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.

Extracting Sub-Networks from Brain Functional Network Using Graph Regularized Nonnegative Matrix Factorization

Currently,functional connectomes constructed from neuroimaging data have emerged as a powerful tool in identifying brain disorders.If one brain disease just manifests as some cognitive dysfunction,it means that the disease may affect some local connectivity in the brain functional network.That is,there are functional abnormalities in the sub-network.Therefore,it is crucial to accurately identify them in pathological diagnosis.To solve these problems,we proposed a sub-network extraction method based on graph regularization nonnegative matrix factorization(GNMF).The dynamic functional networks of normal subjects and early mild cognitive impairment(eMCI)subjects were vectorized and the functional connection vectors(FCV)were assembled to aggregation matrices.Then GNMF was applied to factorize the aggregation matrix to get the base matrix,in which the column vectors were restored to a common sub-network and a distinctive sub-network,and visualization and statistical analysis were conducted on the two sub-networks,respectively.Experimental results demonstrated that,compared with other matrix factorization methods,the proposed method can more obviously reflect the similarity between the common subnetwork of eMCI subjects and normal subjects,as well as the difference between the distinctive sub-network of eMCI subjects and normal subjects,Therefore,the high-dimensional features in brain functional networks can be best represented locally in the lowdimensional space,which provides a new idea for studying brain functional connectomes.

Orthogonal nonnegative matrix factorization based local hidden Markov model for multimode process monitoring

Traditional data driven fault detection methods assume that the process operates in a single mode so that they cannot perform well in processes with multiple operating modes. To monitor multimode processes effectively,this paper proposes a novel process monitoring scheme based on orthogonal nonnegative matrix factorization(ONMF) and hidden Markov model(HMM). The new clustering technique ONMF is employed to separate data from different process modes. The multiple HMMs for various operating modes lead to higher modeling accuracy.The proposed approach does not presume the distribution of data in each mode because the process uncertainty and dynamics can be well interpreted through the hidden Markov estimation. The HMM-based monitoring indication named negative log likelihood probability is utilized for fault detection. In order to assess the proposed monitoring strategy, a numerical example and the Tennessee Eastman process are used. The results demonstrate that this method provides efficient fault detection performance.

Image Fusion Based on Complex Contourlet Transform and Nonnegative Matrix Factorization

An image fusion method combining complex contourlet transform(CCT) with nonnegative matrix factorization(NMF) is proposed in this paper.After two images are decomposed by CCT,NMF is applied to their highand low-frequency components,respectively,and finally an image is synthesized.Subjective-visual-quality of the image fusion result is compared with those of the image fusion methods based on NMF and the combination of wavelet /contourlet /nonsubsampled contourlet with NMF.The experimental results are evaluated quantitatively,and the running time is also contrasted.It is shown that the proposed image fusion method can gain larger information entropy,standard deviation and mean gradient,which means that it can better integrate featured information from all source images,avoid background noise and promote space clearness in the fusion image effectively.

Area-Correlated Spectral Unmixing Based on Bayesian Nonnegative Matrix Factorization

To solve the problem of the spatial correlation for adjacent areas in traditional spectral unmixing methods, we propose an area-correlated spectral unmixing method based on Bayesian nonnegative matrix factorization. In the proposed me-thod, the spatial correlation property between two adjacent areas is expressed by a priori probability density function, and the endmembers extracted from one of the adjacent areas are used to estimate the priori probability density func-tions of the endmembers in the current area, which works as a type of constraint in the iterative spectral unmixing process. Experimental results demonstrate the effectivity and efficiency of the proposed method both for synthetic and real hyperspectral images, and it can provide a useful tool for spatial correlation and comparation analysis between ad-jacent or similar areas.

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.

Vertex centrality of complex networks based on joint nonnegative matrix factorization and graph embedding

Finding crucial vertices is a key problem for improving the reliability and ensuring the effective operation of networks,solved by approaches based on multiple attribute decision that suffer from ignoring the correlation among each attribute or the heterogeneity between attribute and structure. To overcome these problems, a novel vertex centrality approach, called VCJG, is proposed based on joint nonnegative matrix factorization and graph embedding. The potential attributes with linearly independent and the structure information are captured automatically in light of nonnegative matrix factorization for factorizing the weighted adjacent matrix and the structure matrix, which is generated by graph embedding. And the smoothness strategy is applied to eliminate the heterogeneity between attributes and structure by joint nonnegative matrix factorization. Then VCJG integrates the above steps to formulate an overall objective function, and obtain the ultimately potential attributes fused the structure information of network through optimizing the objective function. Finally, the attributes are combined with neighborhood rules to evaluate vertex's importance. Through comparative analyses with experiments on nine real-world networks, we demonstrate that the proposed approach outperforms nine state-of-the-art algorithms for identification of vital vertices with respect to correlation, monotonicity and accuracy of top-10 vertices ranking.

