Semi-Supervised Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a popular method for low-rank approximation of nonnegative matrix, providing a useful tool for representation learning that is valuable for clustering and classification. When a portion of data are labeled, the performance of clustering or classification is improved if the information on class labels is incorporated into NMF. To this end, we present semi-supervised NMF (SSNMF), where we jointly incorporate the data matrix and the (partial) class label matrix into NMF. We develop multiplicative updates for SSNMF to minimize a sum of weighted residuals, each of which involves the nonnegative 2-factor decomposition of the data matrix or the label matrix, sharing a common factor matrix. Experiments on document datasets and EEG datasets in BCI competition confirm that our method improves clustering as well as classification performance, compared to the standard NMF, stressing that semi-supervised NMF yields semi-supervised feature extraction.     

Nonnegative Matrix and Tensor Factorization

In these lecture notes, the authors have outlined several approaches to solve a NMF/NTF problem. The following main conclusions can be drawn: 1) Multiplicative algorithms are not necessary the best approaches for NMF, especially if data representations are not very redundant or sparse. 2) Much better performance can be achieved using the FP-ALS (especially for large-scale problems), IPC, and QN methods. 3) To achieve high performance it is quite important to use the multilayer structure with multistart initialization conditions. 4) To estimate physically meaningful nonnegative components it is often necessary to use some a priori knowledge and impose additional constraints or regularization terms (to control sparsity, boundness, continuity or smoothness of the estimated nonnegative components).     

Notes on n-D Polynomial Matrix Factorizations

This paper discusses a relationship between the prime factorizability of a normal full rank n-D ( n>2) polynomial matrix and its reduced minors. Two conjectures regarding the n-D polynomial matrix prime factorization problem are posed, and a partial solution to one of the conjectures is provided. Another related open problem of factorizing an n-D polynomial matrix that is not of normal full rank as a product of two n-D polynomial matrices of smaller size is also considered, and a partial solution to this problem is presented. An illustrative example is worked out in details.     

非负矩阵分解算法综述

本文介绍了非负矩阵分解(Non-negative Matrix Factorization,NMF)的基本原理和性质,将现有NMF算法分为了基于基本NMF模型的算法和基于改进NMF模型的算法两大类,在此基础上较为系统地分析、总结和比较了它们的构造原则、应用特点以及存在的问题,最后预测和分析了未来NMF算法研究的可能方向.     

基于非负矩阵分解的SAR图像目标识别

 特征提取是合成孔径雷达自动目标识别的关键技术,同时也是难点问题之一。本文提出了一种基于非负矩阵分解算法与Fisher线性判别方法的合成孔径雷达图像目标识别的方法,通过基于基向量非负加权组合的形式构建SAR目标图像,能充分利用目标的局部空间结构信息提取目标特征信息实现目标识别。首先将水平集分割预处理后的SAR目标图像样本构成初始矩阵,然后利用非负矩阵分解后得到的权向量作为目标图像的特征向量,再通过依据Fisher线性判别构成的分类器,实现对MSTAR数据中3类目标的识别,并与目前已有的几种典型方案进行对比。试验结果表明该方法是可行且有效的,并能够明显提高对目标识别的稳定性和正确率。     

Coupled Matrix Factorization for Question Similarity

Community question answering (CQA) has provided an increasingly popular service where users ask and answer questions and access historical question-answer pairs. As a fundamental task in CQA, question similarity measure is to compute the similarity between the queried question and the historical questions which have been solved by other users. We mine and use the most important semantic features as the semantic repre-sentation of questions, and try to incorporate the couplings of semantic features into vector space model. We propose Coupled question similarity (CQS) model, and compute the similarity in matrix factorization framework. Experi-ments conducted on real CQA data sets demonstrate that with the incorporation of such couplings, the performance of sentence similarity is improved compared to a variety of baseline methods significantly.     

