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.

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.

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.

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.

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.

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.

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.

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。

基于NMF图像重构的人脸识别

由传统的人脸识别方法产生的人脸特征子空间通常是由人脸库中所有训练样本产生的一个通用子空间,该空间更多地包含了所有人脸样本的共性特征,而忽略了个性特征。该文提出一种基于NMF图像重构的方法,以单个人的训练样本集获取其人脸特征子空间,将识别图像向每一个特征子空间中进行映射及重构,并以重构图像的误差作为判据实现人脸识别。在ORL标准人脸库进行的计算机仿真证实了该方法的有效性。

基于约束NMF的欠定盲信号分离算法

提出一种约束非负矩阵分解方法用于解决欠定盲信号分离问题。非负矩阵分解直接用于求解欠定盲信号分离时,分解结果不唯一,无法正确分离源信号。在基本非负矩阵分解算法基础上,对分解得到的混合矩阵施加行列式约束,保证分解结果的唯一性;对分解得到的源信号同时施加稀疏性约束和最小相关约束,实现混合信号的唯一分解,提高源信号分离性能。仿真实验证明了算法的有效性。

基于行列式和稀疏性约束的NMF的欠定盲分离方法

非负矩阵分解(NMF)要求分解得到的左矩阵为列满秩,这限制了它在欠定盲分离(UBSS)中的应用。针对此问题,提出基于带行列式和稀疏性约束的NMF的欠定盲分离算法———DSNMF。该算法在基本NMF的基础上,对NMF得到的左矩阵进行行列式准则约束,对右矩阵进行稀疏性约束,平衡了重构误差、混合矩阵的唯一性以及分离信号的稀疏特性,实现了对混合矩阵和源信号的欠定盲分离。仿真结果表明,在源信号稀疏性较好和较差两种情况下,DSNMF都能取得良好的分离效果。

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。

基于（2D）^2NMF及其改进算法的人脸识别

非负矩阵分解(NMF)是基于部分的特征提取方法,能够克服局部遮挡和光照问题,在图像识别任务中效果较好。然而传统算法中,NMF提取的特征是非正交的,且二维图像常被向量化处理,不仅丢失一些结构信息,还导致了数据的高维,不利于提高识别精度和速度。利用图像矩阵取代传统的图像向量表示,提出新的(2D)2NMF方法提取二维图像特征,并通过特征正交化和图像变形等措施,改善了算法性能。人脸识别实验表明,上述措施能够有效提高识别的精度和速度。

LPQ与NMF特征融合的人脸识别

提出一种融合局部相位量化(LPQ)和非负矩阵分解(NMF)进行人脸识别的方法.该方法首先采用LPQ算子提取分块人脸图像的LPQ直方图序列(LPQHS),根据每块的贡献度,得到权重的直方图序列(Weight LPQHS),然后采用NMF方法提取其非负子空间及其系数矩阵,最后根据最近邻原则进行识别.在AR和YALE标准人脸数据库上的实验结果表明,该方法具有较高的识别率.

基于小波域NMF特征提取的SAR图像目标识别方法

该文提出了一种基于小波域非负矩阵分解特征提取的合成孔径雷达图像目标识别方法。该方法对图像二维离散小波分解后提取低频子带图像,用非负矩阵分解对低频子带图像提取特征向量作为目标的特征,利用支持向量机进行分类完成目标识别。将该方法用于对MSTAR数据中三类目标识别,识别率最高可达97.51%,明显提高了目标的正确识别率。实验结果表明,该方法是一种有效的合成孔径雷达图像特征提取与目标识别方法。

基于约束随机分块的NMF图像哈希算法

基于非负矩阵分解(Non-negative Matrix Factorization,NMF)的图像哈希(image hashing)算法对图像有损压缩,低通滤波、尺度拉伸等处理具有很好的稳健性,但对图像旋转比较敏感。为此,该文在对NMF哈希算法的分块模式进行深入研究的基础上,提出一种可抗旋转攻击的NMF图像哈希算法。该方法通过对随机分块的区域进行限制,并选择合适的分块尺寸来减轻旋转攻击对图像造成的不良影响,从而提高了特征的旋转稳健性。实验表明,所提出的图像哈希算法在保持原NMF哈希算法对其它攻击稳健性的同时,能有效地抵抗旋转攻击。

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Fisher块对角LNMF的彩色人脸识别

为提高对彩色人脸的识别率,提出一种基于Fisher块对角局部非负矩阵分解(LNMF)的识别算法。采用块对角矩阵编码彩色图像不同通道的颜色信息,在LNMF算法中增加块对角约束和Fisher判别约束,对不同通道的颜色信息同时进行计算并融入人脸的类别信息,用于提取人脸特征。在CVL和PIE彩色人脸数据库上的实验结果验证了该识别算法的有效性。

基于约束NMF的盲源分离算法

非负矩阵分解(NMF)是解决非独立源信号混合的盲分离的另一条新途径。该文提出一种基于约束NMF的盲源分离算法,在对NMF估计得到的源信号施加最小相关约束的基础上,对混合矩阵估计施加行列式约束,实现NMF的唯一分解。与已有算法相比,本算法放宽了对混合矩阵的稀疏性要求,大幅提高了信号分离质量。该算法仍适用于独立源信号分离问题。

基于RST-NMF模型的微震信号时频分析和识别

针对微震信号难以精确识别的问题,提出一种基于RST-NMF微震信号时频分析和分类方法。首先对微震信号进行S变换得到时频矩阵,然后在频率方向上进行重排,再借助非负矩阵分解技术得到时、频域的分解向量,从中提取宏观、微观统计量构造信号的特征空间,最后采用SVM进行分类。在三道沟井田的试验结果表明,RST时频分析方法对频域分散的能量团有很好的聚集性,时频矩阵经NMF分解最大程度上获取微震信号的局部特征和内在联系,提取分解向量的宏观和微观统计量保证了信号特征空间的完备性,有效地避免了分类时过拟合的发生,分类准确率达到了94%。