Matrix Factorization Method Research Articles

Pollution levels, sources and risk assessment of polycyclic aromatic hydrocarbons in farmland soil and crops near Urumqi Industrial Park, Xinjiang, China

This study investigated the concentration, source, and risk assessment of polycyclic aromatic hydrocarbons (PAHs) in farmland soil and crops around the Urumqi Industrial Park in Xinjiang, China. The total concentration of 16 different PAHs in the soil (Quantity: 51) and crop (Species: onion, cabbage, coriander, beans, spinach, celery, lettuce, and sunflower) samples ranged between 2.32 and 225.11 ng/g and between 132.44 and 504.03 ng/g respectively, with average values of 39.29 ± 2.39 ng/g for the soil samples and 295.81 ± 105.00 ng/g for the crop samples. The source analysis of PAHs was performed using the positive matrix factorization and ratio method and identified the high-temperature combustion of fossil fuels, the volatilization of petroleum, coke oven emissions, and traffic emissions as main sources of PAHs in soil. The ecological risk posed by the PAHs detected in the soil samples was within a safe range. The incremental lifetime cancer risk (ILCR) value quantifies resulting from human exposure to soil containing PAH is at a safe level except for the potential carcinogenic risk to children due to ingestion exposure (ILCRs > 1.0 × 10–6). The ILCR posed by crops exceed 1.0 × 10–6 and the risk from sunflower crop was the highest. The highest ILCR values for each crop high exposed for the adult female population. These results indicate that the farmland soil and crops near the Urumqi Industrial Park have been contaminated by PAHs and require urgent remediation to minimize adverse effects of exposure to carcinogens.

Difference in muscle synergies of the butterfly technique with and without swimmer’s shoulder

This study aimed to investigate whether muscle synergy differs between swimmers with and without swimmer's shoulder in the butterfly technique. Muscle synergies, which can assess muscle coordination, were analyzed using surface electromyography. Twenty elite swimmers were included in this study (swimmer's shoulder: n = 8; control: n = 12). The motions involved in executing the butterfly technique were classified into the early pull-through, late pull-through, and recovery phases. Muscle synergy data analyzed using the nonnegative matrix factorization method were compared between the two groups.The swimming velocities were 1.66 ± 0.09 m・s −1 and 1.69 ± 0.06 m・s −1 for the control and swimmer's shoulder groups, respectively. Four muscle synergies in both groups were identified: synergy #1, which was involved in the early pull; synergy #2, involved in the late pull; synergy #3, involved in the early recovery; and synergy #4, involved in pre- and posthand entry. Compared to the control group, the swimmer's shoulder group had a small contribution from the pectoralis major (p = 0.032) and a high contribution from the rectus femoris during the early pull phase (p = 0.036). In the late pull phase, the contribution of the lower trapezius muscle in the swimmer's shoulder group was low (p = 0.033), while the contribution of the upper trapezius muscle in the pre- and postentry phases was high (p = 0.032). In the rehabilitation of athletes with swimmer's shoulder, it is therefore important to introduce targeted muscle rehabilitation in each phase.

An attention-based deep learning method for solving the cold-start and sparsity issues of recommender systems

Matrix Factorization is a successful approach for generating an effective recommender system. However, most existing matrix factorization methods suffer from the sparsity and cold-start issues of the user-item matrix as the primary information source of recommender systems. Besides, they are not much scalable to apply to large real-world applications. A main idea to overcome the cold-start and sparsity issues is to use additional information sources such as user/item profiles or user reviews on items. In this paper, a novel Attention-based Deep Learning Recommender System, so-called ADLRS, is proposed to employ the information sources in the matrix factorization method framework. The proposed method uses a language model to represent contextual information such that important features are effectively embedded. Moreover, a deep autoencoder reduces the dimensionality of item vectors embedded by the language model. Then, these vectors are used as regularization terms in the matrix factorization framework to form an objective function. Then, an iterative algorithm is designed to solve the objective function and provide a method prediction of unknown rating values. Experimental results show that the proposed method achieves superior performance compared to other state-of-the-art ones in most cases. Moreover, the improvement rate for sparse datasets and cold items proves that the proposed method effectively deals with sparsity, cold start and scalability problems.

