  This paper introduces matrix product state (MPS) decomposition as a new and
systematic method to compress multidimensional data represented by higher-order
tensors. It solves two major bottlenecks in tensor compression: computation and
compression quality. Regardless of tensor order, MPS compresses tensors to
matrices of moderate dimension which can be used for classification. Mainly
based on a successive sequence of singular value decompositions (SVD), MPS is
quite simple to implement and arrives at the global optimal matrix, bypassing
local alternating optimization, which is not only computationally expensive but
cannot yield the global solution. Benchmark results show that MPS can achieve
better classification performance with favorable computation cost compared to
other tensor compression methods.