Further Results on n-D Polynomial Matrix Factorizations

In this paper, some new results on zero prime factorization for a normal full rank n-D (n>2) polynomial matrix are presented. Assume that d is the greatest common divisor (g.c.d.) of the maximal order minors of a given n-D polynomial matrix F ₁. It is shown that if there exists a submatrix F of F ₁, such that the reduced minors of F have no common zeros, and the g.c.d. of the maximal order minors of F equals d, then F ₁ admits a zero right prime (ZRP) factorization if and only if F admits a ZRP factorization. A simple ZRP factorizability of a class of n-D polynomial matrices based on reduced minors is given. An advantage is that the ZRP factorizability can be tested before carrying out the actual matrix factorization. An example is illustrated.     

基于矩阵分解的代数几何码的译码

本文给出了基于矩阵分解的代数几何码的译码算法，该算法可对任意错误个数不超过［（ｄ－１）／２］的接收码字进行译码，且该算法简单，便于理解与实现。     

不完全非负矩阵分解的加速算法

非负矩阵分解(NMF)已成为数据分析与处理的一种日益流行的方法.当数据矩阵不完全时,可用加权非负矩阵分解(WNMF)来分解矩阵.但是在WNMF算法中,对于给定的搜索方向,步长的选取一般来说不是最优的.本文研究了不完全非负矩阵分解(INMF)问题,提出了加速算法(AINMF).首先,将INMF问题转化为交替地求解两个非负...     

基于非负矩阵分解的多波段SPOT图像融合及其应用

SPOT遥感图像多光谱波段信息丰富,在土地覆盖、环境变化等诸多领域中得到广泛应用。图像融合近几年来成为学术界研究的热点,可以有效去除多光谱图像中的冗余,保留有用信息。对不同时段多光谱图像的融合进行地物变化检测,在灾害监测工作中具有重要的应用价值。文章利用基于非负矩阵分解的分时融合方法,对不同时段SPOT多波段图像进行融合,通过构造差值影像对变化区域进行检测。利用本文方法得到的图像可以清晰地表示出目标的变化区域,且正确率较高。结果表明,首先利用非负矩阵分解对不同时段图像进行融合,可以分别得到更为准确的融合图像,从而提高变化检测结果的精度。实验结果与传统方法进行了分析对比,证明了该方法的有效性。      

改进的非负矩阵分解语音增强算法

本文提出了一种改进的非负矩阵分解语音增强算法,该算法可分为训练和增强两部分。首先,为了降低训练复杂度,采用卷积非负矩阵分解只提取噪声字典。增强时,考虑语音信号稀疏性比噪声信号稀疏性强,通过稀疏非负矩阵分解重构出语音幅度谱,采用交替方向乘子法进行优化迭代,克服了经典乘性迭代易陷入局部最优、分母只能收敛到零极限等问题。最后,基于算法融合的思想,将重构的语音幅度谱与谱减法、最小均方误差幅度谱估计得到的幅度谱进行加权融合。仿真实验中,在10种不同噪声环境中,通过多种评价标准证明所提算法能取得较好的增强效果。      

基于非负矩阵分解的频谱感知技术研究

为了提高认知无线电系统中低信噪比条件下的频谱感知性能,提出了基于非负矩阵分解的频谱感知方法。在无需知道被感知信号的先验信息的条件下,将原始信号进行短时傅里叶变换后,利用非负矩阵分解的噪声与信号之间的特征矩阵存在的差异性,将特征矩阵作为检测统计量进行频谱感知。仿真结果表明,基于非负矩阵分解的频谱感知方法在低信噪比条件下,具有较传统的能量检测方法与循环平稳检测方法更优的感知性能。     

一种基于规范矩阵因式分解协同过滤推荐模型的并行改进

基于矩阵因式分解的协同过滤推荐模型具有很高的推荐精度和可扩展性,而其中大多数都是基于串行训练过程构造参数的,如能将其训练过程并行化,能进一步提高可扩展性.为解决上述问题,该文提出一种基于规范矩阵因式分解的协同过滤推荐(RMF)模型的并行改进(P-RMF)模型.P-RMF 模型应用交替随机梯度下降法取代随机梯度下降法训练参数,从而消除用户特征和项目特征在训练过程中的相互依赖,实现训练过程的并行化改进.实验表明,对比现有同类模型,P-RMF 模型在求解协同过滤推荐问题时,具有更快的速度和可扩展性.     

