting capabilities of SERS with the signal separation and detection capabilities of machine learning (ML), we examine whether individual PAHs can be identified through an analysis of the SERS spectra of multicomponent PAH mixtures. We have developed an unsupervised ML method we call Characteristic Peak Extraction, a dimensionality reduction algorithm that extracts characteristic SERS peaks based on counts of detected peaks of the mixture. By analyzing the SERS spectra of two-component and four-component PAH mixtures where the concentration ratios of the various components vary, this algorithm is able to extract the spectra of each unknown component in the mixture of unknowns, which is then subsequently identified against a SERS spectral library of PAHs. Combining the molecular fingerprinting capabilities of SERS with the signal separation and detection capabilities of ML, this effort is a step toward the computational demixing of unknown chemical components occurring in complex multicomponent mixtures.

Comparison of Methods for Estimating Temporal Topic Models From Primary Care Clinical Text Data: Retrospective Closed Cohort Study

BACKGROUND

Health care organizations are collecting increasing volumes of clinical text data. Topic models are a class of unsupervised machine learning algorithms for discovering latent thematic patterns in these large unstructured document collections.

OBJECTIVE

We aimed to comparatively evaluate several methods for estimating temporal topic models using clinical notes obtained from primary care electronic medical records from Ontario, Canada.

METHODS

We used a retrospective closed cohort design. The study spanned from January 01, 2011, through December 31, 2015, discretized into 20 quarterly periods. Patients were included in the study if they generated at least 1 primary care clinical note in each of the 20 quarterly periods. These patients represented a unique cohort of individuals engaging in high-frequency use of the primary care system. The following temporal topic modeling algorithms were fitted to the clinical note corpus: nonnegative matrix factorization, latent Dirichlet allocation, the structural topic model, and the BERTopic model.

RESULTS

Temporal topic models consistently identified latent topical patterns in the clinical note corpus. The learned topical bases identified meaningful activities conducted by the primary health care system. Latent topics displaying near-constant temporal dynamics were consistently estimated across models (eg, pain, hypertension, diabetes, sleep, mood, anxiety, and depression). Several topics displayed predictable seasonal patterns over the study period (eg, respiratory disease and influenza immunization programs).

CONCLUSIONS

Nonnegative matrix factorization, latent Dirichlet allocation, structural topic model, and BERTopic are based on different underlying statistical frameworks (eg, linear algebra and optimization, Bayesian graphical models, and neural embeddings), require tuning unique hyperparameters (optimizers, priors, etc), and have distinct computational requirements (data structures, computational hardware, etc). Despite the heterogeneity in statistical methodology, the learned latent topical summarizations and their temporal evolution over the study period were consistently estimated. Temporal topic models represent an interesting class of models for characterizing and monitoring the primary health care system.

Age-dependent white matter disruptions after military traumatic brain injury: Multivariate analysis results from ENIGMA brain injury

Mild Traumatic brain injury (mTBI) is a signature wound in military personnel, and repetitive mTBI has been linked to age-related neurogenerative disorders that affect white matter (WM) in the brain. However, findings of injury to specific WM tracts have been variable and inconsistent. This may be due to the heterogeneity of mechanisms, etiology, and comorbid disorders related to mTBI. Non-negative matrix factorization (NMF) is a data-driven approach that detects covarying patterns (components) within high-dimensional data. We applied NMF to diffusion imaging data from military Veterans with and without a self-reported TBI history. NMF identified 12 independent components derived from fractional anisotropy (FA) in a large dataset (n = 1,475) gathered through the ENIGMA (Enhancing Neuroimaging Genetics through Meta-Analysis) Military Brain Injury working group. Regressions were used to examine TBI- and mTBI-related associations in NMF-derived components while adjusting for age, sex, post-traumatic stress disorder, depression, and data acquisition site/scanner. We found significantly stronger age-dependent effects of lower FA in Veterans with TBI than Veterans without in four components (q < 0.05), which are spatially unconstrained by traditionally defined WM tracts. One component, occupying the most peripheral location, exhibited significantly stronger age-dependent differences in Veterans with mTBI. We found NMF to be powerful and effective in detecting covarying patterns of FA associated with mTBI by applying standard parametric regression modeling. Our results highlight patterns of WM alteration that are differentially affected by TBI and mTBI in younger compared to older military Veterans.

RNMFLP: Predicting circRNA-disease associations based on robust nonnegative matrix factorization and label propagation

Circular RNAs (circRNAs) are a class of structurally stable endogenous noncoding RNA molecules. Increasing studies indicate that circRNAs play vital roles in human diseases. However, validating disease-related circRNAs in vivo is costly and time-consuming. A reliable and effective computational method to identify circRNA-disease associations deserves further studies. In this study, we propose a computational method called RNMFLP that combines robust nonnegative matrix factorization (RNMF) and label propagation algorithm (LP) to predict circRNA-disease associations. First, to reduce the impact of false negative data, the original circRNA-disease adjacency matrix is updated by matrix multiplication using the integrated circRNA similarity and the disease similarity information. Subsequently, the RNMF algorithm is used to obtain the restricted latent space to capture potential circRNA-disease pairs from the association matrix. Finally, the LP algorithm is utilized to predict more accurate circRNA-disease associations from the integrated circRNA similarity network and integrated disease similarity network, respectively. Fivefold cross-validation of four datasets shows that RNMFLP is superior to the state-of-the-art methods. In addition, case studies on lung cancer, hepatocellular carcinoma and colorectal cancer further demonstrate the reliability of our method to discover disease-related circRNAs.

Single Cell Self-Paced Clustering with Transcriptome Sequencing Data

Single cell RNA sequencing (scRNA-seq) allows researchers to explore tissue heterogeneity, distinguish unusual cell identities, and find novel cellular subtypes by providing transcriptome profiling for individual cells. Clustering analysis is usually used to predict cell class assignments and infer cell identities. However, the performance of existing single-cell clustering methods is extremely sensitive to the presence of noise data and outliers. Existing clustering algorithms can easily fall into local optimal solutions. There is still no consensus on the best performing method. To address this issue, we introduce a single cell self-paced clustering (scSPaC) method with F-norm based nonnegative matrix factorization (NMF) for scRNA-seq data and a sparse single cell self-paced clustering (sscSPaC) method with l21-norm based nonnegative matrix factorization for scRNA-seq data. We gradually add single cells from simple to complex to our model until all cells are selected. In this way, the influences of noisy data and outliers can be significantly reduced. The proposed method achieved the best performance on both simulation data and real scRNA-seq data. A case study about human clara cells and ependymal cells scRNA-seq data clustering shows that scSPaC is more advantageous near the clustering dividing line.

