Matrix Factorization Technique Research Articles

Homology and heterogeneity of soil trace elements of coal power production bases in arid and semi-arid areas of Northwest China.

Coal power activities could cause regional fluctuations of trace elements, but the distribution information of these trace elements in arid and semi-arid areas is insufficient. In this study, the soil trace elements (As, B, Be, Cd, Co, Cr, Cu, Fe, Ga, Ge, Mn, Mo, Ni, Pb, Sb, Sn, Sr, Ti, Tl, and Zn) of Ningdong Coal Power Production Base in China were monitored. Results showed that the concentrations of B, Tl, Mn, Pb, Cr, K, Cu, and Co exceeded background values. The maximum risk index reached 265.66, while the trace elements posed a cancer risk to children. Combining correlation analyses (CA), principal component analysis (PCA), and positive matrix factorization (PMF) techniques, it indicated that trace elements were mainly coming from coal combustion (34.15%), livestock farming (17.44%), traffic emissions (12.42%), and natural factors (35.99%). This study reveals the sources and potential ecological risks of soil trace elements in the Ningdong Coal and Power Production Base. It provides a scientific basis for developing targeted environmental management measures and reducing human health risks.

Uncovering sources, distribution, and seasonal patterns of trace element deposition: the elemental puzzle of the western Himalayas.

The transport and deposition of atmospheric pollutants in the Himalayas have a adverse impact on the climate, cryosphere, ecosystem, and monsoon patterns. Unfortunately, there is a insufficiency of data on trace element concentrations and behaviors in the high-altitude Himalayan region, leading to limited research in this area. This study presents a comprehensive and detailed comprehension of trace element deposition, its spatial distribution, seasonal variations, and anthropogenic signals in the high-altitude Kashmir region of the Western Himalayas. Our investigation involved the analysis of 10 trace elements (Al, Cr, Mn, Fe, Co, Ni, Cu, Zn, Cd, and Pb) in glacier ice, snow pits, surface snow, and rainwater collected at various sites including Kolahoi, Thajwas, Pahalgam (Greater Himalayan ranges), and Kongdori and Shopian (Pir Panjal Ranges) during 2021.The study reveals distinct ranges of concentrations for the trace elements at different sampling sites. Our analysis of trace element concentration depth profiles in snow pits reveals seasonal fluctuations during the deposition year. The highest concentrations were found in the autumn(below 20cm) and summer (top layer), compared to the winter concentration (10-20cm). The high enrichment factors (EFs) suggest the severity of human-induced trace metal deposition in the western Himalayan region, relative to surrounding regions. Surprisingly, the concentrations and EFs of trace elements showed seasonal contradictions, with lower concentration values and higher EFs during the non-monsoon season and vice versa. A source apportionment analysis using the positive matrix factorization (PMF) technique identified five sources of trace element deposition in the region, including crustal sources (32.33%), coal combustion (15.62%), biomass burning (17.63%), traffic emission (18.8%), and industrial sources (15.6%). Additionally, the study incorporated backward trajectories coupled with δ18O using the NOAA HYSPLIT model to estimate moisture sources in the region, which suggests atmospheric pollutants predominately deposited from the large-scale atmospheric circulation from westerlies (75%) during non-monsoon season. These findings underscore the urgent need for enhanced monitoring and research efforts in the future.

Multi-label feature selection via similarity constraints with non-negative matrix factorization

Feature selection plays a key role in preprocessing, effectively addressing the curse of dimensionality in multi-label learning. While current approaches commonly utilize feature or label similarity to construct the weight matrix, typically through manifold learning regularization, there has been a dearth of progress in developing similarity-constrained regularization terms for multi-label feature selection. To address this gap, this paper conducts a comprehensive investigation and proposes a novel similarity constraint leveraging non-negative matrix factorization techniques. Subsequently, a new algorithm is introduced termed Multi-label Feature Selection via Similarity Constraints with Non-negative Matrix Factorization (SCNMF). Initially, the Gaussian similarity matrix among features is computed and factorized into a weight matrix using non-negative matrix factorization. Subsequently, the Cosine distance matrix among labels is computed to constrain the weight matrix. Finally, an objective function is formulated based on the aforementioned constraint mechanisms and iteratively optimized. Extensive experiments conducted across more than 10 multi-label datasets demonstrate the superior performance of our proposed approach. The source code is accessible at the URL: https://github.com/BIGOatMNNU/SCNMF.

