# Principal Component Analysis with Tensor Train Subspace

arXiv: https://arxiv.org/abs/1803.05026 · HTML: https://mlsanity.com/paper/1803.05026/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Mar 2018.

## Built on by (most cited first, 1 of 1)

- [Tensor PCA from basis in tensor space](https://mlsanity.com/paper/2305.02803/) (2023)

## Abstract (arXiv)

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.