Topic Modelling Using Non-Negative Matrix Factorization (NMF) for Telkom University Entry Selection from Instagram Comments

The development of information technology is increasingly rapid, such as social media, which has much influence. Social media is a place or media used to express and express various opinions on a topic. One example is Instagram. Instagram is a social media platform with many features, such as posting photos, videos, comments, likes, and others. The comments feature that Instagram has contained much public opinion that can be used as data. Nothing but the post on the SMB Telkom University Instagram account about the entrance to the university. In posts about the entrance to Telkom university, many Instagram users comment on the post. This can be convenient for the marketing team to get topics or discussions that most followers need from Telkom University's Instagram account. Therefore, a topic modelling of Instagram users' perceptions of comments posted on the entrance to Telkom university was carried out using the Nonnegative Matrix Factorization (NMF) method. After doing several research scenarios, the best coherent value was obtained with a coherent value of 0.60628 and the best 4 topics.

Pseudo-Label Guided Collective Matrix Factorization for Multiview Clustering.

Multiview clustering has aroused increasing attention in recent years since real-world data are always comprised of multiple features or views. Despite the existing clustering methods having achieved promising performance, there still remain some challenges to be solved: 1) most existing methods are unscalable to large-scale datasets due to the high computational burden of eigendecomposition or graph construction and 2) most methods learn latent representations and cluster structures separately. Such a two-step learning scheme neglects the correlation between the two learning stages and may obtain a suboptimal clustering result. To address these challenges, a pseudo-label guided collective matrix factorization (PLCMF) method that jointly learns latent representations and cluster structures is proposed in this article. The proposed PLCMF first performs clustering on each view separately to obtain pseudo-labels that reflect the intraview similarities of each view. Then, it adds a pseudo-label constraint on collective matrix factorization to learn unified latent representations, which preserve the intraview and interview similarities simultaneously. Finally, it intuitively incorporates latent representation learning and cluster structure learning into a joint framework to directly obtain clustering results. Besides, the weight of each view is learned adaptively according to data distribution in the joint framework. In particular, the joint learning problem can be solved with an efficient iterative updating method with linear complexity. Extensive experiments on six benchmark datasets indicate the superiority of the proposed method over state-of-the-art multiview clustering methods in both clustering accuracy and computational efficiency.

Recommendation system using a deep learning and graph analysis approach

AbstractWhen a user connects to the Internet to fulfill his needs, he often encounters a huge amount of related information. Recommender systems are the techniques for massively filtering information and offering the items that users find them satisfying and interesting. The advances in machine learning methods, especially deep learning, have led to great achievements in recommender systems, although these systems still suffer from challenges such as cold‐start and sparsity problems. To solve these problems, context information such as user communication network is usually used. In this article, we have proposed a novel recommendation method based on matrix factorization and graph analysis methods, namely Louvain for community detection and HITS for finding the most important node within the trust network. In addition, we leverage deep autoencoders to initialize users and items latent factors, and the Node2vec deep embedding method gathers users' latent factors from the user trust graph. The proposed method is implemented on Ciao and Epinions standard datasets. The experimental results and comparisons demonstrate that the proposed approach is superior to the existing state‐of‐the‐art recommendation methods. Our approach outperforms other comparative methods and achieves great improvements, that is, 15.56% RMSE improvement for Epinions and 18.41% RMSE improvement for Ciao.