Identification of key nodes in complex networks by using a joint technique of nonnegative matrix factorization and regularization

Identifying key nodes in complex networks is essential to deeply understand and fully utilize the properties and functions of complex systems. Currently, existing traditional methods perform critical nodes identification by manually selecting important attribute features of nodes, but there are limitations in this approach. Manual selection of attribute features may overlook non-obvious features related to nodes criticality and correlations between attribute features. To compensate for the shortcomings of traditional methods, a Joint Technique for identifying critical nodes, called JTNMFR, is presented based on Nonnegative Matrix Factorization and Regularization. Factorization of weighted adjacency matrix is performed to obtain potential attribute features of nodes, and communicability network matrix and similarity matrix are introduced as regularization terms to control sparsity of the decomposition results. Ultimately, the importance of nodes is assessed by constructing an objective function that integrates these two aspects and utilizing alternative iteration to obtain the attribute matrix. To validate the accuracy and reliability of JTNMFR, we compare it with nine other identification approaches on eight real networks. Experimental results show that JTNMFR not only significantly outperforms the other algorithms in terms of accuracy of node importance, monotonicity, and node spreading ability but also provides a more accurate means of assessing node importance.

An Evaluation of Machine Learning Algorithms Used for Recommender Systems in Streaming Services

With the exponential growth of streaming services, the demand for effective recommender systems has become paramount. Recommender systems, powered by machine learning algorithms, play a critical role in analyzing user behavior and preferences to deliver personalized content recommendations. However, the abundance of available algorithms poses a challenge for streaming platforms in determining the most suitable approach for their recommender systems. This research paper presents an evaluation of various machine learning algorithms used in recommender systems for streaming services. Through a comparative analysis of collaborative filtering, content-based filtering, matrix factorization techniques, deep learning algorithms, and emerging approaches such as reinforcement learning and hybrid models, this study aims to provide insights into the strengths, limitations, and performance of each approach. By assessing the effectiveness of these algorithms, exploring their applications, and discussing recent advancements, this research contributes to the advancement of recommendation technology in streaming services, ultimately enhancing user satisfaction and engagement.

Integrating Multi-omics Data for Alzheimer's Disease to Explore Its Biomarkers Via the Hypergraph-Regularized Joint Deep Semi-Non-Negative Matrix Factorization Algorithm.

Alzheimer's disease (AD) is a progressive and irreversible neurodegenerative disorder. Its etiology may be associated with genetic, environmental, and lifestyle factors. With the advancement of technology, the integration of genomics, transcriptomics, and imaging data related to AD allows simultaneous exploration of molecular information at different levels and their interaction within the organism. This paper proposes a hypergraph-regularized joint deep semi-non-negative matrix factorization (HR-JDSNMF) algorithm to integrate positron emission tomography (PET), single-nucleotide polymorphism (SNP), and gene expression data for AD. The method employs matrix factorization techniques to nonlinearly decompose the original data at multiple layers, extracting deep features from different omics data, and utilizes hypergraph mining to uncover high-order correlations among the three types of data. Experimental results demonstrate that this approach outperforms several matrix factorization-based algorithms and effectively identifies multi-omics biomarkers for AD. Additionally, single-cell RNA sequencing (scRNA-seq) data for AD were collected, and genes within significant modules were used to categorize different types of cell clusters into high and low-risk cell groups. Finally, the study extensively explores the differences in differentiation and communication between these two cell types. The multi-omics biomarkers unearthed in this study can serve as valuable references for the clinical diagnosis and drug target discovery for AD. The realization of the algorithm in this paper code is available at https://github.com/ShubingKong/HR-JDSNMF .

High Performance NMF based Intrusion Detection System for Big Data IoT Traffic

With the emergence of smart devices and the Internet of Things (IoT), millions of users connected to the network produce massive network traffic datasets. These vast datasets of network traffic, Big Data are challenging to store, deal with and analyse using a single computer. In this paper we developed parallel implementation using a High Performance Computer (HPC) for the Non-Negative Matrix Factorization technique as an engine for an Intrusion Detection System (HPC-NMF-IDS). The large IoT traffic datasets of order of millions samples are distributed evenly on all the computing cores for both storage and speedup purpose. The distribution of computing tasks involved in the Matrix Factorization takes into account the reduction of the communication cost between the computing cores. The experiments we conducted on the proposed HPC-IDS-NMF give better results than the traditional ML-based intrusion detection systems. We could train the HPC model with datasets of one million samples in only 31 seconds instead of the 40 minutes using one processor), that is a speed up of 87 times. Moreover, we have got an excellent detection accuracy rate of 98% for KDD dataset.

