Matrix Product State for Higher-Order Tensor Compression and Classification

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.

12 pages, 4 figures

References in corpus (3)

• The density-matrix renormalization group in the age of matrix product states
• DMRG and periodic boundary conditions: a quantum information perspective
• Efficient tensor completion for color image and video recovery: Low-rank tensor train

Cited by in corpus (5)

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• Data compression for quantum machine learning
• Efficient MPS representations and quantum circuits from the Fourier modes of classical image data
• A Matrix Product State Model for Simultaneous Classification and Generation
• Fast Hypergraph Regularized Nonnegative Tensor Ring Factorization Based on Low-Rank Approximation