A Survey on Multi-View Clustering

Clustering is a machine learning paradigm of dividing sample subjects into a number of groups such that subjects in the same groups are more similar to those in other groups. With advances in information acquisition technologies, samples can frequently be viewed from different angles or in different modalities, generating multi-view data. Multi-view clustering, that clusters subjects into subgroups using multi-view data, has attracted more and more attentions. Although MVC methods have been developed rapidly, there has not been enough survey to summarize and analyze the current progress. Therefore, we propose a novel taxonomy of the MVC approaches. Similar to other machine learning methods, we categorize them into generative and discriminative classes. In discriminative class, based on the way of view integration, we split it further into five groups: Common Eigenvector Matrix, Common Coefficient Matrix, Common Indicator Matrix, Direct Combination and Combination After Projection. Furthermore, we relate MVC to other topics: multi-view representation, ensemble clustering, multi-task clustering, multi-view supervised and semi-supervised learning. Several representative real-world applications are elaborated for practitioners. Some benchmark multi-view datasets are introduced and representative MVC algorithms from each group are empirically evaluated to analyze how they perform on benchmark datasets. To promote future development of MVC approaches, we point out several open problems that may require further investigation and thorough examination.

Metabolic Reprogramming and Risk Stratification of Hepatocellular Carcinoma Studied by Using Gas Chromatography-Mass Spectrometry-Based Metabolomics

Hepatocellular carcinoma (HCC) displays a high degree of metabolic and phenotypic heterogeneity and has dismal prognosis in most patients. Here, a gas chromatography-mass spectrometry (GC-MS)-based nontargeted metabolomics method was applied to analyze the metabolic profiling of 130 pairs of hepatocellular tumor tissues and matched adjacent noncancerous tissues from HCC patients. A total of 81 differential metabolites were identified by paired nonparametric test with false discovery rate correction to compare tumor tissues with adjacent noncancerous tissues. Results demonstrated that the metabolic reprogramming of HCC was mainly characterized by highly active glycolysis, enhanced fatty acid metabolism and inhibited tricarboxylic acid cycle, which satisfied the energy and biomass demands for tumor initiation and progression, meanwhile reducing apoptosis by counteracting oxidative stress. Risk stratification was performed based on the differential metabolites between tumor and adjacent noncancerous tissues by using nonnegative matrix factorization clustering. Three metabolic clusters displaying different characteristics were identified, and the cluster with higher levels of free fatty acids (FFAs) in tumors showed a worse prognosis. Finally, a metabolite classifier composed of six FFAs was further verified in a dependent sample set to have potential to define the patients with poor prognosis. Together, our results offered insights into the molecular pathological characteristics of HCC.

Nonnegative matrix factorization-based bioinformatics analysis reveals that TPX2 and SELENBP1 are two predictors of the inner sub-consensuses of lung adenocarcinoma

Background

Lung adenocarcinoma (LUAD) is a heterogeneous disease. However the inner sub‐groups of LUAD have not been fully studied. Markers predicted the sub‐groups and prognosis of LUAD are badly needed.

Aims

To identify biomarkers associated with the sub‐groups and prognosis of LUAD.

Materials and Methods

Using nonnegative matrix factorization (NMF) clustering, LUAD patients from The Cancer Genome Atlas (TCGA), Gene Expression Omnibus (GEO) datasets and LUAD cell lines from Genomics of Drug Sensitivity in Cancer (GDSC) dataset were divided into different sub‐consensuses based on the gene expression profiling. The overall survival of LUAD patients in each sub‐consensus was determined by Kaplan‐Meier survival analysis. The common genes which were differentially expressed in each sub‐consensus of LUAD patients and LUAD cell lines were identified using TBtools. The predictive accuracy of TPX2 and SELENBP1 for theinner sub‐consensuses of LUAD was determined by Receiver operator characteristic (ROC) analysis. The Kaplan‐Meier survival analysis was also used to test the prognostic significance of TPX2 and SELENBP1 in LUAD patients.

Results

Using nonnegative matrix factorization clustering, LUAD patients in The Cancer Genome Atlas (TCGA), GSE30219, GSE42127, GSE50081, GSE68465, and GSE72094 datasets were divided into three sub‐consensuses. Sub‐consensus3 LUAD patients were with low overall survival and were with high TP53 mutations. Similarly, LUAD cell lines were also divided into three sub‐consensuses by NMF method, and sub‐consensus2 cell lines were resistant to EGFR inhibitors. Identification of the common genes which were differentially expressed in different sub‐consensuses of LUAD patients and LUAD cell lines revealed that TPX2 was highly expressed in sub‐consensus3 LUAD patients and sub‐consensus2 LUAD cell lines. On the contrary, SELENBP1 was highly expressed in sub‐consensus1 LUAD patients and sub‐consensus1 LUAD cell lines. The expression levels of TPX2 and SELENBP1 could distinguish sub‐consensus3 LUAD patients or sub‐consensus2 LUAD cell lines from other sub‐consensuses of LUAD patients or cell lines. Moreover, compared with normal lung tissues, TPX2 was highly expressed, while, SELENBP1 was lowly expressed in LUAD tissues. Furthermore, the higher expression levels of TPX2 were associated with the lower relapse‐free survival and the lower overall survival of LUAD patients. While, the higher expression levels of SELENBP1 were associated with the higher relapse‐free survival and higher overall survival. At last, we showed that TP53 mutant LUAD patients were with higher TPX2 and lower SELENBP1 expressions.

Discussion

Both iCluster and NMF method are proved to be robust LUAD classification systems. However, the LUAD patients in different iclusters had no significant clinical overall survival, while, sub‐consensus3 LUAD patients from NMF classification were with lower overall survival than other sub‐consensuses.

Conclusions

By integrated analysis of 1765 LUAD patients and 64 LUAD cell lines, we showed that NMF was a robust inner sub‐consensuses classification method of LUAD. TPX2 and SELENBP1 were differentially expressed in different LUAD sub‐ consensuses, and predicted the inner sub‐consensuses of LUAD with high accuracy. TPX2 was an unfavorable prognostic biomarker of LUAD which was up‐regulated in LUAD tissues and associated with the low overall survival of LUAD. SELENBP1 was a favorable prognostic biomarker of LUAD which was down‐regulated in LUAD tissues and associated with the prolonged overall survival of LUAD.

Matrix decomposition in meta-analysis for extraction of adverse event pattern and patient-level safety profile

The purpose of assessing adverse events (AEs) in clinical studies is to evaluate what AE patterns are likely to occur during treatment. In contrast, it is difficult to specify which of these patterns occurs in each patient. To tackle this challenging issue, we constructed a new statistical model including nonnegative matrix factorization by incorporating background knowledge of AE-specific structures such as severity and drug mechanism of action. The model uses a meta-analysis framework for integrating data from multiple clinical studies because insufficient information is derived from a single trial. We demonstrated the proposed method by applying it to real data consisting of three Phase III studies, two mechanisms of action, five anticancer treatments, 3317 patients, 848 AE types, and 99,546 AEs. The extracted typical treatment-specific AE patterns coincided with medical knowledge. We also demonstrated patient-level safety profiles using the data of AEs that were observed by the end of the second cycle.

