Subspace power method for symmetric tensor decomposition and generalized PCA
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We introduce the Subspace Power Method (SPM) for decomposing symmetric even-order tensors. This algorithm relies on a power method iteration applied to a modified tensor, constructed from a matrix flattening. For tensors of rank up to roughly the square root of the number of tensor entries, we obtain provable guarantees for most steps of SPM, by drawing on results from algebraic geometry and dynamical systems. Numerical simulations indicate that SPM significantly outperforms state-of-the-art algorithms in terms of speed, while performing robustly for low-rank tensors subjected to additive noise. We also extend SPM to compute a certain generalized tensor decomposition, enabling generalized principal component analysis at extremely low SNR.
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