Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives

By Andrzej S. Cichocki, Anh Huy Phan, Qibin Zhao, Namgil Lee, Ivan V. Oseledets, Masashi Sugiyama, Danilo P. Mandic. Found. Trends Mach. Learn., 2017

341 citations recorded by the source corpus.

This monograph builds on Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions by discussing tensor network models for super-compressed higher-order representation of data/parameters and cost functions, together with an outline of their applications in machine learning and data analytics. A particular emphasis is on elucidating, through graphical illustrations, that by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volume of data/parameters, thereby alleviating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification, generalized eigenvalue decomposition and in the optimization of deep neural networks. The monograph focuses on tensor train (TT) and Hierarchical Tucker (HT) decompositions and their extensions, and on demonstrating the ability of tensor networks to provide scalable solutions for a variety of otherwise intractable large-scale optimization problems. Tensor Networks for Dimensionality Reduction and Large-scale Optimization Parts 1 and 2 can be used as stand-alone texts, or together as a comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions. See also: Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions. ISBN 978-1-68083-222-8

Subfields: Computational Mathematics, Radiology, Nuclear Medicine and Imaging, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/33fc100fa2a003ae068e7db503576591aa521c01

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Citations in the corpus

Tensorial Neural Networks: Generalization of Neural Networks and Application to Model Compression (2018, background): “These techniques can be grouped into two categories: (1) compressing an existing model and (2) novel compact designs.”
Geometric Methods on Low-Rank Matrix and Tensor Manifolds (2020, background): “For further reading we would like to refer to the several overview articles taking different perspectives on low-rank optimization, see [61, 37, 16, 7, 15, 17, 100], and the monographs [39, 51, 53].”