  This paper introduces matrix product state (MPS) decomposition as a
computational tool for extracting features of multidimensional data represented
by higher-order tensors. Regardless of tensor order, MPS extracts its relevant
features to the so-called core tensor of maximum order three which can be used
for classification. Mainly based on a successive sequence of singular value
decompositions (SVD), MPS is quite simple to implement without any recursive
procedure needed for optimizing local tensors. Thus, it leads to substantial
computational savings compared to other tensor feature extraction methods such
as higher-order orthogonal iteration (HOOI) underlying the Tucker decomposition
(TD). Benchmark results show that MPS can reduce significantly the feature
space of data while achieving better classification performance compared to
HOOI.