DeFusion: a denoised network regularization framework for multi-omics integration

With diverse types of omics data widely available, many computational methods have been recently developed to integrate these heterogeneous data, providing a comprehensive understanding of diseases and biological mechanisms. But most of them hardly take noise effects into account. Data-specific patterns unique to data types also make it challenging to uncover the consistent patterns and learn a compact representation of multi-omics data. Here we present a multi-omics integration method considering these issues. We explicitly model the error term in data reconstruction and simultaneously consider noise effects and data-specific patterns. We utilize a denoised network regularization in which we build a fused network using a denoising procedure to suppress noise effects and data-specific patterns. The error term collaborates with the denoised network regularization to capture data-specific patterns. We solve the optimization problem via an inexact alternating minimization algorithm. A comparative simulation study shows the method's superiority at discovering common patterns among data types at three noise levels. Transcriptomics-and-epigenomics integration, in seven cancer cohorts from The Cancer Genome Atlas, demonstrates that the learned integrative representation extracted in an unsupervised manner can depict survival information. Specially in liver hepatocellular carcinoma, the learned integrative representation attains average Harrell's C-index of 0.78 in 10 times 3-fold cross-validation for survival prediction, which far exceeds competing methods, and we discover an aggressive subtype in liver hepatocellular carcinoma with this latent representation, which is validated by an external dataset GSE14520. We also show that DeFusion is applicable to the integration of other omics types.

Incorporating Latent Variables Using Nonnegative Matrix Factorization Improves Risk Stratification in Brugada Syndrome

Background

A combination of clinical and electrocardiographic risk factors is used for risk stratification in Brugada syndrome. In this study, we tested the hypothesis that the incorporation of latent variables between variables using nonnegative matrix factorization can improve risk stratification compared with logistic regression.

Methods and Results

This was a retrospective cohort study of patients presented with Brugada electrocardiographic patterns between 2000 and 2016 from Hong Kong, China. The primary outcome was spontaneous ventricular tachycardia/ventricular fibrillation. The external validation cohort included patients from 3 countries. A total of 149 patients with Brugada syndrome (84% males, median age of presentation 50 [38–61] years) were included. Compared with the nonarrhythmic group (n=117, 79%), the spontaneous ventricular tachycardia/ ventricular fibrillation group (n=32, 21%) were more likely to suffer from syncope (69% versus 37%, P=0.001) and atrial fibrillation (16% versus 4%, P=0.023) as well as displayed longer QTc intervals (424 [399–449] versus 408 [386–425]; P=0.020). No difference in QRS interval was observed (108 [98–114] versus 102 [95–110], P=0.104). Logistic regression found that syncope (odds ratio, 3.79; 95% CI, 1.64–8.74; P=0.002), atrial fibrillation (odds ratio, 4.15; 95% CI, 1.12–15.36; P=0.033), QRS duration (odds ratio, 1.03; 95% CI, 1.002–1.06; P=0.037) and QTc interval (odds ratio, 1.02; 95% CI, 1.01–1.03; P=0.009) were significant predictors of spontaneous ventricular tachycardia/ventricular fibrillation. Increasing the number of latent variables of these electrocardiographic indices incorporated from n=0 (logistic regression) to n=6 by nonnegative matrix factorization improved the area under the curve of the receiving operating characteristics curve from 0.71 to 0.80. The model improves area under the curve of external validation cohort (n=227) from 0.64 to 0.71.

Conclusions

Nonnegative matrix factorization improves the predictive performance of arrhythmic outcomes by extracting latent features between different variables.

Integration of Imaging (epi)Genomics Data for the Study of Schizophrenia Using Group Sparse Joint Nonnegative Matrix Factorization

Schizophrenia (SZ) is a complex disease. Single nucleotide polymorphism (SNP), brain activity measured by functional magnetic resonance imaging (fMRI) and DNA methylation are all important biomarkers that can be used for the study of SZ. To our knowledge, there has been little effort to combine these three datasets together. In this study, we propose a group sparse joint nonnegative matrix factorization (GSJNMF) model to integrate SNP, fMRI, and DNA methylation for the identification of multi-dimensional modules associated with SZ, which can be used to study regulatory mechanisms underlying SZ at multiple levels. The proposed GSJNMF model projects multiple types of data onto a common feature space, in which heterogeneous variables with large coefficients on the same projected bases are used to identify multi-dimensional modules. We also incorporate group structure information available from each dataset. The genomic factors in such modules have significant correlations or functional associations with several brain activities. At the end, we have applied the method to the analysis of real data collected from the Mind Clinical Imaging Consortium (MCIC) for the study of SZ and identified significant biomarkers. These biomarkers were further used to discover genes and corresponding brain regions, which were confirmed to be significantly associated with SZ.

Semi-Supervised Nonnegative Matrix Factorization of Wide-Field Fluorescence Microscopic Images for Tissue Diagnosis

This study tests the use of a constrained nonnegative matrix factorization (NMF) algorithm to explore the comparatively new field of chemometric microscopy to support tissue diagnosis. The algorithm can extract the spectral signature and the absolute concentration map of endogenous fluorophores from wide-field microscopic images. The resultant data distinguished normal and fibrous calvarial tissues, based on the changes in their spectral signatures. The absolute concentration map of endogenous fluorophores, nicotinamide adenine dinucleotide (NADH), flavin adenine dinucleotide (FAD), and lipofuscin were derived from microscopic images and compared with the fluorescence from pure fluorophores. While the absolute concentration of NADH increased, the same of FAD and lipofuscin decreased from a normal to fibrous calvarial condition. An increase in the optical redox ratio, possibly due to the metabolic changes during the development of fibrosis, was observed. Differentiating tissue types using the absolute concentration map was found to be considerably more precise than that achievable with relative concentration. The quantification of fluorophores with reference to the absolute concentration map can eliminate uncertainties due to system responses or measurement details, thereby generating more biologically apposite data. Wide-field microscopy augmented with a constrained NMF algorithm could emerge as an advanced diagnostic tool, potentially heralding the emergence of chemometric microscopy.

Nonnegative decomposition of functional count data

We present a novel decomposition of nonnegative functional count data that draws on concepts from nonnegative matrix factorization. Our decomposition, which we refer to as NARFD (nonnegative and regularized function decomposition), enables the study of patterns in variation across subjects in a highly interpretable manner. Prototypic modes of variation are estimated directly on the observed scale of the data, are local, and are transparently added together to reconstruct observed functions. This contrasts with generalized functional principal component analysis, an alternative approach that estimates functional principal components on a transformed scale, produces components that typically vary across the entire functional domain, and reconstructs observations using complex patterns of cancellation and multiplication of functional principal components. NARFD is implemented using an alternating minimization algorithm, and we evaluate our approach in simulations. We apply NARFD to an accelerometer dataset comprising observations of physical activity for healthy older Americans.

