2015/03/02 by Johann A. Bengua, Ho N. Phien, Bengua, Johann A. +7 · 4 citations
Chemistry · Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Algorithms and Data Compression #Artificial intelligence #Business #Chemistry #Chromatography #Computer Vision and Pattern Recognition (cs.CV) #Computer science #Data Structures and Algorithms (cs.DS) #Extraction (chemistry) #FOS: Computer and information sciences #Feature (linguistics) #Geometry #Machine Learning (cs.LG) #Mathematics #Matrix (chemical analysis) #Matrix multiplication #Matrix product state #Model Reduction and Neural Networks #Order (exchange) #Pattern recognition (psychology) #Philosophy #Physics #Product (mathematics) #Quantum mechanics #State (computer science) #Tensor decomposition and applications #cs.CV #cs.DS #cs.LG
paper · pdf · doi:10.48550/arxiv.1503.00516
published in arXiv (Cornell University) (Cornell University) · 10 pages, 3 figures, updated introduction, submitted to IEEE Transactions on Signal Processing
openalex publication_date 2015/03/02 · arxiv created 2016/01/20 · arxiv updated 2016/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.