Principal Component Analysis with Tensor Train Subspace

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.

References in corpus (4)

• Low-Rank Tensor Networks for Dimensionality Reduction and Large-Scale Optimization Problems: Perspectives and Challenges PART 1
• Tensor Train Neighborhood Preserving Embedding
• Tensor Completion by Alternating Minimization under the Tensor Train (TT) Model
• Multilinear Principal Component Analysis Network for Tensor Object Classification

Cited by in corpus (1)

• Tensor-Train Parameterization for Ultra Dimensionality Reduction