Encoding of rat working memory by power of multi-channel local field potentials via sparse non-negative matrix factorization

Working memory plays an important role in human cognition. This study investigated how working memory was encoded by the power of multichannel local field potentials （LFPs） based on sparse non negative matrix factorization （SNMF）. SNMF was used to extract features from LFPs recorded from the prefrontal cortex of four SpragueDawley rats during a memory task in a Y maze, with 10 trials for each rat. Then the powerincreased LFP components were selected as working memoryrelated features and the other components were removed. After that, the inverse operation of SNMF was used to study the encoding of working memory in the time frequency domain. We demonstrated that theta and gamma power increased significantly during the working memory task. The results suggested that postsynaptic activity was simulated well by the sparse activity model. The theta and gamma bands were meaningful for encoding working memory.

Sparseness-controlled non-negative tensor factorization and its application in machinery fault diagnosis

Aiming at the problems of bispectral analysis when applied to machinery fault diagnosis, a machinery fault feature extraction method based on sparseness-controlled non-negative tensor factorization （SNTF） is proposed. First, a non-negative tensor factorization（NTF） algorithm is improved by imposing sparseness constraints on it. Secondly, the bispectral images of mechanical signals are obtained and stacked to form a third-order tensor. Thirdly, the improved algorithm is used to extract features, which are represented by a series of basis images from this tensor. Finally, coefficients indicating these basis images＇ weights in constituting original bispectral images are calculated for fault classification. Experiments on fault diagnosis of gearboxes show that the extracted features can not only reveal some nonlinear characteristics of the system, but also have intuitive meanings with regard to fault characteristic frequencies. These features provide great convenience for the interpretation of the relationships between machinery faults and corresponding bispectra.

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.

Alzheimer’s disease classification based on sparse functional connectivity and non-negative matrix factorization

A novel framework is proposed to obtain physiologically meaningful features for Alzheimer's disease(AD)classification based on sparse functional connectivity and non-negative matrix factorization.Specifically,the non-negative adaptive sparse representation(NASR)method is applied to compute the sparse functional connectivity among brain regions based on functional magnetic resonance imaging(fMRI)data for feature extraction.Afterwards,the sparse non-negative matrix factorization(sNMF)method is adopted for dimensionality reduction to obtain low-dimensional features with straightforward physical meaning.The experimental results show that the proposed framework outperforms the competing frameworks in terms of classification accuracy,sensitivity and specificity.Furthermore,three sub-networks,including the default mode network,the basal ganglia-thalamus-limbic network and the temporal-insular network,are found to have notable differences between the AD patients and the healthy subjects.The proposed framework can effectively identify AD patients and has potentials for extending the understanding of the pathological changes of AD.

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.

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.

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 Fast LDL-factorization Approach for Large Sparse Positive Definite System and Its Application to One-to-one Marketing Optimization Computation

LDL-factorization is an efficient way of solving Ax = b for a large symmetric positive definite sparse matrix A. This paper presents a new method that further improves the efficiency of LDL-factorization. It is based on the theory of elimination trees for the factorization factor. It breaks the computations involved in LDL-factorization down into two stages： 1） the pattern of nonzero entries of the factor is predicted, and 2） the numerical values of the nonzero entries of the factor are computed. The factor is stored using the form of an elimination tree so as to reduce memory usage and avoid unnecessary numerical operations. The calculation results for some typical numerical examples demonstrate that this method provides a significantly higher calculation efficiency for the one-to-one marketing optimization algorithm.

