Matrix Factorization Method Research Articles

An efficient system matrix factorization method for scanning diffraction based strain tensor tomography.

Diffraction-based tomographic strain tensor reconstruction problems in which a strain tensor field is determined from measurements made in different crystallographic directions are considered in the context of sparse matrix algebra. Previous work has shown that the estimation of the crystal elastic strain field can be cast as a linear regression problem featuring a computationally involved assembly of a system matrix forward operator. This operator models the perturbation in diffraction signal as a function of spatial strain tensor state. The structure of this system matrix is analysed and a block-partitioned factorization is derived that reveals the forward operator as a sum of weighted scalar projection operators. Moreover, the factorization method is generalized for another diffraction model in which strain and orientation are coupled and can be reconstructed jointly. The proposed block-partitioned factorization method provides a bridge to classical absorption tomography and allows exploitation of standard tomographic ray-tracing libraries for implementation of the forward operator and its adjoint. Consequently, RAM-efficient, GPU-accelerated, on-the-fly strain/orientation tensor reconstruction is made possible, paving the way for higher spatial resolution studies of intragranular deformation.

Supervised discovery of interpretable gene programs from single-cell data

Factor analysis decomposes single-cell gene expression data into a minimal set of gene programs that correspond to processes executed by cells in a sample. However, matrix factorization methods are prone to technical artifacts and poor factor interpretability. We address these concerns with Spectra, an algorithm that combines user-provided gene programs with the detection of novel programs that together best explain expression covariation. Spectra incorporates existing gene sets and cell-type labels as prior biological information, explicitly models cell type and represents input gene sets as a gene–gene knowledge graph using a penalty function to guide factorization toward the input graph. We show that Spectra outperforms existing approaches in challenging tumor immune contexts, as it finds factors that change under immune checkpoint therapy, disentangles the highly correlated features of CD8+ T cell tumor reactivity and exhaustion, finds a program that explains continuous macrophage state changes under therapy and identifies cell-type-specific immune metabolic programs.

Source apportionment and migration characteristics of heavy metal(loid)s in soil and groundwater of contaminated site

The rapid industrial growth has generated heavy metal(loid)s contamination in the soil, which poses a serious threat to the ecology and human health. In this study, 580 samples were collected in Henan Province, China, for source apportionment, migration characterization and health risk evaluation using self-organizing map, positive matrix factorization and multivariate risk assessment methods. The results showed that samples were classified into four groups and pollution sources included chromium slag dump, soil parent rock and abandoned factory. The contents of Cr, Pb, As and Hg were low in Group 1. Group 2 was characterized by total Cr, Cr(Ⅵ) and pH. The enrichment of total Cr and Cr(Ⅵ) in soil was mainly attributed to chromium slag dump, accounting for more than 84.0%. Group 3 was dominated by Hg and Pb. Hg and Pb were primarily attributed to abandoned factory, accounting for 84.7% and 70.0%, respectively. Group 4 was characterized by As. The occurrence of As was not limited to one individual region. The contribution of soil parent rock reached 83.0%. Furthermore, the vertical migration of As, Hg, Pb and Cr(Ⅵ) in soil was mainly influenced by medium permeability, pH and organic matter content. The trends of As, Pb, and Hg with depth were basically consistent with the trends of organic matter with depth, and were negatively correlated with the change in pH with depth. The trends of Cr(Ⅵ) with depth were basically consistent with the changes in pH with the depth. The content of Cr(Ⅵ) in the deep soil did not exceed the detection limits and Cr(Ⅵ) contamination occurred in the deep aquifer, suggesting that Cr(Ⅵ) in the deep groundwater originated from the leakage of shallow groundwater. The assessment indicated that the non-carcinogenic and carcinogenic risks for children and adults could not be neglected. Moreover, children were more susceptible than adults.

