Semi-supervised community detection on attributed networks using non-negative matrix tri-factorization with node popularity

The World Wide Web generates more and more data with links and node contents,which are always modeled as attributed networks.The identification of network communities plays an important role for people to understand and utilize the semantic functions of the data.A few methods based on non-negative matrix factorization(NMF)have been proposed to detect community structure with semantic information in attributed networks.However,previous methods have not modeled some key factors(which affect the link generating process together),including prior information,the heterogeneity of node degree,as well as the interactions among communities.The three factors have been demonstrated to primarily affect the results.In this paper,we propose a semi-supervised community detection method on attributed networks by simultaneously considering these three factors.First,a semi-supervised non-negative matrix tri-factorization model with node popularity(i.e.,PSSNMTF)is designed to detect communities on the topology of the network.And then node contents are integrated into the PSSNMTF model to find the semantic communities more accurately,namely PSSNMTFC.Parameters of the PSSNMTFC model is estimated by using the gradient descent method.Experiments on some real and artificial networks illustrate that our new method is superior over some related stateof-the-art methods in terms of accuracy.

Prognostic model for prostate cancer based on glycolysis-related genes and non-negative matrix factorization analysis

Background:Establishing an appropriate prognostic model for PCa is essential for its effective treatment.Glycolysis is a vital energy-harvesting mechanism for tumors.Developing a prognostic model for PCa based on glycolysis-related genes is novel and has great potential.Methods:First,gene expression and clinical data of PCa patients were downloaded from The Cancer Genome Atlas(TCGA)and Gene Expression Omnibus(GEO),and glycolysis-related genes were obtained from the Molecular Signatures Database(MSigDB).Gene enrichment analysis was performed to verify that glycolysis functions were enriched in the genes we obtained,which were used in nonnegative matrix factorization(NMF)to identify clusters.The correlation between clusters and clinical features was discussed,and the differentially expressed genes(DEGs)between the two clusters were investigated.Based on the DEGs,we investigated the biological differences between clusters,including immune cell infiltration,mutation,tumor immune dysfunction and exclusion,immune function,and checkpoint genes.To establish the prognostic model,the genes were filtered based on univariable Cox regression,LASSO,and multivariable Cox regression.Kaplan–Meier analysis and receiver operating characteristic analysis validated the prognostic value of the model.A nomogram of the risk score calculated by the prognostic model and clinical characteristics was constructed to quantitatively estimate the survival probability for PCa patients in the clinical setting.Result:The genes obtained from MSigDB were enriched in glycolysis functions.Two clusters were identified by NMF analysis based on 272 glycolysis-related genes,and a prognostic model based on DEGs between the two clusters was finally established.The prognostic model consisted of LAMPS,SPRN,ATOH1,TANC1,ETV1,TDRD1,KLK14,MESP2,POSTN,CRIP2,NAT1,AKR7A3,PODXL,CARTPT,and PCDHGB2.All sample,training,and test cohorts from The Cancer Genome Atlas(TCGA)and the external validation cohort from GEO showed significant differences between the high-risk and low-risk groups.The area under the ROC curve showed great performance of this prognostic model.Conclusion:A prognostic model based on glycolysis-related genes was established,with great performance and potential significance to the clinical application.

Evaluating Partitioning Based Clustering Methods for Extended Non-negative Matrix Factorization (NMF)

Data is humongous today because of the extensive use of World WideWeb, Social Media and Intelligent Systems. This data can be very important anduseful if it is harnessed carefully and correctly. Useful information can beextracted from this massive data using the Data Mining process. The informationextracted can be used to make vital decisions in various industries. Clustering is avery popular Data Mining method which divides the data points into differentgroups such that all similar data points form a part of the same group. Clusteringmethods are of various types. Many parameters and indexes exist for the evaluationand comparison of these methods. In this paper, we have compared partitioningbased methods K-Means, Fuzzy C-Means (FCM), Partitioning AroundMedoids (PAM) and Clustering Large Application (CLARA) on secure perturbeddata. Comparison and identification has been done for the method which performsbetter for analyzing the data perturbed using Extended NMF on the basis of thevalues of various indexes like Dunn Index, Silhouette Index, Xie-Beni Indexand Davies-Bouldin Index.