Narrowing the Gap Between In Vitro and In Vivo Genetic Profiles by Deconvoluting Toxicogenomic Data In Silico

Toxicogenomics (TGx) is a powerful method to evaluate toxicity and is widely used in both in vivo and in vitro assays. For in vivo TGx, reduction, refinement, and replacement represent the unremitting pursuit of live-animal tests, but in vitro assays, as alternatives, usually demonstrate poor correlation with real in vivo assays. In living subjects, in addition to drug effects, inner-environmental reactions also affect genetic variation, and these two factors are further jointly reflected in gene abundance. Thus, finding a strategy to factorize inner-environmental factor from in vivo assays based on gene expression levels and to further utilize in vitro data to better simulate in vivo data is needed. We proposed a strategy based on post-modified non-negative matrix factorization, which can estimate the gene expression profiles and contents of major factors in samples. The applicability of the strategy was first verified, and the strategy was then utilized to simulate in vivo data by correcting in vitro data. The similarities between real in vivo data and simulated data (single-dose 0.72, repeat-doses 0.75) were higher than those observed when directly comparing real in vivo data with in vitro data (single-dose 0.56, repeat-doses 0.70). Moreover, by keeping environment-related factor, a simulation can always be generated by using in vitro data to provide potential substitutions for in vivo TGx and to reduce the launch of live-animal tests.

Optimization Techniques to Deeply Mine the Transcriptomic Profile of the Sub-Genomes in Hybrid Fish Lineage

It has been shown that reciprocal cross allodiploid lineage with sub-genomes derived from the cross of Megalobrama amblycephala (BSB) × Culter alburnus (TC) generates the variations in phenotypes and genotypes, but it is still a challenge to deeply mine biological information in the transcriptomic profile of this lineage owing to its genomic complexity and lack of efficient data mining methods. In this paper, we establish an optimization model by non-negative matrix factorization approach for deeply mining the transcriptomic profile of the sub-genomes in hybrid fish lineage. A new so-called spectral conjugate gradient algorithm is developed to solve a sequence of large-scale subproblems such that the original complicated model can be efficiently solved. It is shown that the proposed method can provide a satisfactory result of taxonomy for the hybrid fish lineage such that their genetic characteristics are revealed, even for the samples with larger detection errors. Particularly, highly expressed shared genes are found for each class of the fish. The hybrid progeny of TC and BSB displays significant hybrid characteristics. The third generation of TC-BSB hybrid progeny (BTF3 and TBF3) shows larger trait separation.

An Efficient and Flexible Method for Deconvoluting Bulk RNA-Seq Data with Single-Cell RNA-Seq Data

Estimating cell type compositions for complex diseases is an important step to investigate the cellular heterogeneity for understanding disease etiology and potentially facilitate early disease diagnosis and prevention. Here, we developed a computationally statistical method, referring to Multi-Omics Matrix Factorization (MOMF), to estimate the cell-type compositions of bulk RNA sequencing (RNA-seq) data by leveraging cell type-specific gene expression levels from single-cell RNA sequencing (scRNA-seq) data. MOMF not only directly models the count nature of gene expression data, but also effectively accounts for the uncertainty of cell type-specific mean gene expression levels. We demonstrate the benefits of MOMF through three real data applications, i.e., Glioblastomas (GBM), colorectal cancer (CRC) and type II diabetes (T2D) studies. MOMF is able to accurately estimate disease-related cell type proportions, i.e., oligodendrocyte progenitor cells and macrophage cells, which are strongly associated with the survival of GBM and CRC, respectively.

Prediction of Disease-related microRNAs through Integrating Attributes of microRNA Nodes and Multiple Kinds of Connecting Edges

Identifying disease-associated microRNAs (disease miRNAs) contributes to the understanding of disease pathogenesis. Most previous computational biology studies focused on multiple kinds of connecting edges of miRNAs and diseases, including miRNA-miRNA similarities, disease-disease similarities, and miRNA-disease associations. Few methods exploited the node attribute information related to miRNA family and cluster. The previous methods do not completely consider the sparsity of node attributes. Additionally, it is challenging to deeply integrate the node attributes of miRNAs and the similarities and associations related to miRNAs and diseases. In the present study, we propose a novel method, known as MDAPred, based on nonnegative matrix factorization to predict candidate disease miRNAs. MDAPred integrates the node attributes of miRNAs and the related similarities and associations of miRNAs and diseases. Since a miRNA is typically subordinate to a family or a cluster, the node attributes of miRNAs are sparse. Similarly, the data for miRNA and disease similarities are sparse. Projecting the miRNA and disease similarities and miRNA node attributes into a common low-dimensional space contributes to estimating miRNA-disease associations. Simultaneously, the possibility that a miRNA is associated with a disease depends on the miRNA's neighbour information. Therefore, MDAPred deeply integrates projections of multiple kinds of connecting edges, projections of miRNAs node attributes, and neighbour information of miRNAs. The cross-validation results showed that MDAPred achieved superior performance compared to other state-of-the-art methods for predicting disease-miRNA associations. MDAPred can also retrieve more actual miRNA-disease associations at the top of prediction results, which is very important for biologists. Additionally, case studies of breast, lung, and pancreatic cancers further confirmed the ability of MDAPred to discover potential miRNA-disease associations.

Predicting Drug-Target Interactions with Neighbor Interaction Information and Discriminative Low-rank Representation

BACKGROUND

Inferring drug-target interaction (DTI) candidates for new drugs or targets without any interaction information is a critical challenge for modern drug design and discovery. Results from existing DTI inference methods indicate that these approaches necessitate further improvement.

METHODS

In this paper, we developed a novel DTI identification model (PreNNDS) by integrating Neighbor interaction profiles, Nonnegative matrix factorization, Discriminative low-rank representation, and Sparse representation classification into a unified framework.

RESULTS

AUPR values on four types of datasets show that PreNNDS can efficiently identify potential DTIs for new drugs or targets. We listed predicted top 20 drugs interacting with hsa1132 and hsa1124 and top 20 targets interacting with D00255 and D00195.

CONCLUSIONS

PreNNDS can be applied to identify multi-target drugs and multi-drug resistance proteins, as well as to provide clues for microRNA-disease and gene-disease association prediction.

Multiple Partial Regularized Nonnegative Matrix Factorization for Predicting Ontological Functions of lncRNAs

Long non-coding RNAs (LncRNA) are critical regulators for biological processes, which are highly related to complex diseases. Even though the next generation sequence technology facilitates the discovery of a great number of lncRNAs, the knowledge about the functions of lncRNAs is limited. Thus, it is promising to predict the functions of lncRNAs, which shed light on revealing the mechanisms of complex diseases. The current algorithms predict the functions of lncRNA by using the features of protein-coding genes. Generally speaking, these algorithms fuse heterogeneous genomic data to construct lncRNA-gene associations via a linear combination, which cannot fully characterize the function-lncRNA relations. To overcome this issue, we present an nonnegative matrix factorization algorithm with multiple partial regularization (aka MPrNMF) to predict the functions of lncRNAs without fusing the heterogeneous genomic data. In details, for each type of genomic data, we construct the lncRNA-gene associations, resulting in multiple associations. The proposed method integrates separately them via regularization strategy, rather than fuse them into a single type of associations. The results demonstrate that the proposed algorithm outperforms state-of-the-art methods based network-analysis. The model and algorithm provide an effective way to explore the functions of lncRNAs.