An end-member modelling approach to pseudo-Thellier palaeointensity data

SUMMARY Absolute palaeointensities are notoriously hard to obtain, because conventional thermal Thellier palaeointensity experiments often have low success rates for volcanic samples. The thermal treatments necessary for these experiments potentially induce (magnetic) alteration in the samples, preventing a reliable palaeointensity estimate. These heating steps can be avoided by pseudo-Thellier measurements, where samples are demagnetized and remagnetized with alternating fields. However, pseudo-Thellier experiments intrinsically produce relative palaeointensities. Over the past years, attempts were made to calibrate pseudo-Thellier results into absolute palaeointensities for lavas by mapping laboratory induced anhysteretic remanent magnetizations (ARMs) to the thermally acquired natural remanent magnetizations (NRMs). Naturally occurring volcanic rocks, however, are assemblages of minerals differing in grain size, shape and chemistry. These different minerals all have their own characteristic mapping between ARMs and thermal NRMs. Here, we show that it is possible to find these characteristic mappings by unmixing the NRM demagnetization and the ARM acquisition curves into end-members, with an iterative method of non-negative matrix factorization. In turn, this end-member modelling approach (EMMA) allows for the calculation of absolute palaeointensities from pseudo-Thellier measurements. We tested our EMMA using a noise-free numerical data set, yielding a perfect reconstruction of the palaeointensities. When adding noise up to levels beyond what is expected in natural samples, the end-member model still produces the known palaeointensities well. In addition, we made a synthetic data set with natural volcanic samples from different volcanic edifices that were given a magnetization by heating and cooling them in a controlled magnetic field in the lab. The applied fields ranged between 10 and 70 µT. The average absolute difference between the calculated palaeointensity and the known lab field is around 10 µT for the models with 2–4 end-members, while the palaeointensity of almost all flows can be retrieved within a deviation of ±20 µT. The deviations between the palaeointensities and the known lab fields are almost Gaussian distributed around the expected values. Although the two data sets in our study show that there is potential for using this end-member modelling technique for finding absolute palaeointensities from pseudo-Thellier data, these synthetic data sets cannot be directly related to natural samples. Therefore, it is necessary to compile a data set of known palaeointensities from different volcanic sites that recently cooled in a known magnetic field to find the universal end-members in future studies.

Global and local similarity learning in multi-kernel space for nonnegative matrix factorization

Most of existing nonnegative matrix factorization (NMF) methods do not fully exploit global and local similarity information from data. In this paper, we propose a novel local similarity learning approach in the convex NMF framework, which encourages inter-class separability that is desired for clustering. Thus, the new model is capable of enhancing intra-class similarity and inter-class separability with simultaneous global and local learning. Moreover, the model learns the factor matrices in an augmented kernel space, which is a convex combination of pre-defined kernels with auto-learned weights. Thus, the learnings of cluster structure, representation factor matrix, and the optimal kernel mutually enhance each other in a seamlessly integrated model, which leads to informative representation. Multiplicative updating rules are developed with theoretical convergence guarantee. Extensive experimental results have confirmed the effectiveness of the proposed model.

Quantifying the seasonal variations in and regional transport of PM2.5 in the Yangtze River Delta region, China: characteristics, sources, and health risks

Abstract. Given the increasing complexity of the chemical composition of PM2.5, identifying and quantitatively assessing the contributions of pollution sources has played an important role in formulating policies to control particle pollution. This study provides a comprehensive assessment between PM2.5 chemical characteristics, sources, and health risks based on sampling data conducted over 1 year (March 2018 to February 2019) in Nanjing. Results show that PM2.5 exhibits a distinct variation across different seasons, which is primarily driven by emissions, meteorological conditions, and the chemical conversion of gaseous pollutants. First, the chemical mass reconstruction shows that secondary inorganic aerosols (62.5 %) and carbonaceous aerosols (21.3 %) contributed most to the PM2.5 mass. The increasing oxidation rates of SO2 and NO2 from summer to winter indicate that the secondary transformation of gaseous pollutants is strongly positively correlated with relative humidity. Second, the positive matrix factorization (PMF) method shows that identified PM2.5 sources include secondary inorganic aerosol source (SIS, 42.5 %), coal combustion (CC, 22.4 %), industry source (IS, 17.3 %), vehicle emission (VE, 10.7 %), fugitive dust (FD, 5.8 %), and other sources (1.3 %). The Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model and the concentration-weighted trajectory (CWT) analysis are used to further explore different spatial distributions and regional transport of sources. The concentrations (10–11 µg m−3) of SIS and CC distribute in Nanjing and central China in winter. The concentrations (8–10 µg m−3) of IS and VE are potentially located north of Jiangsu, Anhui, and Jiangxi. Finally, the health risk assessment indicates that the carcinogenic and non-carcinogenic risks of toxic elements (Cr, As, Ni, Mn, V, and Pb) mainly come from IS, VE, and CC, which are within the tolerance or acceptable level. Although the main source of pollution in Nanjing is SIS at present, we should pay more attention to the health burden of vehicle emissions, coal combustion, and industrial processes.

