Appendix: Tensor Decompositions via Two-Mode Higher-Order SVD (HOSVD)
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منابع مشابه
Developing Tensor Operations with an Underlying Group Structure
Tensor computations frequently involve factoring or decomposing a tensor into a sum of rank-1 tensors (CANDECOMP-PARAFAC, HOSVD, etc.). These decompositions are often considered as different higher-order extensions of the matrix SVD. The HOSVD can be described using the n-mode product, which describes multiplication between a higher-order tensor and a matrix. Generalizing this multiplication le...
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Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal’s uniqueness theorem to decompose symmetric, nearly orthogonally decomposable tensors. Unlike the classical higher-order singular value decomposition which unfolds a ten...
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The Higher-Order SVD (HOSVD) is a generalization of the Singular Value Decomposition (SVD) to higher-order tensors (i.e. arrays with more than two indices) and plays an important role in various domains. Unfortunately, this decomposition is computationally demanding. Indeed, the HOSVD of a third-order tensor involves the computation of the SVD of three matrices, which are referred to as "modes"...
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A main challenging problem for many machine learning and data mining applications is that the amount of data and features are very large, so that low-rank approximations of original data are often required for efficient computation. We propose new multi-level clustering based low-rank matrix approximations which are comparable and even more compact than Singular Value Decomposition (SVD). We ut...
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The Singular Value Decomposition (SVD) may be extended to tensors at least in two very different ways. One is the High-Order SVD (HOSVD), and the other is the Canonical Decomposition (CanD). Only the latter is closely related to the tensor rank. Important basic questions are raised in this short paper, such as the maximal achievable rank of a tensor of given dimensions, or the computation of a ...
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تاریخ انتشار 2017