Binary multi-modal matrix factorization for fast item cold-start recommendation

Hashing technology can support large-scale recommendation very effectively due to its advantages of low storage cost and high recommendation efficiency. However, existing hashing-based recommendation methods often suffer from item cold-start problem. This is because they simply consider the user-item interaction and the single content information of the items, but the full interaction history is not always available and the single auxiliary information may be missing. To solve this issue, in this paper we propose a Binary Multi-modal Matrix Factorization (BMMF) method. First, we propose an efficient consensus multi-modal mapping to transform the heterogeneous multi-modal features to the unified factors by exploiting the complementarity of multiple modalities. Then, binary matrix factorization is simultaneously performed on the multi-modal features of the items and past user preferences to learn the compact binary codes of the users/items in a common Hamming space. In addition, inspired by the observation that similar instances often have similar binary codes within a short Hamming distance, we formulate a semantic structure regularization term to preserve the similarities of the items during the binary embedding process. Finally, we develop an effective Discrete Coordinate Descent (DCD) approach to tackle the formulated discrete hash optimization problem directly. Experiments on three publicly available real-world datasets demonstrate the superiority of the proposed method against the state-of-the-art methods. Our source codes and testing datasets are available athttps://github.com/pcm1217/BMMF.

MATRIX FACTORIZATION, DECOMPOSITION AND SPLITTING METHODS AND ITS APPLICATIONS IN PHYSICAL PROBLEMS

Matrix factorization is the process that transforms a matrix into the product of some constituent matrices. This is comparable to factoring a number into the product of several numbers. Matrix splitting methods are similar to matrix factorization process which transforms a matrix into the sum of some basis matrices. In this short review article, we address the different types of matrix factorization and matrix splitting methods as well as their applications in the physical problems rather than exhibiting their computational procedure. Some matrix structural facts are shown to exhibit the fundamental pattern of different matrix decompositions.

An effective short-text topic modelling with neighbourhood assistance-driven NMF in Twitter.

Social media such as Twitter connect billions of people by allowing them to exchange their thoughts via short-text communication. Topic modelling is a widely used technique for analysing short texts. Discovering topic clusters in short-text collections faces issues with distance-based, density-based and dimensionality reduction-based methods due to their higher dimensionality and short length which results in extremely sparse text representation matrices. We propose the ‘neighbourhood-based assistance’-driven non-negative matrix factorization (NMF) method to handle high-dimensional sparse short-text representation with lower-dimensional projection effectively. We utilized NMF that aligned with the natural non-negativity of text data coupled with the symmetric document affinity information to identify topic distribution in the short text. Neighbourhood information within documents is captured using Jaccard similarity to assist information loss, resulting in higher-to-lower-dimensional projection. Experimental results with Twitter data sets show that the proposed approach is able to attain high accuracy compared to state-of-the-art methods quantitatively, while qualitative analysis with case studies validates the ability of the proposed approach in generating meaningful topic clusters.

Matrix factorization with denoising autoencoders for prediction of drug-target interactions.

Drug-target interaction is crucial in the discovery of new drugs. Computational methods can be used to identify new drug-target interactions at low costs and with reasonable accuracy. Recent studies pay more attention to machine-learning methods, ranging from matrix factorization to deep learning, in the DTI prediction. Since the interaction matrix is often extremely sparse, DTI prediction performance is significantly decreased with matrix factorization-based methods. Therefore, some matrix factorization methods utilize side information to address both the sparsity issue of the interaction matrix and the cold-start issue. By combining matrix factorization and autoencoders, we propose a hybrid DTI prediction model that simultaneously learn the hidden factors of drugs and targets from their side information and interaction matrix. The proposed method is composed of two steps: the pre-processing of the interaction matrix, and the hybrid model. We leverage the similarity matrices of both drugs and targets to address the sparsity problem of the interaction matrix. The comparison of our approach against other algorithms on the same reference datasets has shown good results regarding area under receiver operating characteristic curve and the area under precision-recall curve. More specifically, experimental results achieve high accuracy on golden standard datasets (e.g., Nuclear Receptors, GPCRs, Ion Channels, and Enzymes) when performed with five repetitions of tenfold cross-validation. Display graphical of the hybrid model of Matrix Factorization with Denoising Autoencoders with the help side information of drugs and targets for Prediction of Drug-Target Interactions.