Muscle Synergies Obtained from Comprehensive Mapping of the Cortical Forelimb Representation Using Stimulus Triggered Averaging of EMG Activity

Neuromuscular control of voluntary movement may be simplified using muscle synergies similar to those found using non-negative matrix factorization. We recently identified synergies in electromyography (EMG) recordings associated with both voluntary movement and movement evoked by high-frequency long-duration intracortical microstimulation applied to the forelimb representation of the primary motor cortex (M1). The goal of this study was to use stimulus-triggered averaging (StTA) of EMG activity to investigate the synergy profiles and weighting coefficients associated with poststimulus facilitation, as synergies may be hard-wired into elemental cortical output modules and revealed by StTA. We applied StTA at low (LOW, ∼15 μA) and high intensities (HIGH, ∼110 μA) to 247 cortical locations of the M1 forelimb region in two male rhesus macaques while recording the EMG of 24 forelimb muscles. Our results show that 10-11 synergies accounted for 90% of the variation in poststimulus EMG facilitation peaks from the LOW-intensity StTA dataset while only 4-5 synergies were needed for the HIGH-intensity dataset. Synergies were similar across monkeys and current intensities. Most synergy profiles strongly activated only one or two muscles; all joints were represented and most, but not all, joint directions of motion were represented. Cortical maps of the synergy weighting coefficients suggest only a weak organization. StTA of M1 resulted in highly diverse muscle activations, suggestive of the limiting condition of requiring a synergy for each muscle to account for the patterns observed.SIGNIFICANCE STATEMENT Coordination of muscle activity and the neural origin of potential muscle synergies remains a fundamental question of neuroscience. We previously demonstrated that high-frequency long-duration intracortical microstimulation-evoked synergies were unrelated to voluntary movement synergies and were not clearly organized in the cortex. Here we present stimulus-triggered averaging facilitation-related muscle synergies, suggesting that when fundamental cortical output modules are activated, synergies approach the limit of single-muscle control. Thus, we conclude that if the CNS controls movement via linear synergies, those synergies are unlikely to be called from M1. This information is critical for understanding neural control of movement and the development of brain-machine interfaces.

A diffusion model-free framework with echo time dependence for free-water elimination and brain tissue microstructure characterization

Purpose

The compartmental nature of brain tissue microstructure is typically studied by diffusion MRI, MR relaxometry or their correlation. Diffusion MRI relies on signal representations or biophysical models, while MR relaxometry and correlation studies are based on regularized inverse Laplace transforms (ILTs). Here we introduce a general framework for characterizing microstructure that does not depend on diffusion modeling and replaces ill‐posed ILTs with blind source separation (BSS). This framework yields proton density, relaxation times, volume fractions, and signal disentanglement, allowing for separation of the free‐water component.

Theory and Methods

Diffusion experiments repeated for several different echo times, contain entangled diffusion and relaxation compartmental information. These can be disentangled by BSS using a physically constrained nonnegative matrix factorization.

Results

Computer simulations, phantom studies, together with repeatability and reproducibility experiments demonstrated that BSS is capable of estimating proton density, compartmental volume fractions and transversal relaxations. In vivo results proved its potential to correct for free‐water contamination and to estimate tissue parameters.

Conclusion

Formulation of the diffusion‐relaxation dependence as a BSS problem introduces a new framework for studying microstructure compartmentalization, and a novel tool for free‐water elimination.

Adaptive Multiview Nonnegative Matrix Factorization Algorithm for Integration of Multimodal Biomedical Data

The amounts and types of available multimodal tumor data are rapidly increasing, and their integration is critical for fully understanding the underlying cancer biology and personalizing treatment. However, the development of methods for effectively integrating multimodal data in a principled manner is lagging behind our ability to generate the data. In this article, we introduce an extension to a multiview nonnegative matrix factorization algorithm (NNMF) for dimensionality reduction and integration of heterogeneous data types and compare the predictive modeling performance of the method on unimodal and multimodal data. We also present a comparative evaluation of our novel multiview approach and current data integration methods. Our work provides an efficient method to extend an existing dimensionality reduction method. We report rigorous evaluation of the method on large-scale quantitative protein and phosphoprotein tumor data from the Clinical Proteomic Tumor Analysis Consortium (CPTAC) acquired using state-of-the-art liquid chromatography mass spectrometry. Exome sequencing and RNA-Seq data were also available from The Cancer Genome Atlas for the same tumors. For unimodal data, in case of breast cancer, transcript levels were most predictive of estrogen and progesterone receptor status and copy number variation of human epidermal growth factor receptor 2 status. For ovarian and colon cancers, phosphoprotein and protein levels were most predictive of tumor grade and stage and residual tumor, respectively. When multiview NNMF was applied to multimodal data to predict outcomes, the improvement in performance is not overall statistically significant beyond unimodal data, suggesting that proteomics data may contain more predictive information regarding tumor phenotypes than transcript levels, probably due to the fact that proteins are the functional gene products and therefore a more direct measurement of the functional state of the tumor. Here, we have applied our proposed approach to multimodal molecular data for tumors, but it is generally applicable to dimensionality reduction and joint analysis of any type of multimodal data.

Mutation Clusters from Cancer Exome

We apply our statistically deterministic machine learning/clustering algorithm *K-means (recently developed in https://ssrn.com/abstract=2908286) to 10,656 published exome samples for 32 cancer types. A majority of cancer types exhibit a mutation clustering structure. Our results are in-sample stable. They are also out-of-sample stable when applied to 1389 published genome samples across 14 cancer types. In contrast, we find in- and out-of-sample instabilities in cancer signatures extracted from exome samples via nonnegative matrix factorization (NMF), a computationally-costly and non-deterministic method. Extracting stable mutation structures from exome data could have important implications for speed and cost, which are critical for early-stage cancer diagnostics, such as novel blood-test methods currently in development.