Dynamic matrix factorization-based collaborative filtering in movie recommendation services

Movies are a primary source of entertainment, but finding specific content can be challenging given the exponentially increasing number of movies produced each year. Recommendation systems are extremely useful for solving this problem. While various approaches exist, Collaborative Filtering (CF) is the most straightforward. CF leverages user input and historical preferences to determine user similarity and suggest movies. Matrix Factorization (MF) is one of the most popular Collaborative Filtering (CF) techniques. It maps users and items into a joint latent space, using a vector of latent features to represent each user or item. However, traditional MF techniques are static, while user cognition and product variety are constantly evolving. As a result, traditional MF approaches struggle to accommodate the dynamic nature of user-item interactions. To address this challenge, we propose a Dynamic Matrix Factorization CF model for movie recommendation systems (DMF-CF) that considers the dynamic changes in user interactions. To validate our approach, we conducted evaluations using the standard MovieLens dataset and compared it to state-of-the-art models. Our preliminary findings highlight the substantial benefits of DMF-CF, which outperforms recent models on the MovieLens-100K and MovieLens-1M datasets in terms of Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) metrics.

Comprehensive analyses of m1A regulator-mediated modification patterns determining prognosis in lower-grade glioma (running title: m1A in LGG)

N1-methyladenosine (m1A) modification is a crucial post-transcriptional regulatory mechanism of messenger RNA (mRNA) in living organisms. Few studies have focused on analysis of m1A regulators in lower-grade gliomas (LGG). We employed the Nonnegative Matrix Factorization (NMF) technique on The Cancer Genome Atlas (TCGA) dataset to categorize LGG patients into 2 groups. These groups exhibited substantial disparities in terms of both overall survival (OS) and levels of infiltrating immune cells. We collected the significantly differentially expressed immune-related genes between the 2 clusters, and performed LASSO regression analysis to obtain m1AScores, and established an m1A-related immune-related gene signature (m1A-RIGS). Next, we categorized all patients with LGG into high- and low-risk subgroups, predictive significance of m1AScore was confirmed by conducting univariate/multivariate Cox regression analyses. Additionally, we confirmed variations in immune-related cells and ssGSEA and among the high-/low-risk subcategories in the TCGA dataset. Finally, our study characterized the effects of MSR1 and BIRC5 on LGG cells utilizing Edu assay and flow cytometry to explore the effects of modulation of these genes on glioma. The results of this study suggested that m1A-RIGS may be an excellent prognostic indicator for patients with LGG, and could also promote development of novel immune-based treatment strategies for LGG. Additionally, BIRC5 and MSR1 may be potential therapeutic targets for LGG.

Parallel Fractional Stochastic Gradient Descent With Adaptive Learning for Recommender Systems

The structural change toward the digital transformation of online sales elevates the importance of parallel processing techniques in recommender systems, particularly in the pandemic and post-pandemic era. Matrix factorization (MF) is a popular and scalable approach in collaborative filtering (CF) to predict user preferences in recommender systems. Researchers apply Stochastic Gradient Descent (SGD) as one of the most famous optimization techniques for MF. Paralleling SGD methods help address Big Data challenges due to the wide range of products and the sparsity in user ratings. However, these methods’ convergence rate and accuracy are affected by the dependency between the user and item latent factors, specifically in large-scale problems. Besides, the performance is sensitive to the applied learning rates. This paper proposes a new parallel method to remove dependencies and boost speed-up by using fractional calculus to improve accuracy and convergence rate. We also apply adaptive learning rates to enhance the performance of our proposed method. The proposed method is based on Compute Unified Device Architecture (CUDA) platform. We evaluate the performance of our proposed method using real-world data and compare the results with the close baselines. The results show that our method can obtain high accuracy and convergence rate in addition to high parallelism.