Estimating longitudinal change in latent variable means: a comparison of non-negative matrix factorization and other item non-response methods

ABSTRACT Estimates of longitudinal change in the parameters of latent (i.e. unobserved) variables, including means, are affected by non-response on the items or indicators of the latent variable. This study used Monte Carlo simulation and a numeric example to compare four ordinal item non-response methods: non-negative matrix factorization (NNMF), multiple imputation with conditional proportional odds model (POM), full information maximum likelihood (FIML) and complete-case analysis, when estimating the longitudinal change in latent variable means. The mean squared error for the NNMF method was more than 40% lower than for the FIML and POM methods when the latent variable correlations over time were strong, percentage of missing data was 25% or more, and sample size was large. The NNMF method is a promising method to address item non-response. It is relatively efficient when sample size is large, and the percentage of missing data is high but has limitations under other data-analytic conditions.

Nine-year trends of PM10 sources and oxidative potential in a rural background site in France

Abstract. Long-term monitoring at sites with relatively low particulate pollution could provide an opportunity to identify changes in pollutant concentration and potential effects of current air quality policies. In this study, 9-year sampling of PM10 (particles with an aerodynamic diameter below 10 µm) was performed in a rural background site in France (Observatoire Pérenne de l'Environnement or OPE) from 28 February 2012 to 22 December 2020. The positive matrix factorization (PMF) method was used to apportion sources of PM10 based on quantified chemical constituents and specific chemical tracers analysed on collected filters. Oxidative potential (OP), an emerging health metric that measures PM capability to potentially cause anti-oxidant imbalance in the lung, was also measured using two acellular assays: dithiothreitol (DTT) and ascorbic acid (AA). The sources of OP were also estimated using multiple linear regression (MLR) analysis. In terms of mass contribution, the dominant sources are secondary aerosols (nitrate- and sulfate-rich) associated with long-range transport (LRT). However, in terms of OP contributions, the main drivers are traffic, mineral dust, and biomass burning factors. There is also some OP contribution apportioned to the sulfate- and nitrate-rich sources influenced by processes and ageing during LRT that could have encouraged mixing with other anthropogenic sources. The study indicates much lower OP values than in urban areas. A substantial decrease (58 % reduction from the year 2012 to 2020) in the mass contributions from the traffic factor was found, even though this is not clearly reflected in its OP contribution. Nevertheless, the findings in this long-term study at the OPE site could indicate effectiveness of implemented emission control policies, as also seen in other long-term studies conducted in Europe, mainly for urban areas.

M6Adecom: Analysis of m6A profile matrix based on graph regularized non-negative matrix factorization.

Epitranscriptomic m6A methylation is shown to mediate extensive regulations under the context of various RNA binding protein (RBP) readers. With m6A methylation data has reached a sizable scale, the functional context-aware analysis of m6A profiles is becoming more feasible and demanded. In this study, we employed graph regularized non-negative matrix factorization (GNMF) for m6A profile analysis and comparison, where the RBP binding preference of m6A sites were incorporated as the functional context-based graph constraint term. Compared to the baseline non-negative matrix factorization (NMF) method, this GNMF-based method could better capture the distinctions in multiple functional characteristics between different group of m6A sites, including but not limited to the associated biological pathways and disease genes. We further established m6Adecom, an online tool that can be used for correlation and enrichment analysis of m6A profiles using the matrix decomposition result from GNMF, and gene set enrichment analysis based on the high-score m6A sites. m6Adecom is freely accessible at http://www.rnanut.net/m6adecom.

Scalable Discrete Matrix Factorization and Semantic Autoencoder for Cross-Media Retrieval.