Ranking Causal Anomalies via Temporal and Dynamical Analysis on Vanishing Correlations

Modern world has witnessed a dramatic increase in our ability to collect, transmit and distribute real-time monitoring and surveillance data from large-scale information systems and cyber-physical systems. Detecting system anomalies thus attracts significant amount of interest in many fields such as security, fault management, and industrial optimization. Recently, invariant network has shown to be a powerful way in characterizing complex system behaviours. In the invariant network, a node represents a system component and an edge indicates a stable, significant interaction between two components. Structures and evolutions of the invariance network, in particular the vanishing correlations, can shed important light on locating causal anomalies and performing diagnosis. However, existing approaches to detect causal anomalies with the invariant network often use the percentage of vanishing correlations to rank possible casual components, which have several limitations: 1) fault propagation in the network is ignored; 2) the root casual anomalies may not always be the nodes with a high-percentage of vanishing correlations; 3) temporal patterns of vanishing correlations are not exploited for robust detection. To address these limitations, in this paper we propose a network diffusion based framework to identify significant causal anomalies and rank them. Our approach can effectively model fault propagation over the entire invariant network, and can perform joint inference on both the structural, and the time-evolving broken invariance patterns. As a result, it can locate high-confidence anomalies that are truly responsible for the vanishing correlations, and can compensate for unstructured measurement noise in the system. Extensive experiments on synthetic datasets, bank information system datasets, and coal plant cyber-physical system datasets demonstrate the effectiveness of our approach.

Muscle synergies obtained from comprehensive mapping of the primary motor cortex forelimb representation using high-frequency, long-duration ICMS

Simplifying neuromuscular control for movement has previously been explored by extracting muscle synergies from voluntary movement electromyography (EMG) patterns. The purpose of this study was to investigate muscle synergies represented in EMG recordings associated with direct electrical stimulation of single sites in primary motor cortex (M1). We applied single-electrode high-frequency, long-duration intracortical microstimulation (HFLD-ICMS) to the forelimb region of M1 in two rhesus macaques using parameters previously found to produce forelimb movements to stable spatial end points (90-150 Hz, 90-150 μA, 1,000-ms stimulus train lengths). To develop a comprehensive representation of cortical output, stimulation was applied systematically across the full extent of M1. We recorded EMG activity from 24 forelimb muscles together with movement kinematics. Nonnegative matrix factorization (NMF) was applied to the mean stimulus-evoked EMG, and the weighting coefficients associated with each synergy were mapped to the cortical location of the stimulating electrode. Synergies were found for three data sets including 1) all stimulated sites in the cortex, 2) a subset of sites that produced stable movement end points, and 3) EMG activity associated with voluntary reaching. Two or three synergies accounted for 90% of the overall variation in voluntary movement EMG whereas four or five synergies were needed for HFLD-ICMS-evoked EMG data sets. Maps of the weighting coefficients from the full HFLD-ICMS data set show limited regional areas of higher activation for particular synergies. Our results demonstrate fundamental NMF-based muscle synergies in the collective M1 output, but whether and how the central nervous system might coordinate movements using these synergies remains unclear.NEW & NOTEWORTHY While muscle synergies have been investigated in various muscle activity sets, it is unclear whether and how synergies may be organized in the cortex. We have investigated muscle synergies resulting from high-frequency, long-duration intracortical microstimulation (HFLD-ICMS) applied throughout M1. We compared HFLD-ICMS synergies to synergies from voluntary movement. While synergies can be identified from M1 stimulation, they are not clearly related to voluntary movement synergies and do not show an orderly topographic organization across M1.

Patterns of coordinated cortical remodeling during adolescence and their associations with functional specialization and evolutionary expansion

During adolescence, the human cortex undergoes substantial remodeling to support a rapid expansion of behavioral repertoire. Accurately quantifying these changes is a prerequisite for understanding normal brain development, as well as the neuropsychiatric disorders that emerge in this vulnerable period. Past accounts have demonstrated substantial regional heterogeneity in patterns of brain development, but frequently have been limited by small samples and analytics that do not evaluate complex multivariate imaging patterns. Capitalizing on recent advances in multivariate analysis methods, we used nonnegative matrix factorization (NMF) to uncover coordinated patterns of cortical development in a sample of 934 youths ages 8-20, who completed structural neuroimaging as part of the Philadelphia Neurodevelopmental Cohort. Patterns of structural covariance (PSCs) derived by NMF were highly reproducible over a range of resolutions, and differed markedly from common gyral-based structural atlases. Moreover, PSCs were largely symmetric and showed correspondence to specific large-scale functional networks. The level of correspondence was ordered according to their functional role and position in the evolutionary hierarchy, being high in lower-order visual and somatomotor networks and diminishing in higher-order association cortex. Furthermore, PSCs showed divergent developmental associations, with PSCs in higher-order association cortex networks showing greater changes with age than primary somatomotor and visual networks. Critically, such developmental changes within PSCs were significantly associated with the degree of evolutionary cortical expansion. Together, our findings delineate a set of structural brain networks that undergo coordinated cortical thinning during adolescence, which is in part governed by evolutionary novelty and functional specialization.

Patterns of coordinated cortical remodeling during adolescence and their associations with functional specialization and evolutionary expansion

During adolescence, the human cortex undergoes substantial remodeling to support a rapid expansion of behavioral repertoire. Accurately quantifying these changes is a prerequisite for understanding normal brain development, as well as the neuropsychiatric disorders that emerge in this vulnerable period. Past accounts have demonstrated substantial regional heterogeneity in patterns of brain development, but frequently have been limited by small samples and analytics that do not evaluate complex multivariate imaging patterns. Capitalizing on recent advances in multivariate analysis methods, we used nonnegative matrix factorization (NMF) to uncover coordinated patterns of cortical development in a sample of 934 youths ages 8-20, who completed structural neuroimaging as part of the Philadelphia Neurodevelopmental Cohort. Patterns of structural covariance (PSCs) derived by NMF were highly reproducible over a range of resolutions, and differed markedly from common gyral-based structural atlases. Moreover, PSCs were largely symmetric and showed correspondence to specific large-scale functional networks. The level of correspondence was ordered according to their functional role and position in the evolutionary hierarchy, being high in lower-order visual and somatomotor networks and diminishing in higher-order association cortex. Furthermore, PSCs showed divergent developmental associations, with PSCs in higher-order association cortex networks showing greater changes with age than primary somatomotor and visual networks. Critically, such developmental changes within PSCs were significantly associated with the degree of evolutionary cortical expansion. Together, our findings delineate a set of structural brain networks that undergo coordinated cortical thinning during adolescence, which is in part governed by evolutionary novelty and functional specialization.

On identifying kinematic and muscle synergies: a comparison of matrix factorization methods using experimental data from the healthy population

Human motor behavior is highly goal directed, requiring the central nervous system to coordinate different aspects of motion generation to achieve the motion goals. The concept of motor synergies provides an approach to quantify the covariation of joint motions and of muscle activations, i.e., elemental variables, during a task. To analyze goal-directed movements, factorization methods can be used to reduce the high dimensionality of these variables while accounting for much of the variance in large data sets. Three factorization methods considered in this paper are principal component analysis (PCA), nonnegative matrix factorization (NNMF), and independent component analysis (ICA). Bilateral human reaching data sets are used to compare the methods, and advantages of each are presented and discussed. PCA and NNMF had a comparable performance on both EMG and joint motion data and both outperformed ICA. However, NNMF's nonnegativity condition for activation of basis vectors is a useful attribute in identifying physiologically meaningful synergies, making it a more appealing method for future studies. A simulated data set is introduced to clarify the approaches and interpretation of the synergy structures returned by the three factorization methods.