Feature Extraction and Recognition for Rolling Element Bearing Fault Utilizing Short-Time Fourier Transform and Non-negative Matrix Factorization

Due to the non-stationary characteristics of vibration signals acquired from rolling element bearing fault, thc time-frequency analysis is often applied to describe the local information of these unstable signals smartly. However, it is difficult to classitythe high dimensional feature matrix directly because of too large dimensions for many classifiers. This paper combines the concepts of time-frequency distribution（TFD） with non-negative matrix factorization（NMF）, and proposes a novel TFD matrix factorization method to enhance representation and identification of bearing fault. Throughout this method, the TFD of a vibration signal is firstly accomplished to describe the localized faults with short-time Fourier transform（STFT）. Then, the supervised NMF mapping is adopted to extract the fault features from TFD. Meanwhile, the fault samples can be clustered and recognized automatically by using the clustering property of NMF. The proposed method takes advantages of the NMF in the parts-based representation and the adaptive clustering. The localized fault features of interest can be extracted as well. To evaluate the performance of the proposed method, the 9 kinds of the bearing fault on a test bench is performed. The proposed method can effectively identify the fault severity and different fault types. Moreover, in comparison with the artificial neural network（ANN）, NMF yields 99.3% mean accuracy which is much superior to ANN. This research presents a simple and practical resolution for the fault diagnosis problem of rolling element bearing in high dimensional feature space.

Graph Regularized L_p Smooth Non-negative Matrix Factorization for Data Representation

This paper proposes a Graph regularized Lpsmooth non-negative matrix factorization(GSNMF) method by incorporating graph regularization and L_p smoothing constraint, which considers the intrinsic geometric information of a data set and produces smooth and stable solutions. The main contributions are as follows: first, graph regularization is added into NMF to discover the hidden semantics and simultaneously respect the intrinsic geometric structure information of a data set. Second,the Lpsmoothing constraint is incorporated into NMF to combine the merits of isotropic(L_2-norm) and anisotropic(L_1-norm)diffusion smoothing, and produces a smooth and more accurate solution to the optimization problem. Finally, the update rules and proof of convergence of GSNMF are given. Experiments on several data sets show that the proposed method outperforms related state-of-the-art methods.

Total Variation Constrained Non-Negative Matrix Factorization for Medical Image Registration

This paper presents a novel medical image registration algorithm named total variation constrained graphregularization for non-negative matrix factorization(TV-GNMF).The method utilizes non-negative matrix factorization by total variation constraint and graph regularization.The main contributions of our work are the following.First,total variation is incorporated into NMF to control the diffusion speed.The purpose is to denoise in smooth regions and preserve features or details of the data in edge regions by using a diffusion coefficient based on gradient information.Second,we add graph regularization into NMF to reveal intrinsic geometry and structure information of features to enhance the discrimination power.Third,the multiplicative update rules and proof of convergence of the TV-GNMF algorithm are given.Experiments conducted on datasets show that the proposed TV-GNMF method outperforms other state-of-the-art algorithms.

Obtaining Profiles Based on Localized Non-negative Matrix Factorization

Nonnegative matrix factorization (NMF) is a method to get parts-based features of information and form the typical profiles. But the basis vectors NMF gets are not orthogonal so that parts-based features of information are usually redundancy. In this paper, we propose two different approaches based on localized non-negative matrix factorization (LNMF) to obtain the typical user session profiles and typical semantic profiles of junk mails. The LNMF get basis vectors as orthogonal as possible so that it can get accurate profiles. The experiments show that the approach based on LNMF can obtain better profiles than the approach based on NMF. Key words localized non-negative matrix factorization - profile - log mining - mail filtering CLC number TP 391 Foundation item: Supported by the National Natural Science Foundation of China (60373066, 60303024), National Grand Fundamental Research 973 Program of China (2002CB312000), National Research Foundation for the Doctoral Program of Higher Education of China (20020286004).Biography: Jiang Ji-xiang (1980-), male, Master candidate, research direction: data mining, knowledge representation on the Web.

