Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 2 Applications and Future Perspectives (Foundations and Trends(r) in Machine Learning)
暫譯: 張量網絡在降維與大規模優化中的應用與未來展望：第二部分（機器學習的基礎與趨勢）
Andrzej Cichocki, Namgil Lee, Ivan Oseledets
- 出版商: Now Publishers Inc
- 出版日期: 2017-05-30
- 售價: $3,650
- 貴賓價: 9.5 折 $3,468
- 語言: 英文
- 頁數: 262
- 裝訂: Paperback
- ISBN: 168083276X
- ISBN-13: 9781680832761
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相關分類:
Machine Learning
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商品描述
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
商品描述(中文翻譯)
這本專著基於《Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions》，討論了張量網絡模型在數據/參數和成本函數的超壓縮高階表示中的應用，並概述了它們在機器學習和數據分析中的應用。特別強調通過圖形插圖來闡明，由於基礎的低秩張量近似和核心張量的複雜收縮，張量網絡能夠對其他情況下過於龐大的數據/參數進行分佈式計算，從而減輕維度詛咒。這一概念的實用性在多個應用領域中得到了說明，包括廣義回歸和分類、廣義特徵值分解以及深度神經網絡的優化。專著重點介紹了張量列（TT）和層次塔克（HT）分解及其擴展，並展示了張量網絡在各種本來難以處理的大規模優化問題中提供可擴展解決方案的能力。
《Tensor Networks for Dimensionality Reduction and Large-scale Optimization》第一部分和第二部分可以作為獨立的文本使用，或一起作為低秩張量網絡和張量分解這一激動人心領域的綜合回顧。
另見：《Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions》。ISBN 978-1-68083-222-8