NEW & NOTEWORTHY

Literature on comparing factorization methods in identifying motor synergies using numerically generated, simulation, and muscle activation data from animal studies already exists. We present an empirical evaluation of the performance of three of these methods on muscle activation and joint angles data from human reaching motion: principal component analysis, nonnegative matrix factorization, and independent component analysis. Using numerical simulation, we also studied the meaning and differences in the synergy structures returned by each method. The results can be used to unify approaches in identifying and interpreting motor synergies.

Clustering Tree-Structured Data on Manifold

Tree-structured data usually contain both topological and geometrical information, and are necessarily considered on manifold instead of euclidean space for appropriate data parameterization and analysis. In this study, we propose a novel tree-structured data parameterization, called Topology-Attribute matrix (T-A matrix), so the data clustering task can be conducted on matrix manifold. We incorporate the structure constraints embedded in data into the non-negative matrix factorization method to determine meta-trees from the T-A matrix, and the signature vector of each single tree can then be extracted by meta-tree decomposition. The meta-tree space turns out to be a cone space, in which we explore the distance metric and implement the clustering algorithm based on the concepts like Fréchet mean. Finally, the T-A matrix based clustering (TAMBAC) framework is evaluated and compared using both simulated data and real retinal images to illustrate its efficiency and accuracy.

Prediction of Soil Salinity Using Near-Infrared Reflectance Spectroscopy with Nonnegative Matrix Factorization

As a key, yet difficult, issue currently in the quantitative remote sensing analysis of soil, the accurate and stable monitoring of soil salinity content (SSC) in situ should be studied and improved. The purpose of this study is to explore the method of fusing spectra outdoors with spectra indoors and improve the estimation precision of SSC based on near-infrared (NIR) reflectance hyper-spectra. First, samples of saline soil from the Yellow River delta of China were collected and analyzed. We measured three groups of sample spectra using a spectrometer: (1) situ-spectra, measured at sampling points in situ; (2) out-spectra, measured outdoors on air-dried samples; and, (3) lab-spectra, measured in a dark laboratory with the above air-dried samples. Second, four algorithms (multiplicative update, alternating least-squares, sparse affine non-negative matrix factorization (NMF), and gradient projection algorithms) of NMF were used to fuse the situ-spectra or out-spectra with the lab-spectra for the calibration of SSC. Finally, estimation models of SSC were built using the multiple linear regression method based on the first derivatives of the un-fused and fused spectra. The results indicate that using the NMF method to fuse the situ-spectra or out-spectra with the lab-spectra can heighten the correlation between SSC and the outdoor spectra in most wavelength ranges and improve the accuracy of the prediction model. The gradient projection algorithm shows the best performance with fewer variables and highest accuracy of the SSC model based on the NIR spectra.

CGC: A Flexible and Robust Approach to Integrating Co-Regularized Multi-Domain Graph for Clustering

Multi-view graph clustering aims to enhance clustering performance by integrating heterogeneous information collected in different domains. Each domain provides a different view of the data instances. Leveraging cross-domain information has been demonstrated an effective way to achieve better clustering results. Despite the previous success, existing multi-view graph clustering methods usually assume that different views are available for the same set of instances. Thus instances in different domains can be treated as having strict one-to-one relationship. In many real-life applications, however, data instances in one domain may correspond to multiple instances in another domain. Moreover, relationships between instances in different domains may be associated with weights based on prior (partial) knowledge. In this paper, we propose a flexible and robust framework, CGC (Co-regularized Graph Clustering), based on non-negative matrix factorization (NMF), to tackle these challenges. CGC has several advantages over the existing methods. First, it supports many-to-many cross-domain instance relationship. Second, it incorporates weight on cross-domain relationship. Third, it allows partial cross-domain mapping so that graphs in different domains may have different sizes. Finally, it provides users with the extent to which the cross-domain instance relationship violates the in-domain clustering structure, and thus enables users to re-evaluate the consistency of the relationship. We develop an efficient optimization method that guarantees to find the global optimal solution with a given confidence requirement. The proposed method can automatically identify noisy domains and assign smaller weights to them. This helps to obtain optimal graph partition for the focused domain. Extensive experimental results on UCI benchmark data sets, newsgroup data sets and biological interaction networks demonstrate the effectiveness of our approach.

Sparse Nonnegative Matrix Factorization Strategy for Cochlear Implants

Current cochlear implant (CI) strategies carry speech information via the waveform envelope in frequency subbands. CIs require efficient speech processing to maximize information transfer to the brain, especially in background noise, where the speech envelope is not robust to noise interference. In such conditions, the envelope, after decomposition into frequency bands, may be enhanced by sparse transformations, such as nonnegative matrix factorization (NMF). Here, a novel CI processing algorithm is described, which works by applying NMF to the envelope matrix (envelopogram) of 22 frequency channels in order to improve performance in noisy environments. It is evaluated for speech in eight-talker babble noise. The critical sparsity constraint parameter was first tuned using objective measures and then evaluated with subjective speech perception experiments for both normal hearing and CI subjects. Results from vocoder simulations with 10 normal hearing subjects showed that the algorithm significantly enhances speech intelligibility with the selected sparsity constraints. Results from eight CI subjects showed no significant overall improvement compared with the standard advanced combination encoder algorithm, but a trend toward improvement of word identification of about 10 percentage points at +15 dB signal-to-noise ratio (SNR) was observed in the eight CI subjects. Additionally, a considerable reduction of the spread of speech perception performance from 40% to 93% for advanced combination encoder to 80% to 100% for the suggested NMF coding strategy was observed.

A method for extracting fetal ECG based on EMD-NMF single channel blind source separation algorithm

Nowadays, detecting fetal ECG using abdominal signal is a commonly used method, but fetal ECG signal will be affected by maternal ECG. Current FECG extraction algorithms are mainly aiming at multiple channels signal. They often assume there is only one fetus and did not consider multiple births. This paper proposed a single channel blind source separation algorithm to process single abdominal acquired signal. This algorithm decomposed single abdominal signal into multiple intrinsic mode function (IMF) utilizing empirical mode decomposition (EMD). Correlation matrix of IMF was calculated and independent ECG signal number was estimated using eigenvalue method. Nonnegative matrix was constructed according to determined number and decomposed IMF. Separation of MECG and FECG was achieved utilizing nonnegative matrix factorization (NMF). Experiments selected four channels man-made signal and two channels ECG to verify correctness and feasibility of proposed algorithm. Results showed that the proposed algorithm could determine number of independent signal in single acquired signal. FECG could be extracted from single channel observed signal and the algorithm can be used to solve separation of MECG and FECG.