High Quality Audio Object Coding Framework Based on Non-Negative Matrix Factorization

Object-based audio coding is the main technique of audio scene coding. It can effectively reconstruct each object trajectory, besides provide sufficient flexibility for personalized audio scene reconstruction. So more and more attentions have been paid to the object-based audio coding. However, existing object-based techniques have poor sound quality because of low parameter frequency domain resolution. In order to achieve high quality audio object coding, we propose a new coding framework with introducing the non-negative matrix factorization(NMF) method. We extract object parameters with high resolution to improve sound quality, and apply NMF method to parameter coding to reduce the high bitrate caused by high resolution. And the experimental results have shown that the proposed framework can improve the coding quality by 25%, so it can provide a better solution to encode audio scene in a more flexible and higher quality way.

A novel trilinear decomposition algorithm:Three-dimension non-negative matrix factorization

Non-negative matrix factorization （NMF） is a technique for dimensionality reduction by placing non-negativity constraints on the matrix. Based on the PARAFAC model, NMF was extended for three-dimension data decomposition. The three-dimension nonnegative matrix factorization （NMF3） algorithm, which was concise and easy to implement, was given in this paper. The NMF3 algorithm implementation was based on elements but not on vectors. It could decompose a data array directly without unfolding, which was not similar to that the traditional algorithms do, It has been applied to the simulated data array decomposition and obtained reasonable results. It showed that NMF3 could be introduced for curve resolution in chemometrics.

Clustering Student Discussion Messages on Online Forumby Visualization and Non-Negative Matrix Factorization

The use of online discussion forum can?effectively engage students in their studies. As the number of messages posted on the forum is increasing, it is more difficult for instructors to read and respond to them in a prompt way. In this paper, we apply non-negative matrix factorization and visualization to clustering message data, in order to provide a summary view of messages that disclose their deep semantic relationships. In particular, the NMF is able to find the underlying issues hidden in the messages about which most of the students are concerned. Visualization is employed to estimate the initial number of clusters, showing the relation communities. The experiments and comparison on a real dataset have been reported to demonstrate the effectiveness of the approaches.

Unsupervised Multi-Level Non-Negative Matrix Factorization Model: Binary Data Case

Rank determination issue is one of the most significant issues in non-negative matrix factorization (NMF) research. However, rank determination problem has not received so much emphasis as sparseness regularization problem. Usually, the rank of base matrix needs to be assumed. In this paper, we propose an unsupervised multi-level non-negative matrix factorization model to extract the hidden data structure and seek the rank of base matrix. From machine learning point of view, the learning result depends on its prior knowledge. In our unsupervised multi-level model, we construct a three-level data structure for non-negative matrix factorization algorithm. Such a construction could apply more prior knowledge to the algorithm and obtain a better approximation of real data structure. The final bases selection is achieved through L2-norm optimization. We implement our experiment via binary datasets. The results demonstrate that our approach is able to retrieve the hidden structure of data, thus determine the correct rank of base matrix.

A Novel CCA-NMF Whitening Method for Practical Machine Learning Based Underwater Direction of Arrival Estimation

Underwater direction of arrival(DOA)estimation has always been a very challenging theoretical and practical problem.Due to the serious non-stationary,non-linear,and non-Gaussian characteristics,machine learning based DOA estimation methods trained on simulated Gaussian noised array data cannot be directly applied to actual underwater DOA estimation tasks.In order to deal with this problem,environmental data with no target echoes can be employed to analyze the non-Gaussian components.Then,the obtained information about non-Gaussian components can be used to whiten the array data.Based on these considerations,a novel practical sonar array whitening method was proposed.Specifically,based on a weak assumption that the non-Gaussian components in adjacent patches with and without target echoes are almost the same,canonical cor-relation analysis(CCA)and non-negative matrix factorization(NMF)techniques are employed for whitening the array data.With the whitened array data,machine learning based DOA estimation models trained on simulated Gaussian noised datasets can be used to perform underwater DOA estimation tasks.Experimental results illustrated that,using actual underwater datasets for testing with known machine learning based DOA estimation models,accurate and robust DOA estimation performance can be achieved by using the proposed whitening method in different underwater con-ditions.