SPATIO-TEMPORAL PATTERNS OF CORTICAL-MUSCULAR INTERACTION DURING LOCOMOTION

The paper considers the synergetic effects manifested at the cortical and muscular levels during locomotor activity showed in conditions of horizontal hanging of the lower extremities. The analysis of the synergies’ spatio-temporal structure was carried out using the data matrix factorization methods. It was found out the control of the movements’ structure is mainly realized through the three muscle synergies. The activity synchronization of the motor, associative, visual and sensorimotor regions of the cortex bilateral part is due to the specifics of performing locomotion in conditions of gravitational unloading and the associated features of receptor signaling. The identified components indicating synchronization of different areas of the right and left cortex may reflect the control processes associated with the control of alternate activation of the flexor and extensor muscles of the contralateral limb during locomotion. The data on the cortical activity spatial-temporal structuring indicate the separate management of muscle synergies through synchronization of cortical commands and the temporary organization of muscle synergies in the frequency ranges 0.30 to 8.00 Hz. Such patterns may reflect the activity of the rhythm-generating mechanism involved in the management of cyclic locomotor activity.

Enhancement of PM2.5 source appointment in a large industrial city of Korea by applying the elemental carbon tracer method for positive matrix factorization (PMF) model

The concentration of particulate matter with an aerodynamic diameter less than 2.5 μm (PM2.5) measured in an industrial area is strongly influenced by the industrial characteristics of the region. Ulsan, an industrial city in Korea, has a large regional impact on PM2.5 concentration because various industries, such as the petrochemical, automobile manufacturing, and shipbuilding, are located in this city. As such, the PM2.5 pollution sources must be identified to enable its management. In this study, PM2.5 source apportionment was conducted in Ulsan. In this process, the contribution to secondary organic formation was estimated considering the secondary organic carbon (SOC) calculated using the elemental carbon (EC) tracer method. Sources were classified into ten categories (i.e., coal-related, industry, sea salt, secondary sulfate, soil, oil combustion, secondary nitrate, traffic-related, SOC formation, and primary emission). Of these, secondary formation contributed approximately 71%. The high rate of secondary production seems to be influenced by the industry in the area. Contributions of secondary sulfate and secondary nitrate were related to the seasons, contributing to the most, in summer and winter, respectively. SOC formation was highest in spring, not summer, which seems to be due to the decrease in organic carbon (OC) concentration due to the washing effect of summer. The contribution of secondary formation in Ulsan was likely overestimated due to the influence of local sources. The positive matrix factorization (PMF) with SOC performed in this study can help to easily separate the PM2.5 sources of secondary formation and primary emissions.

Spatial distribution and quantitative identification of contributions for nutrient and beneficial elements in top- and sub-soil of Huairou District of Beijing, China

To control agricultural and ecological risk, it is significant to monitor the quality of nutrient and beneficial elements (NBEs) in soils, particularly in agricultural area. For this purpose, it is important to clarify NBEs content and distribution, potential sources, and enrichment or depletion mechanism in soils. However, in present studies, the sources identification for soil NBEs and quantification of contributions for multiple sources, remains controversial. In order to solve these problems, in this case, a total of 977 topsoil samples and 258 subsoil samples were collected at Huairou District of Beijing. The content of some NBEs (K, Ca, Mg, V, Mn, F, Ge, N, Se, P, Zn, and S) were analyzed for each sample, and spatial distribution were presented with some values indicating soil properties (TFe2O3, Al2O3/SiO2, total organic carbon (TOC), and pH). The main influence factors of NBEs distibutions in soils were determined by the methods of principal component analysis (PCA), redundancy analysis (RDA), and positive matrix factorization (PMF) analysis. Combined with analysis result and geochemical process, it suggested the enrichment mechanism of NBEs in soils mainly impacted by soil parent material, the local external sources, and elements migration of eluviation in study area. Furthermore, the major contribittions of each NBEs either in topsoil or in subsoil were quantitatively determined. Generally both in topsoils and in subsoils, the source inherited from soil parent material account for 34.65–58.97% contribution to Zn, Mn, Mg, V, F, Ca, K, and Ge; the local external sources accounted 40.66–68.99% for N, S, Se, and Zn; and eluviation contributed 37.45–67.07% of Ca, P, and K. The enrichment degree of NBEs in topsoils were processed by standardized concentration ratio model, which effectively demonstrated elements inheritance from subsoils to topsoils. In addition, the soil quality evaluation was conducted on the basis of NBEs concentration classificaiton. This study quantitatively estimated NBEs sources in soils and their quality, which provided a basis for agricultural activities and ecological environment protection in typical suburban area.

