2016/09/15 by Johann A. Bengua, Ho N. Phien, Phien N. Ho +4
Computer Science · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Algorithm #Applied mathematics #Cartesian tensor #Compression (physics) #Computation #Computer science #Data compression #Dimension (graph theory) #Eigenvalues and eigenvectors #Exact solutions in general relativity #Mathematical analysis #Mathematical optimization #Mathematics #Matrix (chemical analysis) #Matrix decomposition #Matrix multiplication #Parallel Computing and Optimization Techniques #Pure mathematics #Singular value decomposition #Tensor (intrinsic definition) #Tensor decomposition #Tensor decomposition and applications #Tensor density #Tensor field #Tensor product #Tucker decomposition #cs.CV #cs.DS #stat.ML
paper · pdf · doi:10.1109/tsp.2017.2703882
12 pages, 4 figures
arxiv created 2016/09/15 · openalex publication_date 2017/05/12 · arxiv updated 2017/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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, 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.