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详细说明: Part 2 of this monograph builds on the introduction to tensor net- works and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpre- tations which reflect the scalability of the tensor network a pproach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated con- tractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support ten- sor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimiza- tion, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions. ...展开收缩
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