Towards comprehensive air quality management using low-cost sensors for pollution source apportionment

Successful air quality management and control not only requires measurements of air pollution levels. It also requires information on the sources of air pollution, and their relative magnitudes and importance, to plan and enact cost-effective control measures. This paper provides an important breakthrough towards the wider and more comprehensive use of source apportionment via low-cost techniques. Low-cost sensor measurements, along with the statistical methods of Positive Matrix Factorization (PMF) and k-means clustering, were able to successfully pinpoint and quantify the main sources of pollution in three regulatory important sites (a construction site, a quarry and a roadside). The anticipated levels of pollution, which were dependent on meteorological conditions and temporal variations, were assessed. The analysis provides information crucial for successful air quality management and control at a significantly lower cost than previously achieved. The strengths and weaknesses of the methodologies used are illustrated and discussed.

A combined method of autoregressive model and matrix factorization for recovery and forecasting of cyclic structural health monitoring data

Structures such as bridges, offshore platforms, wind power facilities, and drilling rigs generate a corresponding periodic structural response under cyclic loads such as solar radiation, tides and sea-land breeze. Data recovery and forecasting are major parts of the work to ensure structural safety using periodic structural health monitoring data. In this context, a combined method of autoregressive (AR) model and matrix factorization (MF) method is presented to reaching the tasks of data imputation and prediction. The combined method with a graph-based temporal regularizer can well capture the cyclic characteristics and random character. The verification of the method is conducted using an in-situ temperature monitoring dataset of a high-speed railway steel bridge. The application of the method for both data recovery and forecasting with structured missing entries is carried out, which indicates the combined method owns outstanding performance in accurately recover missing entries and making predictions. In the last part, the analysis of rank order and length of time lag is made to show its influence on imputation accuracy.

Multi-Dimensional Surface Water Quality Analyses in the Manawatu River Catchment, New Zealand

Land Use and Land Cover (LULC) properties give vital information about pollution signatures in rivers, and they help develop best management practices (BMPs) for effective water resource management. This work employs multivariate statistical methods, receptor modeling, connectivity analysis, and univariate trend analysis to investigate pollution sources across spatiotemporal scales in the Manawatu River, New Zealand. A positive matrix factorization (PMF) method was applied to interpret possible contamination sources. A 25-year dataset (1989–2014) comprising 12 water quality variables from three sites was used. Runoff connectivity analyses identified high-producing grassland (HG) as the most dominant pollution class in all sub-catchments. Univariate analyses revealed that nutrients and sediments were higher than in the initial monitoring years. The PMF analysis found possible pollutants causing impairment, which required attention from waste managers. PMF also showed that point, natural, and agricultural sources significantly contributed to pollution downstream of the river. In the midstream, the erosion, point, and agricultural sources were significant contributing factors. Agricultural pollution and soil erosion were the main contributors to the upstream sub-catchment area. This study suggests that BMPs with a high retention capacity are needed in specific locations in the catchment area to filter high concentrations of pollutants generated.

A comparison of non-negative matrix underapproximation methods for the decomposition of magnetic resonance spectroscopy data from human brain tumors.

