Tensor Networks for Dimensionality Reduction and Large-scale Optimization

Part 2 Applications and Future Perspectives
1. Auflage 2017
ISBN: 978-1-68083-276-1
Verlag: Now Publishers

Buch, Englisch, Band 30, 256 Seiten, Format (B × H): 156 mm x 234 mm

Reihe: Foundations and Trends® in Machine Learning

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

Autoren/Hrsg.

Cichocki, Andrzej

Lee, Namgil

Oseledets, Ivan

Phan, Anh-Huy

Zhao, Qibin

Mandic, Danilo P.

Fachgebiete

• Mathematik | Informatik EDV | Informatik Informatik Künstliche Intelligenz Maschinelles Lernen

Inhaltsverzeichnis

1: Tensorization and Structured Tensors 2: Supervised Learning with Tensors 3: Tensor Train Networks for Selected Huge-Scale Optimization Problems 4: Tensor Networks for Deep Learning 5: Discussion and Conclusions. Appendices. References.