Fourier PCA and Robust Tensor Decomposition

25 Jun 2013 Navin Goyal Santosh Vempala Ying Xiao

Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a pair of tensors sharing the same vectors in rank-$1$ decompositions. Our main application is the first provably polynomial-time algorithm for underdetermined ICA, i.e., learning an $n \times m$ matrix $A$ from observations $y=Ax$ where $x$ is drawn from an unknown product distribution with arbitrary non-Gaussian components... (read more)

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