Principal Component Analysis with Tensor Train Subspace
Machine Learning
2018-03-15 v1 Computer Vision and Pattern Recognition
Information Theory
Numerical Analysis
math.IT
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.
Cite
@article{arxiv.1803.05026,
title = {Principal Component Analysis with Tensor Train Subspace},
author = {Wenqi Wang and Vaneet Aggarwal and Shuchin Aeron},
journal= {arXiv preprint arXiv:1803.05026},
year = {2018}
}