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CORR
2016
Springer

Tensor and Its Tucker Core: the Invariance Relationships

8 years 7 months ago
Tensor and Its Tucker Core: the Invariance Relationships
In [12], Hillar and Lim famously demonstrated that “multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard”. Despite many recent advancements, the state-of-the-art methods for computing such ‘tensor analogues’ still suffer severely from the curse of dimensionality. In this paper we show that the Tucker core of a tensor however, retains many properties of the original tensor, including the CP rank, the border rank, the tensor Schatten quasi norms, and the Z-eigenvalues. Since the core is typically smaller than the original tensor, this property leads to considerable computational advantages, as confirmed by our numerical experiments. In our analysis, we in fact work with a generalized Tucker-like decomposition that can accommodate any full column-rank factorization matrices.
Bo Jiang, Fan Yang, Shuzhong Zhang
Added 01 Apr 2016
Updated 01 Apr 2016
Type Journal
Year 2016
Where CORR
Authors Bo Jiang, Fan Yang, Shuzhong Zhang
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