Principal Component Analysis with Tensor Train Subspace
This work addresses dimensionality reduction for large-scale multidimensional data, such as in image processing, but it appears incremental as it builds on existing tensor network methods.
The paper tackles the problem of estimating a Tensor Train subspace from multidimensional data to alleviate the curse of dimensionality, proposing the TT-PCA algorithm, which shows improved robustness to noise compared to PCA or Tucker-PCA, as demonstrated numerically on the Extended YaleFace Dataset B.
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.