Tensor Principal Component Analysis in High Dimensional CP Models. (arXiv:2108.04428v3 [stat.ML] UPDATED)

Web: http://arxiv.org/abs/2108.04428

The CP decomposition for high dimensional non-orthogonal spiked tensors is an
important problem with broad applications across many disciplines. However,
previous works with theoretical guarantee typically assume restrictive
incoherence conditions on the basis vectors for the CP components. In this
paper, we propose new computationally efficient composite PCA and concurrent
orthogonalization algorithms for tensor CP decomposition with theoretical
guarantees under mild incoherence conditions. The composite PCA applies the
principal component or singular value decompositions twice, first to a matrix
unfolding …

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