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 ap...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.展开更多
Hyperspectral imagery generally contains a very large amount of data due to hundreds of spectral bands.Band selection is often applied firstly to reduce computational cost and facilitate subsequent tasks such as land-...Hyperspectral imagery generally contains a very large amount of data due to hundreds of spectral bands.Band selection is often applied firstly to reduce computational cost and facilitate subsequent tasks such as land-cover classification and higher level image analysis.In this paper,we propose a new band selection algorithm using sparse nonnegative matrix factorization (sparse NMF).Though acting as a clustering method for band selection,sparse NMF need not consider the distance metric between different spectral bands,which is often the key step for most common clustering-based band selection methods.By imposing sparsity on the coefficient matrix,the bands' clustering assignments can be easily indicated through the largest entry in each column of the matrix.Experimental results showed that sparse NMF provides considerable insight into the clustering-based band selection problem and the selected bands are good for land-cover classification.展开更多
Nonnegative Matrix Factorization(NMF)is a powerful technique to perform dimension reduction and pattern recognition through single-layer data representation learning.However,deep learning networks,with their carefully...Nonnegative Matrix Factorization(NMF)is a powerful technique to perform dimension reduction and pattern recognition through single-layer data representation learning.However,deep learning networks,with their carefully designed hierarchical structure,can combine hidden features to form more representative features for pattern recognition.In this paper,we proposed sparse deep NMF models to analyze complex data for more accurate classification and better feature interpretation.Such models are designed to learn localized features or generate more discriminative representations for samples in distinct classes by imposing L1-norm penalty on the columns of certain factors.By extending a one-layer model into a multilayer model with sparsity,we provided a hierarchical way to analyze big data and intuitively extract hidden features due to nonnegativity.We adopted the Nesterov’s accelerated gradient algorithm to accelerate the computing process.We also analyzed the computing complexity of our frameworks to demonstrate their efficiency.To improve the performance of dealing with linearly inseparable data,we also considered to incorporate popular nonlinear functions into these frameworks and explored their performance.We applied our models using two benchmarking image datasets,and the results showed that our models can achieve competitive or better classification performance and produce intuitive interpretations compared with the typical NMF and competing multilayer models.展开更多
Aiming at the low recognition accuracy of non-negative matrix factorization(NMF)in practical application,an improved spare graph NMF(New-SGNMF)is proposed in this paper.New-SGNMF makes full use of the inherent geometr...Aiming at the low recognition accuracy of non-negative matrix factorization(NMF)in practical application,an improved spare graph NMF(New-SGNMF)is proposed in this paper.New-SGNMF makes full use of the inherent geometric structure of image data to optimize the basis matrix in two steps.A threshold value s was first set to judge the threshold value of the decomposed base matrix to filter the redundant information in the data.Using L2 norm,sparse constraints were then implemented on the basis matrix,and integrated into the objective function to obtain the objective function of New-SGNMF.In addition,the derivation process of the algorithm and the convergence analysis of the algorithm were given.The experimental results on COIL20,PIE-pose09 and YaleB database show that compared with K-means,PCA,NMF and other algorithms,the proposed algorithm has higher accuracy and normalized mutual information.展开更多
提出一种基于交替方向乘子法的(Alternating Direction Method of Multipliers,ADMM)稀疏非负矩阵分解语音增强算法,该算法既能克服经典非负矩阵分解(Nonnegative Matrix Factorization,NMF)语音增强算法存在收敛速度慢、易陷入局部最...提出一种基于交替方向乘子法的(Alternating Direction Method of Multipliers,ADMM)稀疏非负矩阵分解语音增强算法,该算法既能克服经典非负矩阵分解(Nonnegative Matrix Factorization,NMF)语音增强算法存在收敛速度慢、易陷入局部最优等问题,也能发挥ADMM分解矩阵具有的强稀疏性。算法分为训练和增强两个阶段:训练时,采用基于ADMM非负矩阵分解算法对噪声频谱进行训练,提取噪声字典,保存其作为增强阶段的先验信息;增强时,通过稀疏非负矩阵分解算法,从带噪语音频谱中对语音字典和语音编码进行估计,重构原始干净的语音,实现语音增强。实验表明,该算法速度更快,增强后语音的失真更小,尤其在瞬时噪声环境下效果显著。展开更多
文摘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.
