Faster Robust Tensor Power Method for Arbitrary Order

Understand

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.