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
Industrial big data was usually multi-source, heterogeneous, and deeply intertwined. It had a wide range of data sources, high data dimensions, and strong data correlation. In order to effectively analyze and process ...Industrial big data was usually multi-source, heterogeneous, and deeply intertwined. It had a wide range of data sources, high data dimensions, and strong data correlation. In order to effectively analyze and process streaming industrial big data generated by edge computing, it was very important to provide an effective real-time incremental data method. However, in the process of incremental processing, industrial big data incremental computing faced the challenges of dimensional disaster, repeated calculations, and the explosion of intermediate results. Therefore, in order to solve the above problems effectively, a QR-based tensor-train(TT) decomposition(TTD) method and a QR-based incremental TTD(QRITTD) method were proposed. This algorithm combined the incremental QR-based decomposition algorithm with an approximate singular value decomposition(SVD) algorithm and had good scalability. In addition, the computational complexity, space complexity, and approximation error analysis were analyzed in detail. The effectiveness of the three algorithms of QRITTD, non-incremental TTD(NITTD), and TT rank-1(TTr1) SVD(TTr1 SVD)were verified by comparison. Experimental results show that the SVD QRITTD method has better performance under the premise of ensuring the same tensor size.展开更多
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.
基金supported by the Science and Technology Project in Shaanxi Province of China (2019ZDLGY07-08)the Natural Science Foundation Research Program of Shaanxi Province, China。
文摘Industrial big data was usually multi-source, heterogeneous, and deeply intertwined. It had a wide range of data sources, high data dimensions, and strong data correlation. In order to effectively analyze and process streaming industrial big data generated by edge computing, it was very important to provide an effective real-time incremental data method. However, in the process of incremental processing, industrial big data incremental computing faced the challenges of dimensional disaster, repeated calculations, and the explosion of intermediate results. Therefore, in order to solve the above problems effectively, a QR-based tensor-train(TT) decomposition(TTD) method and a QR-based incremental TTD(QRITTD) method were proposed. This algorithm combined the incremental QR-based decomposition algorithm with an approximate singular value decomposition(SVD) algorithm and had good scalability. In addition, the computational complexity, space complexity, and approximation error analysis were analyzed in detail. The effectiveness of the three algorithms of QRITTD, non-incremental TTD(NITTD), and TT rank-1(TTr1) SVD(TTr1 SVD)were verified by comparison. Experimental results show that the SVD QRITTD method has better performance under the premise of ensuring the same tensor size.