基金Project (No.60872071) supported by the National Natural Science Foundation of China
文摘Hyperspectral imagery generally contains a very large amount of data due to hundreds of spectral bands.Band selection is often applied firstly to reduce computational cost and facilitate subsequent tasks such as land-cover classification and higher level image analysis.In this paper,we propose a new band selection algorithm using sparse nonnegative matrix factorization (sparse NMF).Though acting as a clustering method for band selection,sparse NMF need not consider the distance metric between different spectral bands,which is often the key step for most common clustering-based band selection methods.By imposing sparsity on the coefficient matrix,the bands' clustering assignments can be easily indicated through the largest entry in each column of the matrix.Experimental results showed that sparse NMF provides considerable insight into the clustering-based band selection problem and the selected bands are good for land-cover classification.
基金supported by the National Natural Science Foundation of China(Nos.11661141019 and 61621003)the National Ten Thousand Talent Program for Young Topnotch Talents+1 种基金Chinese Academy Science(CAS)Frontier Science Research Key Project for Top Young Scientist(No.QYZDB-SSW-SYS008)the Key Laboratory of Random Complex Structures and Data Science,CAS(No.2008DP173182).
文摘Nonnegative Matrix Factorization(NMF)is a powerful technique to perform dimension reduction and pattern recognition through single-layer data representation learning.However,deep learning networks,with their carefully designed hierarchical structure,can combine hidden features to form more representative features for pattern recognition.In this paper,we proposed sparse deep NMF models to analyze complex data for more accurate classification and better feature interpretation.Such models are designed to learn localized features or generate more discriminative representations for samples in distinct classes by imposing L1-norm penalty on the columns of certain factors.By extending a one-layer model into a multilayer model with sparsity,we provided a hierarchical way to analyze big data and intuitively extract hidden features due to nonnegativity.We adopted the Nesterov’s accelerated gradient algorithm to accelerate the computing process.We also analyzed the computing complexity of our frameworks to demonstrate their efficiency.To improve the performance of dealing with linearly inseparable data,we also considered to incorporate popular nonlinear functions into these frameworks and explored their performance.We applied our models using two benchmarking image datasets,and the results showed that our models can achieve competitive or better classification performance and produce intuitive interpretations compared with the typical NMF and competing multilayer models.
基金This work was supported by the National Natural Science Foundation of China(Grant No.61501005)the Anhui Natural Science Foundation(Grant No.1608085 MF 147)+2 种基金the Natural Science Foundation of Anhui Universities(Grant No.KJ2016A057)the Industry Collaborative Innovation Fund of Anhui Polytechnic University and Jiujiang District(Grant No.2021cyxtb4)the Science Research Project of Anhui Polytechnic University(Grant No.Xjky2020120).
文摘Aiming at the low recognition accuracy of non-negative matrix factorization(NMF)in practical application,an improved spare graph NMF(New-SGNMF)is proposed in this paper.New-SGNMF makes full use of the inherent geometric structure of image data to optimize the basis matrix in two steps.A threshold value s was first set to judge the threshold value of the decomposed base matrix to filter the redundant information in the data.Using L2 norm,sparse constraints were then implemented on the basis matrix,and integrated into the objective function to obtain the objective function of New-SGNMF.In addition,the derivation process of the algorithm and the convergence analysis of the algorithm were given.The experimental results on COIL20,PIE-pose09 and YaleB database show that compared with K-means,PCA,NMF and other algorithms,the proposed algorithm has higher accuracy and normalized mutual information.
文摘提出一种基于交替方向乘子法的(Alternating Direction Method of Multipliers,ADMM)稀疏非负矩阵分解语音增强算法,该算法既能克服经典非负矩阵分解(Nonnegative Matrix Factorization,NMF)语音增强算法存在收敛速度慢、易陷入局部最优等问题,也能发挥ADMM分解矩阵具有的强稀疏性。算法分为训练和增强两个阶段:训练时,采用基于ADMM非负矩阵分解算法对噪声频谱进行训练,提取噪声字典,保存其作为增强阶段的先验信息;增强时,通过稀疏非负矩阵分解算法,从带噪语音频谱中对语音字典和语音编码进行估计,重构原始干净的语音,实现语音增强。实验表明,该算法速度更快,增强后语音的失真更小,尤其在瞬时噪声环境下效果显著。