Hashing methods have sparked great attention on multimedia tasks due to their effectiveness and efficiency. However, most existing methods generate binary codes by relaxing the binary constraints, which may cause large quantization error. In addition, most supervised cross-modal approaches preserve the similarity relationship by constructing an n×n large-size similarity matrix, which requires huge computation, making these methods unscalable. To address the above challenges, this article presents a novel algorithm, called scalable discrete matrix factorization and semantic autoencoder method (SDMSA). SDMSA is a two-stage method. In the first stage, the matrix factorization scheme is utilized to learn the latent semantic information, the label matrix is incorporated into the loss function instead of the similarity matrix. Thereafter, the binary codes can be generated by the latent representations. During optimization, we can avoid manipulating a large n×n similarity matrix, and the hash codes can be generated directly. In the second stage, a novel hash function learning scheme based on the autoencoder is proposed. The encoder-decoder paradigm aims to learn projections, the feature vectors are projected to code vectors by encoder, and the code vectors are projected back to the original feature vectors by the decoder. The encoder-decoder scheme ensures the embedding can well preserve both the semantic and feature information. Specifically, two algorithms SDMSA-lin and SDMSA-ker are developed under the SDMSA framework. Owing to the merit of SDMSA, we can get more semantically meaningful binary hash codes. Extensive experiments on several databases show that SDMSA-lin and SDMSA-ker achieve promising performance.

Rating prediction of recommended item based on review deep learning and rating probability matrix factorization

With a sharp improvement in E-commerce and data, the precise rating prediction of recommended items under user preferences has been a hot research topic in the EC intelligence domain. The rating data Matrix Factorization based methods have been widely used in item rating predictions in e-commerce recommendation systems. However, “cold start” and “data sparsity” have seriously restricted the accuracy of such methods. In addition to the rating data, as side information, the massive reviews posted by users rich in semantic and emotional information express user preferences and item characteristics, and will certainly improve the accuracy of the rating prediction. Accordingly, this paper combines the deep learning for the review text and the matrix factorization method for rating data to predict the rating of the recommended items accurately. Firstly, based on the Deep Learning methods, self-attention mechanism and bi-directional RNN (Recurrent Neural Network) with the core of GRU (Gated Recurrent Unit), the deep nonlinear features of users and items are learned from review texts. Then, these features are introduced as a prior mean into the classical rating-based probability matrix factorization model to obtain the latent factor vectors of users and items with the rating of the recommended item accurately predicted. Finally, adopting MSE and MAE as the indicators, the extensive experiments conducted on four real datasets verify that the proposed model TFRMF (Topical Features Regularized Matrix Factorization) performs better than other classical counterparts. The achievements of this work will provide powerful methods and decision supports for accurate and personalized e-commerce recommendation practices.

Efficient Federated Matrix Factorization Against Inference Attacks

Recommender systems typically require the revelation of users’ ratings to the recommender server, which will subsequently use these ratings to provide personalized services. However, such revelations make users vulnerable to a broader set of inference attacks, allowing the recommender server to learn users’ private attributes, e.g., age and gender. Therefore, in this paper, we propose an efficient federated matrix factorization method that protects users against inference attacks. The key idea is that we obfuscate one user’s rating to another such that the private attribute leakage is minimized under the given distortion budget, which bounds the recommending loss and overhead of system efficiency. During the obfuscation, we apply differential privacy to control the information leakage between the users. We also adopt homomorphic encryption to protect the intermediate results during training. Our framework is implemented and tested on real-world datasets. The result shows that our method can reduce up to 16.7% of inference attack accuracy compared to using no privacy protections.

Partially latent factors based multi‐view subspace learning

AbstractMulti‐view subspace clustering always performs well in high‐dimensional data analysis, but is sensitive to the quality of data representation. To this end, a two‐stage fusion strategy is proposed to embed representation learning into the process of multi‐view subspace clustering. This article first proposes a novel matrix factorization method that can separate the coupling consistent and complementary information from observations of multiple views. Based on the obtained latent representations, we further propose two subspace clustering strategies: feature‐level fusion and subspace‐level hierarchical strategy. The feature‐level method concatenates all kinds of latent representations from multiple views, and the original problem therefore degenerates to a single‐view subspace clustering process. The subspace‐level hierarchical method performs different self‐expressive reconstruction processes on the corresponding complementary and consistent latent representations coming from each view, that is, the prior constraints imposed on different types of subspace representations are related to the relevant input factors. Finally, extensive experimental results on real‐world datasets demonstrate the superiority of our proposed methods by comparing them against some state‐of‐the‐art subspace clustering algorithms.

