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.

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.

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.

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.

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.

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.

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.

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.

Minimum distance constrained nonnegative matrix factorization for hyperspectral data unmixing

This paper considers a problem of unsupervised spectral unmixing of hyperspectral data. Based on the Linear Mixing Model （ LMM）, a new method under the framework of nonnegative matrix fac- torization （NMF） is proposed, namely minimum distance constrained nonnegative matrix factoriza- tion （MDC-NMF）. In this paper, firstly, a new regularization term, called endmember distance （ED） is considered, which is defined as the sum of the squared Euclidean distances from each end- member to their geometric center. Compared with the simplex volume, ED has better optimization properties and is conceptually intuitive. Secondly, a projected gradient （PG） scheme is adopted, and by the virtue of ED, in this scheme the optimal step size along the feasible descent direction can be calculated easily at each iteration. Thirdly, a finite step （ no more than the number of endmem- bers） terminated algorithm is used to project a point on the canonical simplex, by which the abun- dance nonnegative constraint and abundance sum-to-one constraint can be accurately satisfied in a light amount of computation. The experimental results, based on a set of synthetic data and real da- ta, demonstrate that, in the same running time, MDC-NMF outperforms several other similar meth- ods proposed recently.

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 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.

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.

Isolation of Whole-plant Multiple Oscillations via Non-negative Spectral Decompositio

Constrained spectral non-negative matrix factorization(NMF)analysis of perturbed oscillatory process control loop variable data is performed for the isolation of multiple plant-wide oscillatory sources.The technique is described and demonstrated by analyzing data from both simulated and real plant data of a chemical process plant. Results show that the proposed approach can map multiple oscillatory sources onto the most appropriate control loops,and has superior performance in terms of reconstruction accuracy and intuitive understanding compared with spectral independent component analysis(ICA).

基于TWE-NMF主题模型的Mashup服务聚类方法

随着互联网和面向服务技术的发展,一种新型的Web应用——Mashup服务,开始在互联网上流行并快速增长.如何在众多Mashup服务中找到高质量的服务,已经成为一个大家关注的热点问题.寻找功能相似的服务并进行聚类,能有效提升服务发现的精度与效率.目前国内外主流方法为挖掘Mashup服务中隐含的功能信息,进一步采用特定聚类算法如K-means等进行聚类.然而Mashup服务文档通常为短文本,基于传统的挖掘算法如LDA无法有效处理短文本,导致聚类效果并不理想.针对这一问题,提出一种基于非负矩阵分解的TWE-NMF(nonnegative matrix factorization combining tags and word embedding)模型对Mashup服务进行主题建模.所提方法首先对Mashup服务规范化处理,其次采用一种基于改进的Gibbs采样的狄利克雷过程混合模型,自动估算主题的数量,随后将词嵌入和服务标签等信息与非负矩阵分解相结合,求解Mashup服务主题特征,并通过谱聚类算法将服务聚类.最后,对所提方法的性能进行了综合评价,实验结果表明,与现有的服务聚类方法相比,所提方法在准确率、召回率、F-measure、纯度和熵等评价指标方面都有显著提高.

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.

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.