Matrix Product State for Higher-Order Tensor Compression and Classification

TL;DR

This paper presents matrix product state (MPS) decomposition as an effective method for compressing higher-order tensors, improving classification performance while reducing computational costs compared to existing methods.

Contribution

The paper introduces MPS decomposition for tensor compression, offering a simple, globally optimal solution that enhances classification accuracy and efficiency.

Findings

MPS achieves better classification accuracy than other tensor methods.

MPS reduces computational complexity in tensor compression.

Benchmark results favor MPS over existing approaches.

Abstract

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.