Faster Robust Tensor Power Method for Arbitrary Order

06/01/2023

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by   Yichuan Deng, et al.

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Tensor decomposition is a fundamental method used in various areas to deal with high-dimensional data. Tensor power method (TPM) is one of the widely-used techniques in the decomposition of tensors. This paper presents a novel tensor power method for decomposing arbitrary order tensors, which overcomes limitations of existing approaches that are often restricted to lower-order (less than 3) tensors or require strong assumptions about the underlying data structure. We apply sketching method, and we are able to achieve the running time of O(n^p-1), on the power p and dimension n tensor. We provide a detailed analysis for any p-th order tensor, which is never given in previous works.