On nonnegative matrix factorization algorithms for signal-dependent noise with application to electromyography data

Nonnegative matrix factorization (NMF) by the multiplicative updates algorithm is a powerful machine learning method for decomposing a high-dimensional nonnegative matrix V into two nonnegative matrices, W and H, where V ~ WH. It has been successfully applied in the analysis and interpretation of large-scale data arising in neuroscience, computational biology, and natural language processing, among other areas. A distinctive feature of NMF is its nonnegativity constraints that allow only additive linear combinations of the data, thus enabling it to learn parts that have distinct physical representations in reality. In this letter, we describe an information-theoretic approach to NMF for signal-dependent noise based on the generalized inverse gaussian model. Specifically, we propose three novel algorithms in this setting, each based on multiplicative updates, and prove monotonicity of updates using the EM algorithm. In addition, we develop algorithm-specific measures to evaluate their goodness of fit on data. Our methods are demonstrated using experimental data from electromyography studies, as well as simulated data in the extraction of muscle synergies, and compared with existing algorithms for signal-dependent noise.

Atomic dynamic functional interaction patterns for characterization of ADHD

Modeling abnormal temporal dynamics of functional interactions in psychiatric disorders has been of great interest in the neuroimaging field, and thus a variety of methods have been proposed so far. However, the temporal dynamics and disease-related abnormalities of functional interactions within specific data-driven discovered subnetworks have been rarely explored yet. In this work, we propose a novel computational framework composed of an effective Bayesian connectivity change point model for modeling functional brain interactions and their dynamics simultaneously and an effective variant of nonnegative matrix factorization for assessing the functional interaction abnormalities within subnetworks. This framework has been applied on the resting state fmagnetic resonance imaging (fMRI) datasets of 23 children with attention-deficit/hyperactivity disorder (ADHD) and 45 normal control (NC) children, and has revealed two atomic functional interaction patterns (AFIPs) discovered for ADHD and another two AFIPs derived for NC. Together, these four AFIPs could be grouped into two pairs, one common pair representing the common AFIPs in ADHD and NC, and the other abnormal pair representing the abnormal AFIPs in ADHD. Interestingly, by comparing the abnormal AFIP pair, two data-driven abnormal functional subnetworks are derived. Strikingly, by evaluating the approximation based on the four AFIPs, all of the ADHD children were successfully differentiated from NCs without any false positive.

Social Trust Prediction Using Heterogeneous Networks

Along with increasing popularity of social websites, online users rely more on the trustworthiness information to make decisions, extract and filter information, and tag and build connections with other users. However, such social network data often suffer from severe data sparsity and are not able to provide users with enough information. Therefore, trust prediction has emerged as an important topic in social network research. Traditional approaches are primarily based on exploring trust graph topology itself. However, research in sociology and our life experience suggest that people who are in the same social circle often exhibit similar behaviors and tastes. To take advantage of the ancillary information for trust prediction, the challenge then becomes what to transfer and how to transfer. In this article, we address this problem by aggregating heterogeneous social networks and propose a novel joint social networks mining (JSNM) method. Our new joint learning model explores the user-group-level similarity between correlated graphs and simultaneously learns the individual graph structure; therefore, the shared structures and patterns from multiple social networks can be utilized to enhance the prediction tasks. As a result, we not only improve the trust prediction in the target graph but also facilitate other information retrieval tasks in the auxiliary graphs. To optimize the proposed objective function, we use the alternative technique to break down the objective function into several manageable subproblems. We further introduce the auxiliary function to solve the optimization problems with rigorously proved convergence. The extensive experiments have been conducted on both synthetic and real- world data. All empirical results demonstrate the effectiveness of our method.

The number and choice of muscles impact the results of muscle synergy analyses

One theory for how humans control movement is that muscles are activated in weighted groups or synergies. Studies have shown that electromyography (EMG) from a variety of tasks can be described by a low-dimensional space thought to reflect synergies. These studies use algorithms, such as nonnegative matrix factorization, to identify synergies from EMG. Due to experimental constraints, EMG can rarely be taken from all muscles involved in a task. However, it is unclear if the choice of muscles included in the analysis impacts estimated synergies. The aim of our study was to evaluate the impact of the number and choice of muscles on synergy analyses. We used a musculoskeletal model to calculate muscle activations required to perform an isometric upper-extremity task. Synergies calculated from the activations from the musculoskeletal model were similar to a prior experimental study. To evaluate the impact of the number of muscles included in the analysis, we randomly selected subsets of between 5 and 29 muscles and compared the similarity of the synergies calculated from each subset to a master set of synergies calculated from all muscles. We determined that the structure of synergies is dependent upon the number and choice of muscles included in the analysis. When five muscles were included in the analysis, the similarity of the synergies to the master set was only 0.57 ± 0.54; however, the similarity improved to over 0.8 with more than ten muscles. We identified two methods, selecting dominant muscles from the master set or selecting muscles with the largest maximum isometric force, which significantly improved similarity to the master set and can help guide future experimental design. Analyses that included a small subset of muscles also over-estimated the variance accounted for (VAF) by the synergies compared to an analysis with all muscles. Thus, researchers should use caution using VAF to evaluate synergies when EMG is measured from a small subset of muscles.

Improved image fusion method based on NSCT and accelerated NMF

In order to improve algorithm efficiency and performance, a technique for image fusion based on the Non-subsampled Contourlet Transform (NSCT) domain and an Accelerated Non-negative Matrix Factorization (ANMF)-based algorithm is proposed in this paper. Firstly, the registered source images are decomposed in multi-scale and multi-direction using the NSCT method. Then, the ANMF algorithm is executed on low-frequency sub-images to get the low-pass coefficients. The low frequency fused image can be generated faster in that the update rules for W and H are optimized and less iterations are needed. In addition, the Neighborhood Homogeneous Measurement (NHM) rule is performed on the high-frequency part to achieve the band-pass coefficients. Finally, the ultimate fused image is obtained by integrating all sub-images with the inverse NSCT. The simulated experiments prove that our method indeed promotes performance when compared to PCA, NSCT-based, NMF-based and weighted NMF-based algorithms.

Graphics Processing Units and High-Dimensional Optimization

This paper discusses the potential of graphics processing units (GPUs) in high-dimensional optimization problems. A single GPU card with hundreds of arithmetic cores can be inserted in a personal computer and dramatically accelerates many statistical algorithms. To exploit these devices fully, optimization algorithms should reduce to multiple parallel tasks, each accessing a limited amount of data. These criteria favor EM and MM algorithms that separate parameters and data. To a lesser extent block relaxation and coordinate descent and ascent also qualify. We demonstrate the utility of GPUs in nonnegative matrix factorization, PET image reconstruction, and multidimensional scaling. Speedups of 100 fold can easily be attained. Over the next decade, GPUs will fundamentally alter the landscape of computational statistics. It is time for more statisticians to get on-board.