The nonnegative tensor （matrix） factorization finds more and more applications in various disciplines including machine learning, data mining, and blind source separation, etc. In computation, the optimization probl...The nonnegative tensor （matrix） factorization finds more and more applications in various disciplines including machine learning, data mining, and blind source separation, etc. In computation, the optimization problem involved is solved by alternatively minimizing one factor while the others are fixed. To solve the subproblem efficiently, we first exploit a variable regularization term which makes the subproblem far from ill-condition. Second, an augmented Lagrangian alternating direction method is employed to solve this convex and well-conditioned regularized subproblem, and two accelerating skills are also implemented. Some preliminary numerical experiments are performed to show the improvements of the new method.展开更多
Orthogonal nonnegative matrix factorization(ONMF)is widely used in blind image separation problem,document classification,and human face recognition.The model of ONMF can be efficiently solved by the alternating direc...Orthogonal nonnegative matrix factorization(ONMF)is widely used in blind image separation problem,document classification,and human face recognition.The model of ONMF can be efficiently solved by the alternating direction method of multipliers and hierarchical alternating least squares method.When the given matrix is huge,the cost of computation and communication is too high.Therefore,ONMF becomes challenging in the large-scale setting.The random projection is an efficient method of dimensionality reduction.In this paper,we apply the random projection to ONMF and propose two randomized algorithms.Numerical experiments show that our proposed algorithms perform well on both simulated and real data.展开更多
This paper introduces an algorithm for the nonnegative matrix factorization-and-completion problem, which aims to find nonnegative low-rank matrices X and Y so that the product XY approximates a nonnegative data matri...This paper introduces an algorithm for the nonnegative matrix factorization-and-completion problem, which aims to find nonnegative low-rank matrices X and Y so that the product XY approximates a nonnegative data matrix M whose elements are partially known （to a certain accuracy）. This problem aggregates two existing problems： （i） nonnegative matrix factorization where all entries of M are given, and （ii） low-rank matrix completion where non- negativity is not required. By taking the advantages of both nonnegativity and low-rankness, one can generally obtain superior results than those of just using one of the two properties. We propose to solve the non-convex constrained least-squares problem using an algorithm based on tile classical alternating direction augmented Lagrangian method. Preliminary convergence properties of the algorithm and numerical simulation results are presented. Compared to a recent algorithm for nonnegative matrix factorization, the proposed algorithm produces factorizations of similar quality using only about half of the matrix entries. On tasks of recovering incomplete grayscale and hyperspeetral images, the proposed algorithm yields overall better qualities than those produced by two recent matrix-completion algorithms that do not exploit nonnegativity.展开更多
该文提出一种基于非负张量分解的高光谱图像压缩算法。首先将高光谱图像的每个谱段进行2维离散5／3小波变换，消除高光谱图像的空间冗余。然后将所有谱段的每级小波变换的4个小波子带看作为4个张量。对每个小波子带张量采用改进HALS（Hi...该文提出一种基于非负张量分解的高光谱图像压缩算法。首先将高光谱图像的每个谱段进行2维离散5／3小波变换，消除高光谱图像的空间冗余。然后将所有谱段的每级小波变换的4个小波子带看作为4个张量。对每个小波子带张量采用改进HALS（Hierarchical Alternating Least Squares）算法进行非负分解，来消除光谱冗余和空间残余冗余，同时保护了光谱信息。最后，将分解的因子矩阵进行熵编码。实验结果表明，该文提出的压缩算法具有良好压缩性能，在压缩比32：1-4：1范围内，平均信噪比高于40dB，与传统高光谱图像压缩算法比较，平均峰值信噪比提高了1．499dB。有效地提高了高光谱图像压缩算法的压缩性能和保护了光谱信息。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The nonnegative tensor （matrix） factorization finds more and more applications in various disciplines including machine learning, data mining, and blind source separation, etc. In computation, the optimization problem involved is solved by alternatively minimizing one factor while the others are fixed. To solve the subproblem efficiently, we first exploit a variable regularization term which makes the subproblem far from ill-condition. Second, an augmented Lagrangian alternating direction method is employed to solve this convex and well-conditioned regularized subproblem, and two accelerating skills are also implemented. Some preliminary numerical experiments are performed to show the improvements of the new method.
基金the National Natural Science Foundation of China(No.11901359)Shandong Provincial Natural Science Foundation(No.ZR2019QA017)。
文摘Orthogonal nonnegative matrix factorization(ONMF)is widely used in blind image separation problem,document classification,and human face recognition.The model of ONMF can be efficiently solved by the alternating direction method of multipliers and hierarchical alternating least squares method.When the given matrix is huge,the cost of computation and communication is too high.Therefore,ONMF becomes challenging in the large-scale setting.The random projection is an efficient method of dimensionality reduction.In this paper,we apply the random projection to ONMF and propose two randomized algorithms.Numerical experiments show that our proposed algorithms perform well on both simulated and real data.
文摘This paper introduces an algorithm for the nonnegative matrix factorization-and-completion problem, which aims to find nonnegative low-rank matrices X and Y so that the product XY approximates a nonnegative data matrix M whose elements are partially known （to a certain accuracy）. This problem aggregates two existing problems： （i） nonnegative matrix factorization where all entries of M are given, and （ii） low-rank matrix completion where non- negativity is not required. By taking the advantages of both nonnegativity and low-rankness, one can generally obtain superior results than those of just using one of the two properties. We propose to solve the non-convex constrained least-squares problem using an algorithm based on tile classical alternating direction augmented Lagrangian method. Preliminary convergence properties of the algorithm and numerical simulation results are presented. Compared to a recent algorithm for nonnegative matrix factorization, the proposed algorithm produces factorizations of similar quality using only about half of the matrix entries. On tasks of recovering incomplete grayscale and hyperspeetral images, the proposed algorithm yields overall better qualities than those produced by two recent matrix-completion algorithms that do not exploit nonnegativity.
文摘该文提出一种基于非负张量分解的高光谱图像压缩算法。首先将高光谱图像的每个谱段进行2维离散5／3小波变换，消除高光谱图像的空间冗余。然后将所有谱段的每级小波变换的4个小波子带看作为4个张量。对每个小波子带张量采用改进HALS（Hierarchical Alternating Least Squares）算法进行非负分解，来消除光谱冗余和空间残余冗余，同时保护了光谱信息。最后，将分解的因子矩阵进行熵编码。实验结果表明，该文提出的压缩算法具有良好压缩性能，在压缩比32：1-4：1范围内，平均信噪比高于40dB，与传统高光谱图像压缩算法比较，平均峰值信噪比提高了1．499dB。有效地提高了高光谱图像压缩算法的压缩性能和保护了光谱信息。
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。
