Principal component analysis with tensor train subspace

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 empirically more robust to noise as compared to PCA or Tucker-PCA. This is borne out numerically by testing the proposed approach on the Extended YaleFace Dataset B, MINIST Dataset, CIFAR-10 dataset. This paper shows that the TT-PCA methods achieve less storage requirements, and have computationally faster online implementation with improved classification performance.