基于稀疏约束的SAR目标特征提取方法研究

特征提取是合成孔径雷达目标识别关键技术与核心任务。为了更好地提取目标特征,稀疏约束将被添加在非负矩阵分解法中,并应用于图像目标特征提取,通过利用稀疏约束的非负矩阵分解方法对sAR目标图像进行分解,构建具有稀疏性的目标特征矢量,提高了特征矢量的类内相似性与类间差异性。利用基于支持向量机的分类方法对MSTAR数据进行目标识别试验,试验结果表明,添加稀疏约束的NMF方法与PCA、ICA以及一般NMF特征提取方法相比,能够显著提高目标识别的稳定性和准确率。     

松弛耦合非负矩阵分解的低分辨率人脸识别算法

针对实际监控场景中经常遇到的人脸图像分辨率较低的问题,本文提出了一种利用耦合非负矩阵分解并保持系数松弛的低分辨率人脸识别算法（Relaxed Coupled Nonnegative Matrix Factorization,后文简称RCNMF）。首先,对高低分辨率人脸图像进行非负矩阵矩阵分解（nonnegative matrix factorization,后文简称NMF）,在分解的同时保持组合系数近似一致,从而得到高低分辨率图像的基矩阵。然后,通过低分辨率图像的基矩阵提取训练和测试样本的特征。最后进行识别。实验结果验证了与其他几种基于耦合映射的低分辨率人脸识别方法相比,RCNMF算法的识别性能更好。同时通过实验验证了RCNMF算法的收敛性。      

Nonnegative Matrix Factorization Applied to Nonlinear Speech and Image Cryptosystems

Nonnegative matrix factorization (NMF) is widely used in signal separation and image compression. Motivated by its successful applications, we propose a new cryptosystem based on NMF, where the nonlinear mixing (NLM) model with a strong noise is introduced for encryption and NMF is used for decryption. The security of the cryptosystem relies on following two facts: 1) the constructed multivariable nonlinear function is not invertible; 2) the process of NMF is unilateral, if the inverse matrix of the constructed linear mixing matrix is not nonnegative. Comparing with Lin's method (2006) that is a theoretical scheme using one-time Padding in the cryptosystem, our cipher can be used repeatedly for the practical request, i.e., multitme padding is used in our cryptosystem. Also, there is no restriction on statistical characteristics of the ciphers and the plaintexts. Thus, more signals can be processed (successfully encrypted and decrypted), no matter they are correlative, sparse, or Gaussian. Furthermore, instead of the number of zero-crossing-based method that is often unstable in encryption and decryption, an improved method based on the kurtosis of the signals is introduced to solve permutation ambiguities in waveform reconstruction. Simulations are given to illustrate security and availability of our cryptosystem.      

Analysis of the Security of Perceptual Image Hashing Based on Non-Negative Matrix Factorization

In this letter, we analyze the security of a perceptual image hashing technique based on non-negative matrix factorization which was recently proposed and reported in the literature. We theoretically demonstrate that, although the technique uses different secret keys in subsequent stages, the first key plays an essential role to secure the hashing system. We next act as an attacker and propose a technique to estimate the secret key. Extensive experiments support our theoretical analysis and validate the proposed key estimation technique.      

引入角色的三维访问矩阵模型

传统的主体-客体访问矩阵模型都是基于特定的授权策略,将主／客体与标识或属性一一绑定实现,通用性和可扩展性不高。文章通过引入角色维,提出一种与策略无关的主体-角色-权限三维矩阵模型,可以很好地解决上述问题。