The Impact of Different Self-Selected Walking Speeds on Muscle Synergies in Transfemoral Amputees during Transient-State Gait

Facing above-knee amputation poses a significant hurdle due to its profound impact on walking ability. To overcome this challenge, a complex adaptation strategy is necessary at the neuromuscular level to facilitate safe movement with a prosthesis. Prior research conducted on lower-limb amputees has shown a comparable amount of intricacy exhibited by the neurological system, regardless of the level of amputation and state of walking. This research investigated the differences in muscle synergies among individuals with unilateral transfemoral amputations during walking at three different speeds of transient-state gait. Surface electromyography was recorded from eleven male transfemoral amputees’ intact limbs (TFA), and the concatenated non-negative matrix factorization technique was used to identify muscle synergy components, synergy vectors (S), and activation coefficient profiles (C). Results showed varying levels of correlation across paired-speed comparisons in TFA, categorized as poor (S1), moderate (S3 and S4), and strong (S2). Statistically significant differences were observed in all activation coefficients except C3, particularly during the stance phase. This study can assist therapists in understanding muscle coordination in TFA during unsteady gait, contributing to rehabilitation programs for balance and mobility improvement, and designing myoelectric prosthetic systems to enhance their responsiveness to trips or falls.

Joint inference of clonal structure using single-cell genome and transcriptome sequencing data.

Latest advancements in the high-throughput single-cell genome (scDNA) and transcriptome (scRNA) sequencing technologies enabled cell-resolved investigation of tissue clones. However, it remains challenging to cluster and couple single cells for heterogeneous scRNA and scDNA data generated from the same specimen. In this study, we present a computational framework called CCNMF, which employs a novel Coupled-Clone Non-negative Matrix Factorization technique to jointly infer clonal structure for matched scDNA and scRNA data. CCNMF couples multi-omics single cells by linking copy number and gene expression profiles through their general concordance. It successfully resolved the underlying coexisting clones with high correlations between the clonal genome and transcriptome from the same specimen. We validated that CCNMF can achieve high accuracy and robustness using both simulated benchmarks and real-world applications, including an ovarian cancer cell lines mixture, a gastric cancer cell line, and a primary gastric cancer. In summary, CCNMF provides a powerful tool for integrating multi-omics single-cell data, enabling simultaneous resolution of genomic and transcriptomic clonal architecture. This computational framework facilitates the understanding of how cellular gene expression changes in conjunction with clonal genome alternations, shedding light on the cellular genomic difference of subclones that contributes to tumor evolution.

Revisiting Probabilistic Latent Semantic Analysis: Extensions, Challenges and Insights

This manuscript provides a comprehensive exploration of Probabilistic latent semantic analysis (PLSA), highlighting its strengths, drawbacks, and challenges. The PLSA, originally a tool for information retrieval, provides a probabilistic sense for a table of co-occurrences as a mixture of multinomial distributions spanned over a latent class variable and adjusted with the expectation–maximization algorithm. The distributional assumptions and the iterative nature lead to a rigid model, dividing enthusiasts and detractors. Those drawbacks have led to several reformulations: the extension of the method to normal data distributions and a non-parametric formulation obtained with the help of Non-negative matrix factorization (NMF) techniques. Furthermore, the combination of theoretical studies and programming techniques alleviates the computational problem, thus making the potential of the method explicit: its relation with the Singular value decomposition (SVD), which means that PLSA can be used to satisfactorily support other techniques, such as the construction of Fisher kernels, the probabilistic interpretation of Principal component analysis (PCA), Transfer learning (TL), and the training of neural networks, among others. We also present open questions as a practical and theoretical research window.

An autoencoder-based deep learning model for solving the sparsity issues of Multi-Criteria Recommender System

