2014/05/30 by Namgil Lee, Andrzej Cichocki, Lee, Namgil +1
Mathematics · Medicine · Physics and Astronomy · #15A63 #15A69 #65F25 #65F30 #Advanced Neuroimaging Techniques and Applications #Emerging Technologies (cs.ET) #FOS: Computer and information sciences #FOS: Mathematics #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1405.7786
openalex publication_date 2014/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss extended definitions of linear and multilinear operations such as Kronecker, Hadamard, and contracted products, and establish links between them for tensor calculus. Then we introduce effective low-rank tensor approximation techniques including Candecomp/Parafac (CP), Tucker, and tensor train (TT) decompositions with a number of mathematical and graphical representations. We also provide a brief review of mathematical properties of the TT decomposition as a low-rank approximation technique. With the aim of breaking the curse-of-dimensionality in large-scale numerical analysis, we describe basic operations on large-scale vectors, matrices, and high-order tensors represented by TT decomposition. The proposed representations can be used for describing numerical methods based on TT decomposition for solving large-scale optimization problems such as systems of linear equations and symmetric eigenvalue problems.