Magnetic resonance spectroscopy (MRS) is an MR technique that provides information about the biochemistry of tissues in a noninvasive way. MRS has been widely used for the study of brain tumors, both preoperatively and during follow-up. In this study, we investigated the performance of a range of variants of unsupervised matrix factorization methods of the non-negative matrix underapproximation (NMU) family, namely, sparse NMU, global NMU, and recursive NMU, and compared them with convex non-negative matrix factorization (C-NMF), which has previously shown a good performance on brain tumor diagnostic support problems using MRS data. The purpose of the investigation was 2-fold: first, to ascertain the differences among the sources extracted by these methods; and second, to compare the influence of each method in the diagnostic accuracy of the classification of brain tumors, using them as feature extractors. We discovered that, first, NMU variants found meaningful sources in terms of biological interpretability, but representing parts of the spectrum, in contrast to C-NMF; and second, that NMU methods achieved better classification accuracy than C-NMF for the classification tasks when one class was not meningioma.

Characterizing the key genes of COVID-19 that regulate tumor immune microenvironment and prognosis in hepatocellular carcinoma.

Hepatocellular carcinoma (HCC), a highly heterogeneous malignant tumor associated with a poor prognosis, is a common cause of cancer-related deaths worldwide, with a limited survival benefit for patients despite ongoing therapeutic breakthroughs. Coronavirus disease 2019 (COVID-19), a severe infectious disease caused by severe acute respiratory syndrome coronavirus type 2 (SARS-CoV-2), is a global pandemic and a serious threat to human health. The increased susceptibility to SARS-CoV-2 infection and a poor prognosis in patients with cancer necessitate the exploration of the potential link between the two. No studies have investigated the relationship of COVID-19 genes with the prognosis and tumor development in patients with HCC. We screened prognosis-related COVID-19 genes in HCC, performed molecular typing, developed a stable and reliable COVID-19 genes signature for predicting survival, characterized the immune microenvironment in HCC patients, and explored new molecular therapeutic targets. Datasets of HCC patients, including RNA sequencing data and clinical information, were obtained from The Cancer Genome Atlas (TCGA), International Cancer Genome Consortium (ICGC), and Gene Expression Omnibus (GEO) databases. Prognosis-related COVID-19 genes were identified by univariate Cox analysis. Molecular typing of HCC was performed using the consensus non-negative matrix factorization method (cNMF), followed by the analysis of survival, tumor microenvironment, and pathway enrichment for each subtype. Prognostic signatures were constructed using LASSO-Cox regression models, and receiver operating characteristic (ROC) curves were used to validate the predictive performance of the signature. The same approach was used for the test and external validation sets. Seven software packages were applied to determine the abundance of immune infiltration in HCC patients and investigate its relationship with the risk scores. Gene set enrichment analysis (GSEA) was used to explore the potential mechanisms by which the COVID-19 genes affect hepatocarcinogenesis and prognosis. Three types of machine learning methods were combined to identify the most critical genes in the signature and localize their expression at the single cell level. We identified 53 prognosis-related COVID-19 genes and classified HCC into two molecular subtypes (C1, C2) by using the NMF method. The prognosis of C2 was significantly better than that of C1, and the two subtypes differed remarkably in terms of the tumor immune microenvironment and biological functions. The 17 COVID-19 genes were screened using the LASSO regression method to develop a 17 COVID-19 genes signature, which demonstrated a good predictive performance for 1-, 2- and 3-year OS of patients with HCC. The risk score as an independent prognostic factor for HCC has better predictive accuracy than traditional clinical variables. Patients in the TCGA cohort were categorized by risk score into the high- and low-risk groups, with the high-risk group mainly enriched in the immune modulation-related pathways and the low-risk group mainly enriched in the metabolism-related pathways, suggesting that the COVID-19 genes may affect disease progression and prognosis by regulating the tumor immune microenvironment and metabolism in HCC. NOL10 was identified as the most critical gene in the signature and hypothesized to be a potential therapeutic target for HCC. Objectively, the COVID-19 genes signature developed in this study, as an independent prognostic factor in HCC patients, is closely associated with the prognosis and tumor immune microenvironment of HCC patients and indicates that they may regulate the development of HCC in multiple ways, providing us with new perspectives for understanding the molecular mechanisms of HCC and finding effective therapeutic targets.

