  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.
