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
近年来,基于张量补全的频谱制图得到了广泛研究.目前用于频谱制图的张量补全算法大多隐含地假设张量具有平衡特性,而对于非平衡张量,难以利用其低秩性估计完整的张量信息,导致补全算法性能受损.本文提出基于重叠Ket增强(Overlapping Ket...近年来,基于张量补全的频谱制图得到了广泛研究.目前用于频谱制图的张量补全算法大多隐含地假设张量具有平衡特性,而对于非平衡张量,难以利用其低秩性估计完整的张量信息,导致补全算法性能受损.本文提出基于重叠Ket增强(Overlapping Ket Augmentation,OKA)和张量列车(Tensor Train,TT)的非平衡频谱制图算法,以解决非平衡张量在应用传统张量补全算法时性能下降的问题.首先使用OKA将低阶高维张量表示为高阶低维张量,在无信息损耗的情况下解决非平衡张量无法利用其低秩性进行张量补全的问题;然后使用TT矩阵化得到较平衡的矩阵,在维度较平衡条件下提高补全算法的精确度;最后利用高阶低维张量的低秩性,使用并行矩阵分解或基于F范数的无奇异值分解(Singular Value Decomposition Free,SVDFree)算法完成张量补全.仿真结果表明,针对非平衡张量,所提方案与现有的张量补全算法相比,可以获得更精确的无线电地图,同时所提SVDFree算法具有更低的计算复杂度.展开更多
对实时车辆流量、平均车道占用率等各种交通监控数据的完整获取,是建设智能交通系统、提高交通管理运行效率的重要基础。文章提出一种融合类信息的函数型矩阵填充方法(Functional Matrix Completion Method with Class Information,CFMC...对实时车辆流量、平均车道占用率等各种交通监控数据的完整获取,是建设智能交通系统、提高交通管理运行效率的重要基础。文章提出一种融合类信息的函数型矩阵填充方法(Functional Matrix Completion Method with Class Information,CFMC)。在函数型数据分析框架下,基于非负矩阵分解构造函数型矩阵填充模型,在此基础上通过聚类划分引入样本类信息,借助类内样本相关性插补缺失值,并采用自加权集成学习算法动态赋权计算得到最终插补值。在公共交通数据集PeMS上进行插补实验,结果表明:当缺失率为15%~70%时,CFMC方法相较于K近邻算法、MICE、PACE等10种插补方法,均方根误差(RMSE)、平均绝对误差(MAE)和平均绝对百分比误差(MAPE)分别降低了10.75%~81.69%、0.34%~84.48%和12.5%~81.08%,且耗时可控。所提CFMC方法插补精度高、鲁棒性好,能够保证插补的有效性和准确性。展开更多
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.
文摘近年来,基于张量补全的频谱制图得到了广泛研究.目前用于频谱制图的张量补全算法大多隐含地假设张量具有平衡特性,而对于非平衡张量,难以利用其低秩性估计完整的张量信息,导致补全算法性能受损.本文提出基于重叠Ket增强(Overlapping Ket Augmentation,OKA)和张量列车(Tensor Train,TT)的非平衡频谱制图算法,以解决非平衡张量在应用传统张量补全算法时性能下降的问题.首先使用OKA将低阶高维张量表示为高阶低维张量,在无信息损耗的情况下解决非平衡张量无法利用其低秩性进行张量补全的问题;然后使用TT矩阵化得到较平衡的矩阵,在维度较平衡条件下提高补全算法的精确度;最后利用高阶低维张量的低秩性,使用并行矩阵分解或基于F范数的无奇异值分解(Singular Value Decomposition Free,SVDFree)算法完成张量补全.仿真结果表明,针对非平衡张量,所提方案与现有的张量补全算法相比,可以获得更精确的无线电地图,同时所提SVDFree算法具有更低的计算复杂度.
文摘对实时车辆流量、平均车道占用率等各种交通监控数据的完整获取,是建设智能交通系统、提高交通管理运行效率的重要基础。文章提出一种融合类信息的函数型矩阵填充方法(Functional Matrix Completion Method with Class Information,CFMC)。在函数型数据分析框架下,基于非负矩阵分解构造函数型矩阵填充模型,在此基础上通过聚类划分引入样本类信息,借助类内样本相关性插补缺失值,并采用自加权集成学习算法动态赋权计算得到最终插补值。在公共交通数据集PeMS上进行插补实验,结果表明:当缺失率为15%~70%时,CFMC方法相较于K近邻算法、MICE、PACE等10种插补方法,均方根误差(RMSE)、平均绝对误差(MAE)和平均绝对百分比误差(MAPE)分别降低了10.75%~81.69%、0.34%~84.48%和12.5%~81.08%,且耗时可控。所提CFMC方法插补精度高、鲁棒性好,能够保证插补的有效性和准确性。