In recent times, recommender systems have acquired significant popularity as a solution to the issue of information overload. These systems offer personalised recommendations to users. The superiority of multi-criteria recommender systems over their single-criterion counterparts has been demonstrated, as the former are able to provide more precise recommendations by taking into account multiple dimensions of user preferences when rating items. The prevalent recommendation technique, matrix factorization of collaborative filtering, is hindered by the data sparsity problem of the user-item matrix. On the other hand, it is noteworthy that deep learning techniques have demonstrated significant potential in various research domains, including but not limited to image processing, pattern recognition, computer vision, and natural language processing. In recent times, there has been a surge in the utilisation of deep learning techniques in recommender systems, yielding promising outcomes. This study presents a novel approach to multi-criteria recommender systems through the utilisation of deep learning algorithms to mitigate the data sparsity issue. Specifically, deep autoencoders are utilised to uncover complex, non-linear, and latent relationships between users' multi-criteria preferences followed by matrix factorization technique, ultimately leading to more precise recommendations. The proposed model is evaluated by conducting the experiments on the multi-criteria dataset of Yahoo! Movies. According to the outcomes, the proposed approach outperforms the state of the art recommendation methods by generating more accurate and personalized recommendations. Also, it reduces the data sparsity up to 11% from the multi-criteria dataset.

Matrix Factorization For Augmented Deep Learning Model Generation

This paper aims to address two significant challenges of Deep Learning(DL) model generation, high computational cost involved during the training phase and data interpretability from high dimensional data. The computational cost is curbed using centralized as well as distributed matrix factorization technique known as CUR decomposition. CUR decomposition has the advantage of reducing the dimensions of the dataset without data transformation and minimal information loss. Though Singular Value De-composition(SVD) is the best matrix decomposition technique with least reconstruction error, it transforms the data and hence the original data cannot be interpreted from the decomposed matrices while applying DL technique. So CUR decomposition is leveraged to reduce the number of features in high-dimensional data while preserving the essential information. Extensive experimental analysis is conducted to evaluate and compare the performance of CUR and SVD techniques based on reconstruction error and time complexity in centralized as well as distributed setting. The results exhibit that CUR outperforms SVD in terms of computational efficiency, especially in a distributed setting where the decomposition time for CUR was a fraction compared to SVD. At the same time DL models generated from this reduced dataset exhibit comparable accuracy with the original high dimensional dataset as well as reduced dataset obtained through SVD. This work also enhances the accessibility of the CUR algorithm to users, for which an application is developed that enables users to execute the algorithm on any dataset. The user-friendly interface of the application facilitates the upload of datasets, configuration of desired decomposition rank, and execution of the algorithm with a single click.

Review Polarity-Wise Recommender.

The de facto review-involved recommender systems, using review information to enhance recommendation, have received increasing interest over the past years. Thereinto, one advanced branch is to extract salient aspects from textual reviews (i.e., the item attributes that users express) and combine them with the matrix factorization (MF) technique. However, the existing approaches all ignore the fact that semantically different reviews often include opposite aspect information. In particular, positive reviews usually express aspects that users prefer, while the negative ones describe aspects that users dislike. As a result, it may mislead the recommender systems into making incorrect decisions pertaining to user preference modeling. Toward this end, in this article, we present a review polarity-wise recommender model, dubbed as RPR, to discriminately treat reviews with different polarities. To be specific, in this model, positive and negative reviews are separately gathered and used to model the user-preferred and user-rejected aspects, respectively. Besides, to overcome the imbalance of semantically different reviews, we further develop an aspect-aware importance weighting strategy to align the aspect importance for these two kinds of reviews. Extensive experiments conducted on eight benchmark datasets have demonstrated the superiority of our model when compared with several state-of-the-art review-involved baselines. Moreover, our method can provide certain explanations to real-world rating prediction scenarios.

Latent variable modeling of gamma-ray background in repeated measurements

We propose a novel approach for background subtraction in repeated gamma-ray spectrometric measurements. This entirely data-driven method eliminates the need for Monte Carlo detector simulation. To accomplish this, we utilized the framework of Latent Variable Modeling, incorporating various matrix factorization techniques and artificial neural networks. Subsequently, we applied this method to estimate radionuclide activity through spectrum unmixing. Significant improvements in sensitivity, surpassing traditional methods, were observed for the test case scenario of aerosol filter measurements.