Chatbot-Based Book Recommender System Using Singular Value Decomposition

In the era of information overload, finding the right book that matches one's preferences and interests has become a challenging task for users as many online book provider service websites such as Amazon, Goodreads, and Gramedia provide books of various types and choices. Recommender systems can be used in addressing such issues, it works by filtering information that provides predictions and suggests the best product or service to the user. Currently, various book recommender systems have been developed, but the systems do not provide interaction between the user and the system. Therefore, we propose a recommender system built with a conversational approach so that it can interact with natural language. Recommender system built using matrix factorization method with Singular Value Decomposition (SVD) algorithm, SVD is proven to have advantages for handling large datasets, extracting features, reducing noise and dimensionality so as to speed up computation. We performed two types of evaluation on the system. First, we tested the prediction accuracy using Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE) metrics. Second, we use questionnaires to measure user satisfaction levels. The evaluation of the system shows that the results of the prediction accuracy obtain an MAE value of 0.6481 and an RMSE value of 0.8287. Then, the accuracy performance of the system found that 83.2% of users get recommendations according to their interests. The user satisfaction with the whole system is 87.9%. The system built can provide a fairly good recommendation performance, and the chatbot can interact well with users based on the evaluation results obtained.

Computational prediction of muscle synergy using a finite element framework for a musculoskeletal model on lower limb.

Previous studies have demonstrated that the central nervous system activates muscles in module patterns to reduce the complexity needed to control each muscle while producing a movement, which is referred to as muscle synergy. In previous musculoskeletal modeling-based muscle synergy analysis studies, as a result of simplification of the joints, a conventional rigid-body link musculoskeletal model failed to represent the physiological interactions of muscle activation and joint kinematics. However, the interaction between the muscle level and joint level that exists in vivo is an important relationship that influences the biomechanics and neurophysiology of the musculoskeletal system. In the present, a lower limb musculoskeletal model coupling a detailed representation of a joint including complex contact behavior and material representations was used for muscle synergy analysis using a decomposition method of non-negative matrix factorization (NMF). The complexity of the representation of a joint in a musculoskeletal system allows for the investigation of the physiological interactions in vivo on the musculoskeletal system, thereby facilitating the decomposition of the muscle synergy. Results indicated that, the activities of the 20 muscles on the lower limb during the stance phase of gait could be controlled by three muscle synergies, and total variance accounted for by synergies was 86.42%. The characterization of muscle synergy and musculoskeletal biomechanics is consistent with the results, thus explaining the formational mechanism of lower limb motions during gait through the reduction of the dimensions of control issues by muscle synergy and the central nervous system.

Incremental specialized and specialized-generalized matrix factorization models based on adaptive learning rate optimizers

Recommender systems suggest items that are likely to be preferred by a particular user based on historical behavior, actions, and feedback. In real-world applications, data on users and items are continuously generated at a fast pace, such as in e-commerce, social media, digital marketing, and content consumption applications. Since interactions occur over time, these scenarios can be formulated as a data stream where users’ interests are potentially dynamic, i.e., they change over time. Given that changes are expected to occur, one of the current research challenges in streaming recommender systems is that models must adapt their parameters when changes occur to maintain performance. As such changes do not occur for all users and items in the stream at the same time, we consider adapting learning schemes to account for user or item identifiers and model individual parameters. Therefore, we used specialized parameters to adjust the step size for each dataset user or item. More specifically, this study proposes four specialized and specialized-generalized variants of four well-known adaptive learning rate optimizers and shows how they are combined with incremental matrix factorization methods. We tested our proposed optimization strategies on different datasets and showed that one of the proposed specialized variants, that is, InAMSGradUser, improves the RECALL and NDCG rates by up to 11.1 and 7.5 percentage points, respectively, compared to the traditional stochastic gradient descent (SGD) optimizer.