Randomized Latent Factor Model for High-dimensional and Sparse Matrices from Industrial Applications

Latent factor(LF) models are highly effective in extracting useful knowledge from High-Dimensional and Sparse(HiDS) matrices which are commonly seen in various industrial applications. An LF model usually adopts iterative optimizers,which may consume many iterations to achieve a local optima,resulting in considerable time cost. Hence, determining how to accelerate the training process for LF models has become a significant issue. To address this, this work proposes a randomized latent factor(RLF) model. It incorporates the principle of randomized learning techniques from neural networks into the LF analysis of HiDS matrices, thereby greatly alleviating computational burden. It also extends a standard learning process for randomized neural networks in context of LF analysis to make the resulting model represent an HiDS matrix correctly.Experimental results on three HiDS matrices from industrial applications demonstrate that compared with state-of-the-art LF models, RLF is able to achieve significantly higher computational efficiency and comparable prediction accuracy for missing data.I provides an important alternative approach to LF analysis of HiDS matrices, which is especially desired for industrial applications demanding highly efficient models.

Robust Latent Factor Analysis for Precise Representation of High-Dimensional and Sparse Data

High-dimensional and sparse(HiDS)matrices commonly arise in various industrial applications,e.g.,recommender systems(RSs),social networks,and wireless sensor networks.Since they contain rich information,how to accurately represent them is of great significance.A latent factor(LF)model is one of the most popular and successful ways to address this issue.Current LF models mostly adopt L2-norm-oriented Loss to represent an HiDS matrix,i.e.,they sum the errors between observed data and predicted ones with L2-norm.Yet L2-norm is sensitive to outlier data.Unfortunately,outlier data usually exist in such matrices.For example,an HiDS matrix from RSs commonly contains many outlier ratings due to some heedless/malicious users.To address this issue,this work proposes a smooth L1-norm-oriented latent factor(SL-LF)model.Its main idea is to adopt smooth L1-norm rather than L2-norm to form its Loss,making it have both strong robustness and high accuracy in predicting the missing data of an HiDS matrix.Experimental results on eight HiDS matrices generated by industrial applications verify that the proposed SL-LF model not only is robust to the outlier data but also has significantly higher prediction accuracy than state-of-the-art models when they are used to predict the missing data of HiDS matrices.

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.

Estimating Functional Brain Network with Low-Rank Structure via Matrix Factorization for MCI/ASD Identification

Functional brain networks (FBNs) provide a potential way for understanding the brain organizational patterns and diagnosing neurological diseases. Due to its importance, many FBN construction methods have been proposed currently, including the low-order Pearson’s correlation (PC) and sparse representation (SR), as well as the high-order functional connection (HoFC). However, most existing methods usually ignore the information of topological structures of FBN, such as low-rank structure which can reduce the noise and improve modularity to enhance the stability of networks. In this paper, we propose a novel method for improving the estimated FBNs utilizing matrix factorization (MF). More specifically, we firstly construct FBNs based on three traditional methods, including PC, SR, and HoFC. Then, we reduce the rank of these FBNs via MF model for estimating FBN with low-rank structure. Finally, to evaluate the effectiveness of the proposed method, experiments have been conducted to identify the subjects with mild cognitive impairment (MCI) and autism spectrum disorder (ASD) from norm controls (NCs) using the estimated FBNs. The results on Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset and Autism Brain Imaging Data Exchange (ABIDE) dataset demonstrate that the classification performances achieved by our proposed method are better than the selected baseline methods.

Improved Non-negative Matrix Factorization Algorithm for Sparse Graph Regularization

Aiming at the low recognition accuracy of non-negative matrix factorization(NMF)in practical application,an improved spare graph NMF(New-SGNMF)is proposed in this paper.New-SGNMF makes full use of the inherent geometric structure of image data to optimize the basis matrix in two steps.A threshold value s was first set to judge the threshold value of the decomposed base matrix to filter the redundant information in the data.Using L2 norm,sparse constraints were then implemented on the basis matrix,and integrated into the objective function to obtain the objective function of New-SGNMF.In addition,the derivation process of the algorithm and the convergence analysis of the algorithm were given.The experimental results on COIL20,PIE-pose09 and YaleB database show that compared with K-means,PCA,NMF and other algorithms,the proposed algorithm has higher accuracy and normalized mutual information.