Interpretable machine learning model using Extreme Gradient Boosting with Nonnegative Matrix Factorization improves the accuracy of arrhythmic risk prediction in Brugada Syndrome

Abstract Background Both depolarization and repolarization abnormalities contribute to ventricular arrhythmogenesis in Brugada syndrome (BrS). In this study, we tested the hypothesis that incorporating latent features extracted by various nonnegative matrix factorization (NML) techniques into an interpretable machine learning (IML) prediction model can outperform IML models without latent variables and logistic regression model. Methods This study was based on a published anonymised dataset of BrS patients from the Hong Kong, China. XGBoost was selected as the IML model, with and without incorporating latent features using 11 different NMF techniques: Bayesian nonnegative matrix factorization (BNMF), Iterated Conditional Modes nonnegative matrix factorization (ICM), Fisher Nonnegative Matrix Factorization for learning Local features (LFNMF), Alternating Nonnegative Least Squares Matrix Factorization Using Projected Gradient (bound constrained optimization) method for each subproblem (LSNMF), Non-smooth Nonnegative Matrix Factorization (NSNMF), Probabilistic Nonnegative Matrix Factorization (PMF), Probabilistic Sparse Matrix Factorization (PSMF), Sparse Nonnegative Matrix Factorization (SNMF) based on alternating nonnegativity constrained least squares, Sparse Network-Regularized Multiple Nonnegative Matrix Factorization (SNMNMF), Penalized Matrix Factorization for Constrained Clustering (PMFCC) and Separable Nonnegative Matrix Factorization (SepNMF). Results A total of 548 patients were included (7.3% females, age at diagnosis: 51.0 [38.0-61.0] years old. Of these, 66 suffered from spontaneous ventricular tachyarrhythmias over 84±55 months follow-up. The baseline model using multivariable logistic regression achieved an area under the curve (AUC) of 0.78 [0.72-0.85], which was improved to 0.88 [0.83-0.93] for the IML model without NMF. The AUC was further increased by incorporating additional latent variables extracted using NSNMF (0.95 [0.92-0.98]) and PMFCC (0.94 [0.88-1.00]). Conclusion Incorporation of latent variables by different NMF techniques into an IML prediction model significantly improved the accuracy of risk prediction in BrS.

Robust Mesh Representation Learning via Efficient Local Structure-Aware Anisotropic Convolution.

Mesh is a type of data structure commonly used for 3-D shapes. Representation learning for 3-D meshes is essential in many computer vision and graphics applications. The recent success of convolutional neural networks (CNNs) for structured data (e.g., images) suggests the value of adapting insights from CNN for 3-D shapes. However, 3-D shape data are irregular since each node's neighbors are unordered. Various graph neural networks for 3-D shapes have been developed with isotropic filters or predefined local coordinate systems to overcome the node inconsistency on graphs. However, isotropic filters or predefined local coordinate systems limit the representation power. In this article, we propose a local structure-aware anisotropic convolutional operation (LSA-Conv) that learns adaptive weighting matrices for each template's node according to its neighboring structure and performs shared anisotropic filters. In fact, the learnable weighting matrix is similar to the attention matrix in the random synthesizer-a new Transformer model for natural language processing (NLP). Since the learnable weighting matrices require large amounts of parameters for high-resolution 3-D shapes, we introduce a matrix factorization technique to notably reduce the parameter size, denoted as LSA-small. Furthermore, a residual connection with a linear transformation is introduced to improve the performance of our LSA-Conv. Comprehensive experiments demonstrate that our model produces significant improvement in 3-D shape reconstruction compared to state-of-the-art methods.

A Recommendation Engine Model for Giant Social Media Platforms using a Probabilistic Approach

Existing recommender system algorithms often find it difficult to interpret and, as a result, to extract meaningful recommendations from social media. Because of this, there is a growing demand for more powerful algorithms that are able to extract information from low-dimensional spaces. One such approach would be the cutting-edge matrix factorization technique. Facebook is one of the most widely used social networking platforms. It has more than one billion monthly active users who engage with each other on the platform by sharing status updates, images, events, and other types of content. Facebook's mission includes fostering stronger connections between individuals, and to that end, the platform employs techniques from recommender systems in an effort to better comprehend the actions and patterns of its users, after which it suggests forming new connections with other users. However, relatively little study has been done in this area to investigate the low-dimensional spaces included within the black box system by employing methods such as matrix factorization. Using a probabilistic matrix factorization approach, the interactions that users have with the posts of other users, such as liking, commenting, and other similar activities, were utilized in an effort to generate a list of potential friends that the user who is the focus of this work may not yet be familiar with. The proposed model performed better in terms of suggestion accuracy in comparison to the original matrix factorization, which resulted in the creation of a recommendation list that contained more correct information.