Nonnegative Matrix Factorization with Zellner Penalty

Nonnegative matrix factorization (NMF) is a relatively new unsupervised learning algorithm that decomposes a nonnegative data matrix into a parts-based, lower dimensional, linear representation of the data. NMF has applications in image processing, text mining, recommendation systems and a variety of other fields. Since its inception, the NMF algorithm has been modified and explored by numerous authors. One such modification involves the addition of auxiliary constraints to the objective function of the factorization. The purpose of these auxiliary constraints is to impose task-specific penalties or restrictions on the objective function. Though many auxiliary constraints have been studied, none have made use of data-dependent penalties. In this paper, we propose Zellner nonnegative matrix factorization (ZNMF), which uses data-dependent auxiliary constraints. We assess the facial recognition performance of the ZNMF algorithm and several other well-known constrained NMF algorithms using the Cambridge ORL database.

Cold-Start Link Prediction via Weighted Symmetric Nonnegative Matrix Factorization with Graph Regularization

Link prediction has attracted wide attention among interdisciplinaryresearchers as an important issue in complex network. It aims to predict the missing links in current networks and new links that will appear in future networks.Despite the presence of missing links in the target network of link prediction studies, the network it processes remains macroscopically as a large connectedgraph. However, the complexity of the real world makes the complex networksabstracted from real systems often contain many isolated nodes. This phenomenon leads to existing link prediction methods not to efficiently implement the prediction of missing edges on isolated nodes. Therefore, the cold-start linkprediction is favored as one of the most valuable subproblems of traditional linkprediction. However, due to the loss of many links in the observation network, thetopological information available for completing the link prediction task is extremely scarce. This presents a severe challenge for the study of cold-start link prediction. Therefore, how to mine and fuse more available non-topologicalinformation from observed network becomes the key point to solve the problemof cold-start link prediction. In this paper, we propose a framework for solving thecold-start link prediction problem, a joint-weighted symmetric nonnegative matrixfactorization model fusing graph regularization information, based on low-rankapproximation algorithms in the field of machine learning. First, the nonlinear features in high-dimensional space of node attributes are captured by the designedgraph regularization term. Second, using a weighted matrix, we associate the attribute similarity and first order structure information of nodes and constrain eachother. Finally, a unified framework for implementing cold-start link prediction isconstructed by using a symmetric nonnegative matrix factorization model to integrate the multiple information extracted together. Extensive experimental validationon five real networks with attributes shows that the proposed model has very goodpredictive performance when predicting missing edges of isolated nodes.

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.

基于NMF-KELM的资源环境承载力评价与预测

资源环境承载力评价与预测对区域可持续发展有重要的指导意义。本文提出了基于非负矩阵分解(NMF)和核极限学习机(KELM)的资源环境承载力评价与预测方法,在构建江西省资源环境承载力指标体系的基础上,引入NMF对2005—2020年该地区资源环境承载力状况进行量化测度和系统分析,利用加权灰关联法和全排列多边形图示法对承载力结果验证分析,建立了基于NMF-KELM的承载力预测模型并对承载力的演变趋势进行预测。研究结果表明:①2005—2020年,江西省资源环境承载力指数由0.0963提高至0.7975,整体呈波动上升趋势,高速发展的社会经济是承载力的最直接驱动力。②NMF、加权灰关联法和全排列多边形图示法三者反映的趋势和结论是一致的,NMF评价结果更客观。③环境系统成为制约江西省资源环境承载力提高的主要因素,其中万元GDP工业废气排放量是最重要的影响因素。④与BP神经网络和灰色模型相比,基于NMF-KELM的承载力预测模型拟合精度高,能够更好地预测江西省资源环境承载力的演变趋势。

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.

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.

Assessment of phytoplankton class abundance using fluorescence excitation-emission matrix by parallel factor analysis and nonnegative least squares

The feasibility of using fluorescence excitation-emission matrix(EEM) along with parallel factor analysis(PARAFAC) and nonnegative least squares(NNLS) method for the differentiation of phytoplankton taxonomic groups was investigated. Forty-one phytoplankton species belonging to 28 genera of five divisions were studied. First, the PARAFAC model was applied to EEMs, and 15 fluorescence components were generated. Second, 15 fluorescence components were found to have a strong discriminating capability based on Bayesian discriminant analysis(BDA). Third, all spectra of the fluorescence component compositions for the 41 phytoplankton species were spectrographically sorted into 61 reference spectra using hierarchical cluster analysis(HCA), and then, the reference spectra were used to establish a database. Finally, the phytoplankton taxonomic groups was differentiated by the reference spectra database using the NNLS method. The five phytoplankton groups were differentiated with the correct discrimination ratios(CDRs) of 100% for single-species samples at the division level. The CDRs for the mixtures were above 91% for the dominant phytoplankton species and above 73% for the subdominant phytoplankton species. Sixteen of the 85 field samples collected from the Changjiang River estuary were analyzed by both HPLC-CHEMTAX and the fluorometric technique developed. The results of both methods reveal that Bacillariophyta was the dominant algal group in these 16 samples and that the subdominant algal groups comprised Dinophyta, Chlorophyta and Cryptophyta. The differentiation results by the fluorometric technique were in good agreement with those from HPLC-CHEMTAX. The results indicate that the fluorometric technique could differentiate algal taxonomic groups accurately at the division level.