Multi-view clustering via label-embedded regularized NMF with dual-graph constraints

Nonnegative matrix factorization (NMF) methods have achieved remarkable performances in multi-view clustering due to their effectiveness and efficiency. To better obtain a low-dimensional common representation, the limited labels and the geometric structure of the multi-view data should be fully utilized in clustering. In this work, we introduce a novel multi-view learning approach, dubbed label-embedded regularized NMF with dual-graph constraints (LeNMF-DC), for clustering. Our proposed LeNMF-DC approach mainly utilizes matrix factorization to obtain a low-dimensional common representation of the multi-view data, in which the prior knowledge hidden in data can be fully explored. Specifically, we construct three graph regularization terms to preserve the manifold structure in the data, feature and label space, respectively. Moreover, we take advantage of the labels of the labeled samples without additional parameters. In addition, we develop an alternate iterative optimization scheme to solve the model of LeNMF-DC and then show its convergence rate. Compared with traditional multi-view clustering approaches, the labels of unlabeled samples in our proposed LeNMF-DC approach are assigned by the label constraint matrix rather than the clustering algorithm, and thus it avoids performance loss during the clustering. Experimental results on four benchmark datasets manifest that our LeNMF-DC approach can achieve superior performances than several state-of-the-art approaches in multi-view clustering.

Source apportionment of heavy metal(loid)s in sediments of a typical karst mountain drinking-water reservoir and the associated risk assessment based on chemical speciations.

As important place for water storage and supply, drinking-water reservoirs in karst mountain areas play a key role in ensuring human well-being, and its water quality safety has attracted much attention. Source apportionment and ecological risks of heavy metal(loid)s in sediments of drinking-water reservoir are important for water security, public health, and regional water resources management, especially in karst mountain areas where water resources are scarce. To expound the accumulation, potential ecological risks, and sources of heavy metal(loid)s in a drinking-water reservoir in Northwest Guizhou, China, the surface sediments were collected and analyzed based on the combined use of the geo-accumulation index (Igeo), sequential extraction (BCR), ratios of secondary phase and primary phase (RSP), risk assessment code (RAC), modified potential ecological risk index (MRI), as well as the positive matrix factorization methods. The results indicated that the accumulation of Cd in sediments was obvious, with approximately 61.9% of the samples showing moderate to high accumulation levels, followed by Pb, Cu, Ni, and Zn, whereas the As and Cr were at low levels. A large proportion of BCR-extracted acid extractable and reducible fraction were found in Cd (72.5%) and Pb (40.3%), suggesting high bioavailability. The combined results of RSP, RAC, and MRI showed that Cd was the major pollutant in sediments with high potential ecological risk, while the risk of other elements was low. Source apportionment results of heavy metal(loid)s indicated that Cd (75.76%) and Zn (23.1%) mainly originated from agricultural activities; As (69.82%), Cr (50.05%), Cu (33.47%), and Ni (31.87%) were associated with domestic sources related to residents' lives; Cu (52.36%), Ni (44.57%), Cr (34.33%), As (26.51%), Pb (24.77%), and Zn (23.80%) primarily came from natural geological sources; and Pb (47.56%), Zn (22.46%) and Cr (13.92%) might be introduced by mixed sources of traffic and domestic. The contribution ratios of the four sources were 18.41%, 36.67%, 29.48%, and 15.44%, respectively. Overall, priority control factors for pollution in relation to agricultural sources included Cd, while domestic sources are primarily associated with As. It is crucial to place special emphasis on the impacts of human activities when formulating pollution prevention and control measures. The results of this study can provide valuable reference and insights for water resources management and pollution prevention and control strategies in karst mountainous areas.

FUNCTIONAL SYNERGY ENSURES A TRAMPOLINE JUMP STOPPING

The paper considers the structure of intermuscular synergetic interaction that ensures the athlete’s body stopping on the trampoline after a jump. We compared the spatio-temporal characteristics of muscle synergies extracted from the skeletal muscles electroactivity amplitude and frequency of biopotentials data. The objective of the study was to find out whether the extracted kinematic modules represent the central mechanisms for the movement structure controlling as well as to determine the variables which should be stabilized by muscle synergies activity. The extraction of synergies was carried out using the matrix factorization method. It has been established that trampoline jump stopping can be performed using common patterns of muscle synergies spatio-temporal activation. The synergistic effects obtained using different approaches of instrumental assessment of skeletal muscle electroactivity probably reflect different control mechanisms implemented at different levels of the central nervous system. Muscle synergies are aimed at the stabilizing of the certain anthropometric points movement, as well as body segments, combined into kinematic modules. The structure of the kinematic modules themselves indicates the effective organization of intermuscular interaction, indirectly reflecting the central control mechanisms of complex multi-joint movement.