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.

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.

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.

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.

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).

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.

Frontal and Semi-Frontal Facial Caricature Synthesis Using Non-Negative Matrix Factorization

In this paper,we present a novel approach to synthesizing frontal and semi-frontal cartoon-like facial caricatures from an image.The caricature is generated by warping the input face from the original feature points to the corresponding exaggerated feature points.A 3D mean face model is incorporated to facilitate face to caricatures by inferring the depth of 3D feature points and the spatial transformation.Then the 3D face is deformed by using non-negative matrix factorization and projected back to image plane for future warping.To efficiently solve the nonlinear spatial transformation,we propose a novel initialization scheme to set up Levenberg-Marquardt optimization.According to the spatial transformation,exaggeration is applied to the most salient features by exaggerating their normalized difference from the mean.Non-photorealistic rendering（NPR） based stylization completes the cartoon caricature.Experiments demonstrate that our method outperforms existing methods in terms of view angles and aesthetic visual quality.

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.

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.

PM_(2.5) source apportionment in a French urban coastal site under steelworks emission influences using constrained non-negative matrix factorization receptor model

The constrained weighted-non-negative matrix factorization（CW-NMF） hybrid receptor model was applied to study the influence of steelmaking activities on PM_（2.5）（particulate matter with equivalent aerodynamic diameter less than 2.5 μm） composition in Dunkerque,Northern France. Semi-diurnal PM_（2.5）samples were collected using a high volume sampler in winter 2010 and spring 2011 and were analyzed for trace metals, water-soluble ions, and total carbon using inductively coupled plasma – atomic emission spectrometry（ICP-AES）,ICP- mass spectrometry（ICP-MS）, ionic chromatography and micro elemental carbon analyzer. The elemental composition shows that NO_3^-, SO_4^（2-）, NH_4~＋and total carbon are the main PM_（2.5）constituents. Trace metals data were interpreted using concentration roses and both influences of integrated steelworks and electric steel plant were evidenced. The distinction between the two sources is made possible by the use Zn/Fe and Zn/Mn diagnostic ratios. Moreover Rb/Cr, Pb/Cr and Cu/Cd combination ratio are proposed to distinguish the ISW-sintering stack from the ISW-fugitive emissions. The a priori knowledge on the influencing source was introduced in the CW-NMF to guide the calculation. Eleven source profiles with various contributions were identified： 8 are characteristics of coastal urban background site profiles and 3 are related to the steelmaking activities. Between them,secondary nitrates, secondary sulfates and combustion profiles give the highest contributions and account for 93% of the PM_（2.5）concentration. The steelwork facilities contribute in about 2%of the total PM_（2.5）concentration and appear to be the main source of Cr, Cu, Fe, Mn, Zn.

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.

Relationship between Eukaryotic Translation Initiation Factor 4E and Malignant Angiogenesis in Non-Hodgkin Lymphoma

The relationship between angiogenesis and eukaryotic translation initiation factor 4E （EIF4E） expression level in non Hodgkin lymphoma （NHL） was studied. Mean microvessel density （MVD） and EIF4E were detected in 52 lymph node samples paraffin sections of patients with newly diagnosed NHL by the way of immunohistochemistry. Antisense EIF4E cDNA was cloned into plasmid pcDNA3.1 （＋） and transfected into Raji cells. A series of angiogenesis related factors,including vascular endothelial growth factor （VEGF）, matrix metalloproteinases 9 （MMP-9） and tissue inhibitor of metalloproteinases-2 （TIMP-2） proteins were detected by Western blot. The results showed that： （1） The Expression of EIF4E and MVD was higher in aggressive lymphomas than in indolent lymphomas（P〈0.05）and the expression of EIF4E was positively correlated with MVD in lymph node of NHL（r=0. 695, P〈0.01）. （2） Antisense EIF4E eukaryocytic expression vector （pcDNA3. 1-EIF4Eas） was constructed successfully. （3） EIF4E, VEGF and MMP-9 were expressed at high levels in Raji cells as compared to normal human peripheral blood monocular cells （NHPMC）, and blockage of EIF4E expression brought down the expression of VEGF and MMP-9. However, TIMP-2 was undetectable in Rail cells, although a moderate level of TIMP-2 was detected in NHPMC. It was concluded that the increased EIF4E expression was associated with aggressive property of NHL.

Max-margin non-negative matrix factorization with flexible spatial constraints based on factor analysis

Non-negative matrix factorization （NMF） is a popular feature encoding method for image understanding due to its non-negative properties in representation, but the learnt basis images are not always local due to the lack of explicit constraints in its objective. Various algebraic or geometric local constraints are hence proposed to shape the behaviour of the original NMF. Such constraints are usually rigid in the sense that they have to be specified beforehand instead of learning from the data. In this paper, we propose a flexible spatial constraint method for NMF learning based on factor analysis. Particularly, to learn the local spatial structure of the images, we apply a series of transformations such as orthogonal rotation and thresholding to the factor loading matrix obtained through factor analysis. Then we map the transformed loading matrix into a Laplacian matrix and incorporate this into a max-margin non-negative matrix factorization framework as a penalty term, aiming to learn a representation space which is non-negative, discriminative and localstructure-preserving. We verify the feasibility and effectiveness of the proposed method on several real world datasets with encouraging results.

Class-Driven Non-Negative Matrix Factorization for Image Representation

Non-negative matrix fa^torization （NMF） is a useful technique to learn a parts-based representation by decom- posing the original data matrix into a basis set and coefficients with non-negative constraints. However, as an unsupervised method, the original NMF cannot utilize the discriminative class information. In this paper, we propose a semi-supervised class-driven NMF method to associate a class label with each basis vector by introducing an inhomogeneous representation cost constraint. This constraint forces the learned basis vectors to represent better for their own classes but worse for the others. Therefore, data samples in the same class will have similar representations, and consequently the discriminability in new representations could be boosted. Some experiments carried out on several standard databases validate the effectiveness of our method in comparison with the state-of-the-art approaches.

Aerial Image Information Extraction Based on Non-negative Matrix Factorization

This study was on superiority of the non- negative matrix factorization（NMF） algorithm for application of information extracted with aerial images.First,NMF was used for aerial image information extraction,and then this data was compared with a principal component analysis（PCA） in which r（the number of rows or columns of basic matrix） and Eignum（the number of eigenvalues） were given different values.Experimental results showed that the run time of NMF with r = 20 or 50 was less than that of PCA with an Eignum = 20 or 50.Also,the recognition rate of NMF with r = 50 was higher than that of an Eignum = 50.The experiment showed that nonnegative matrix factorization had advantages of a short time period with a high recognition rate.

基于集成聚类的退役锂电池直接分组

针对退役电池筛选分组效率低的问题,提出了一种基于加权表决集成聚类算法的退役锂离子电池直接分组方法。提取充电电压片段特征,对特征进行降维,并使用集成聚类算法直接对特征进行分组,实现退役锂离子电池分组。该方法只需要得到部分恒流充电曲线便可实现退役锂离子电池的按容量分组,提高了筛选效率。搭建了磷酸铁锂电池仿真和实验平台,对所提的电池筛选、分组策略进行仿真和实验分析。从退役电池分组容量精度和分组效率的角度验证了所提策略的正确性和有效性。