CUR Based Initialization Strategy for Non-Negative Matrix Factorization in Application to Hyperspectral Unmixing

Hyperspectral unmixing is a powerful tool for the remote sensing image mining. Nonnegative matrix factorization (NMF) has been adopted to deal with this issue, while the precision of unmixing is closely related with the local minimizers of NMF. We present two novel initialization strategies that is based on CUR decomposition, which is physically meaningful. In the experimental test, NMF with the new initialization method is used to unmix the urban scene which was captured by airborne visible/infrared imaging spectrometer (AVIRIS) in 1997, numerical results show that the initialization methods work well.

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.

基于Haar-NMF特征和改进SOMPNN的车辆检测算法

为解决传统基于Haar特征和自组织映射概率神经网络(SOMPNN)的车辆检测算法中存在当Haar特征向量维数过大时决策时间缓慢和因平滑因子σ单一易导致分类错误的2个不足,提出了一种用低维的Haar-NMF特征代替Haar特征和平滑因子自适应修正的改进SOMPNN(ISOMPNN)车辆检测算法.首先用非负矩阵分解对Haar特征进行降维,生成低维Haar-NMF特征;其次,以SOM输出层神经元的原型向量数作为修正因子,构建了指数函数形式的平滑因子修正函数,并以修正后的平滑因子训练SOMPNN分类器.实验结果表明,与传统的Haar+SOM PNN算法相比,采用Haar-NM F和ISOM PNN构建的车辆检测分类器在检测率、误检率和检测时间等性能指标上都获得明显提升.

基于小波变换和NMF的人脸识别方法的研究

为了克服PCA、ICA等传统方法在人脸图像特征抽取时存在速度慢、识别率低的缺点,该文提出了一种将非负矩分解思想应用于人脸特征提取的算法。利用小波变换对人脸图像进行分解,对其中包含主要信息的低频子带运用NMF构造特征子空间,在子空间内实现识别。实验结果表明,该方法实用、有效,减少了计算量,提高了系统的识别率,使识别率达到90%以上,有着广泛的研究价值和应用前景。

NMF和增强奇异值分解的自适应零水印算法

针对奇异值分解水印算法导致虚警率高、稳健性不强的问题,提出一种基于分块非负矩阵分解(NMF)和增强奇异值分解(BN-SVD)相结合的自适应零水印算法。首先将原始灰度图像进行二级离散小波变换(DWT),对变换后的二级低频子带(LL2)进行不重叠分块,并对每一个子块进行秩为r的NMF分解;然后对NMF分解得到的特征矩阵采用增强奇异值分解,依据每一个块矩阵的最大奇异值与整体最大奇异值均值的大小关系构成特征向量;利用生成的特征向量与经过Arnold变换与混沌映射双重置乱加密水印图像作异或运算生成零水印,并利用天牛须优化算法(BAS)自适应确定增强奇异值分解中最抗攻击缩放比例的参数β。实验结果表明,在虚警问题上NC值达到0.4以下,JPEG压缩、噪声、滤波、旋转、剪切以及混合攻击下,提取水印图像与原水印图像的归一化系数NC值均可达到99%以上,该方案高效地解决了虚警问题,具有较强的稳健性,能够有效地抵抗各种攻击。

基于显著性检测与HOG-NMF特征的快速行人检测方法

行人检测在机器人、驾驶辅助系统和视频监控等领域有广泛的应用,该文提出一种基于显著性检测与方向梯度直方图-非负矩阵分解(Histogram of Oriented Gradient-Non-negative Matrix Factorization,HOG-NMF)特征的快速行人检测方法。采用频谱调谐显著性检测提取显著图,并基于熵值门限进行感兴趣区域的提取;组合非负矩阵分解和方向梯度直方图生成HOG-NMF特征;采用加性交叉核支持向量机方法(Intersection Kernel Support Vector Machine,IKSVM)。该算法显著降低了特征维数,在相同的计算复杂度下明显改善了线性支持向量机的检测率。在INRIA数据库的实验结果表明,该方法对比HOG/线性SVM和HOG/RBF-SVM显著减少了检测时间,并达到了满意的检测率。