Principal Component Analysis with Tensor Train Subspace

Wenqi Wang; Vaneet Aggarwal; Shuchin Aeron

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arXiv · 1803.05026

Principal Component Analysis with Tensor Train Subspace

Wenqi Wang·Vaneet Aggarwal·Shuchin Aeron

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Abstract

Tensor train is a hierarchical tensor network structure that helps alleviate the curse of dimensionality by parameterizing large-scale multidimensional data via a set of network of low-rank tensors. Associated with such a construction is a notion of Tensor Train subspace and in this paper we propose a TT-PCA algorithm for estimating this structured subspace from the given data. By maintaining low rank tensor structure, TT-PCA is more robust to noise comparing with PCA or Tucker-PCA. This is borne out numerically by testing the proposed approach on the Extended YaleFace Dataset B.

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Wenqi Wang, Vaneet Aggarwal, Shuchin Aeron. 2018-03-13. Principal Component Analysis with Tensor Train Subspace. https://arxiv.org/abs/1803.05026

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