Single Channel Source Separation Using Filterbank and 2D Sparse Matrix Factorization

We present a novel approach to solve the problem of single channel source separation (SCSS) based on filterbank technique and sparse non-negative matrix two dimensional deconvolution (SNMF2D). The proposed approach does not require training information of the sources and therefore, it is highly suited for practicality of SCSS. The major problem of most existing SCSS algorithms lies in their inability to resolve the mixing ambiguity in the single channel observation. Our proposed approach tackles this difficult problem by using filterbank which decomposes the mixed signal into sub-band domain. This will result the mixture in sub-band domain to be more separable. By incorporating SNMF2D algorithm, the spectral-temporal structure of the sources can be obtained more accurately. Real time test has been conducted and it is shown that the proposed method gives high quality source separation performance.

Nonnegative matrix factorization with Log Gabor wavelets for image representation and classification

Many problems in image representation and classification involve some form of dimensionality reduction. Nonnegative matrix factorization （NMF） is a recently proposed unsupervised procedure for learning spatially localized, partsbased subspace representation of objects. An improvement of the classical NMF by combining with Log-Gabor wavelets to enhance its part-based learning ability is presented. The new method with principal component analysis （PCA） and locally linear embedding （LIE） proposed recently in Science are compared. Finally, the new method to several real world datasets and achieve good performance in representation and classification is applied.

Non-Singularity Conditions for Two Z-Matrix Types

A real square matrix whose non-diagonal elements are non-positive is called a Z-matrix. This paper shows a necessary and sufficient condition for non-singularity of two types of Z-matrices. The first is for the Z-matrix whose row sums are all non-negative. The non-singularity condition for this matrix is that at least one positive row sum exists in any principal submatrix of the matrix. The second is for the Z-matrix which satisfies where . Let be the ith row and the jth column element of , and be the jth element of . Let be a subset of which is not empty, and be the complement of if is a proper subset. The non-singularity condition for this matrix is such that or such that for? . Robert Beauwens and Michael Neumann previously presented conditions similar to these conditions. In this paper, we present a different proof and show that these conditions can be also derived from theirs.

Non-negative matrix factorization based modeling and training algorithm for multi-label learning

Multi-label learning is more complicated than single-label learning since the semantics of the instances are usually overlapped and not identical.The effectiveness of many algorithms often fails when the correlations in the feature and label space are not fully exploited.To this end,we propose a novel non-negative matrix factorization(NMF)based modeling and training algorithm that learns from both the adjacencies of the instances and the labels of the training set.In the modeling process,a set of generators are constructed,and the associations among generators,instances,and labels are set up,with which the label prediction is conducted.In the training process,the parameters involved in the process of modeling are determined.Specifically,an NMF based algorithm is proposed to determine the associations between generators and instances,and a non-negative least square optimization algorithm is applied to determine the associations between generators and labels.The proposed algorithm fully takes the advantage of smoothness assumption,so that the labels are properly propagated.The experiments were carried out on six set of benchmarks.The results demonstrate the effectiveness of the proposed algorithms.

TOPIC SPLITTING： A HIERARCHICAL TOPIC MODEL BASED ON NON-NEGATIVE MATRIX FACTORIZATION

Hierarchical topic model has been widely applied in many real applications, because it can build a hierarchy on topics with guaranteeing of topics＇ quality. Most of traditional methods build a hierarchy by adopting low-level topics as new features to construct high-level ones, which will often cause semantic confusion between low-level topics and high-level ones. To address the above problem, we propose a novel topic model named hierarchical sparse NMF with orthogonal constraint （HSOC）, which is based on non-negative matrix factorization and builds topic hierarchy via splitting super-topics into sub-topics. In HSOC, we introduce global independence, local independence and information consistency to constraint the split topics. Extensive experimental results on real-world corpora show that the purposed model achieves comparable performance on topic quality and better performance on semantic feature representation of documents compared with baseline methods.

