Faster Robust Tensor Power Method for Arbitrary Order

• URL: http://arxiv.org/abs/2306.00406v1
• Date: Thu, 1 Jun 2023 07:12:00 GMT
• Title: Faster Robust Tensor Power Method for Arbitrary Order
• Authors: Yichuan Deng, Zhao Song, Junze Yin
• Abstract summary: emphTensor power method (TPM) is one of the widely-used techniques in the decomposition of tensors. We apply sketching method, and we are able to achieve the running time of $widetildeO(np-1)$ on the power $p$ and dimension $n$ tensor.
• Score: 15.090593955414137
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Tensor decomposition is a fundamental method used in various areas to deal with high-dimensional data. \emph{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 $\widetilde{O}(n^{p-1})$, 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.

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