Measurement report: Atmospheric new particle formation in a coastal agricultural site explained with binPMF analysis of nitrate CI-APi-TOF spectra

Abstract. The occurrence of new particle formation (NPF) events detected in a coastal agricultural site, at Qvidja, in Southwestern Finland, was investigated using the data measured with a nitrate ion-based chemical-ionization atmospheric-pressure-interface time-of-flight (CI-APi-TOF) mass spectrometer. The binned positive matrix factorization method (binPMF) was applied to the measured spectra. It resulted in eight factors describing the time series of ambient gas and cluster composition at Qvidja during spring 2019. The most interesting factors related to the observed NPF events were the two factors with the highest mass-to-charge ratios, numbered 7 and 8, both having profiles with patterns of highly oxygenated organic molecules with one nitrogen atom. It was observed that factor 7 had elevated intensities during the NPF events. A variable with an even better connection to the observed NPF events is fF7, which denotes the fraction of the total spectra within the studied mass-to-charge ratio range between 169 and 450 Th being in a form of factor 7. Values of fF7 higher than 0.50±0.05 were observed during the NPF events, of which durations also correlated with the duration of fF7 exceeding this critical value. It was also observed that factor 8 acts like a precursor for factor 7 with solar radiation and that the formation of factor 8 is associated with ozone levels.

Context-Aware Matrix Factorization for the Identification of Urban Functional Regions with POI and Taxi OD Data

The identification of urban functional regions (UFRs) is important for urban planning and sustainable development. Because this involves a set of interrelated processes, it is difficult to identify UFRs using only single data sources. Data fusion methods have the potential to improve the identification accuracy. However, the use of existing fusion methods remains challenging when mining shared semantic information among multiple data sources. In order to address this issue, we propose a context-coupling matrix factorization (CCMF) method which considers contextual relationships. This method was designed based on the fact that the contextual relationships embedded in all of the data are shared and complementary to one another. An empirical study was carried out by fusing point-of-interest (POI) data and taxi origin–destination (OD) data in Beijing, China. There are three steps in CCMF. First, contextual information is extracted from POI and taxi OD trajectory data. Second, fusion is performed using contextual information. Finally, spectral clustering is used to identify the functional regions. The results show that the proposed method achieved an overall accuracy (OA) of 90% and a kappa of 0.88 in the study area. The results were compared with the results obtained using single sources of non-fused data and other fusion methods in order to validate the effectiveness of our method. The results demonstrate that an improvement in the OA of about 5% in comparison to a similar method in the literature could be achieved using this method.

Necroptosis-Related Genes Associated With Immune Activity and Prognosis of Colorectal Cancer

This study aims at screening out the key necroptosis-related genes in colorectal cancer and elucidating the role of necroptosis-related genes in the immune activity and prognosis of colorectal cancer (CRC). The CRC patients’ data were downloaded from The Cancer Genome Atlas (TCGA). The non-negative matrix factorization method was applied to identify new molecular subgroups. Survival analysis and single sample Gene Set Enrichment Analysis were performed to determinate the differences in the overall survival time and immune status of the subgroups. Prognostic model was constructed on the basis of univariate Cox regression and LASSO analysis. Functional analyses were used to explore the potential mechanisms. Based on prognostic related necroptosis genes, we identify two molecular subgroups with significantly different survival. The better prognosis was associated with more active immune infiltration and upregulated expression of immune checkpoints. We screened nine necroptosis related genes as key prognostic genes and established a risk model, which showed a good potential for survival prediction in colorectal cancer. Nomogram assessment showed that the model had high reliability for predicting the prognosis of colorectal cancer patients. The high-risk and low-risk group also has different sensitivity to immunotherapy and commonly used drugs for colorectal cancer. Overall, necroptosis related genes were involved in the immune microenvironment of colorectal cancer patient, could be utilized to predict the prognosis of colorectal cancer and develop more individualized treatment.