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林海onrush
(2023-04-30 23:31):
#paper,Tensor Decompositions and Applications∗,DOI: 10.1137/07070111X,张量分解在诸多领域都有深入的尝试，高阶张量（即N≥3的N路数组）在心理测量学、化学计量学、信号处理、数值线性代数、计算机视觉、数值分析、数据挖掘、神经科学、图分析和其他方面均有应用。这篇paper讲述了张量运算的基础，对张量的运算基础进行了详细的探讨，我认为非常有学习价值，未来会在很多行业的发展上具有重大贡献。
Abstract:
This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or N-way array. Decompositions of higher-order tensors (i.e., N-way arrays with …
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This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or N-way array. Decompositions of higher-order tensors (i.e., N-way arrays with N≥3) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.
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