Non-negative matrix factorization based unmixing for principal component transformed hyperspectral data

Non-negative matrix factorization(NMF) has been widely used in mixture analysis for hyperspectral remote sensing. When used for spectral unmixing analysis, however, it has two main shortcomings:(1) since the dimensionality of hyperspectral data is usually very large, NMF tends to suffer from large computational complexity for the popular multiplicative iteration rule;(2) NMF is sensitive to noise(outliers), and thus the corrupted data will make the results of NMF meaningless. Although principal component analysis(PCA) can be used to mitigate these two problems, the transformed data will contain negative numbers, hindering the direct use of the multiplicative iteration rule of NMF. In this paper, we analyze the impact of PCA on NMF, and find that multiplicative NMF can also be applicable to data after principal component transformation. Based on this conclusion, we present a method to perform NMF in the principal component space, named ‘principal component NMF'(PCNMF). Experimental results show that PCNMF is both accurate and time-saving.

Multi-label Emotion Classification of COVID–19 Tweets with Deep Learning and Topic Modelling

The COVID-19 pandemic has become one of the severe diseases in recent years.As it majorly affects the common livelihood of people across the universe,it is essential for administrators and healthcare professionals to be aware of the views of the community so as to monitor the severity of the spread of the outbreak.The public opinions are been shared enormously in microblogging med-ia like twitter and is considered as one of the popular sources to collect public opinions in any topic like politics,sports,entertainment etc.,This work presents a combination of Intensity Based Emotion Classification Convolution Neural Net-work(IBEC-CNN)model and Non-negative Matrix Factorization(NMF)for detecting and analyzing the different topics discussed in the COVID-19 tweets as well the intensity of the emotional content of those tweets.The topics were identified using NMF and the emotions are classified using pretrained IBEC-CNN,based on predefined intensity scores.The research aimed at identifying the emotions in the Indian tweets related to COVID-19 and producing a list of topics discussed by the users during the COVID-19 pandemic.Using the Twitter Application Programming Interface(Twitter API),huge numbers of COVID-19 tweets are retrieved during January and July 2020.The extracted tweets are ana-lyzed for emotions fear,joy,sadness and trust with proposed Intensity Based Emotion Classification Convolution Neural Network(IBEC-CNN)model which is pretrained.The classified tweets are given an intensity score varies from 1 to 3,with 1 being low intensity for the emotion,2 being the moderate and 3 being the high intensity.To identify the topics in the tweets and the themes of those topics,Non-negative Matrix Factorization(NMF)has been employed.Analysis of emotions of COVID-19 tweets has identified,that the count of positive tweets is more than that of count of negative tweets during the period considered and the negative tweets related to COVID-19 is less than 5%.Also,more than 75%nega-tive tweets expressed sadness,fear are of low intensity.A qualitative analysis has also been conducted and the topics detected are grouped into themes such as eco-nomic impacts,case reports,treatments,entertainment and vaccination.The results of analysis show that the issues related to the pandemic are expressed dif-ferent emotions in twitter which helps in interpreting the public insights during the pandemic and these results are beneficial for planning the dissemination of factual health statistics to build the trust of the people.The performance comparison shows that the proposed IBEC-CNN model outperforms the conventional models and achieved 83.71%accuracy.The%of COVID-19 tweets that discussed the different topics vary from 7.45%to 26.43%on topics economy,Statistics on cases,Government/Politics,Entertainment,Lockdown,Treatments and Virtual Events.The least number of tweets discussed on politics/government on the other hand the tweets discussed most about treatments.

Robust non-negative matrix factorization

Non-negative matrix factorization(NMF)is a recently popularized technique for learning partsbased,linear representations of non-negative data.The traditional NMF is optimized under the Gaussian noise or Poisson noise assumption,and hence not suitable if the data are grossly corrupted.To improve the robustness of NMF,a novel algorithm named robust nonnegative matrix factorization(RNMF)is proposed in this paper.We assume that some entries of the data matrix may be arbitrarily corrupted,but the corruption is sparse.RNMF decomposes the non-negative data matrix as the summation of one sparse error matrix and the product of two non-negative matrices.An efficient iterative approach is developed to solve the optimization problem of RNMF.We present experimental results on two face databases to verify the effectiveness of the proposed method.