Tensor Networks for Dimensionality Reduction and Large-scale Optimization (häftad)
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Format
Häftad (Paperback / softback)
Språk
Engelska
Antal sidor
196
Utgivningsdatum
2016-12-19
Förlag
now publishers Inc
Medarbetare
Mandic, Danilo P. (förf)
Illustrationer
colour illustrations
Volymtitel
Part 1 Low-Rank Tensor Decompositions
Dimensioner
234 x 156 x 11 mm
Vikt
281 g
Antal komponenter
1
Komponenter
1349:Standard Color 6.14 x 9.21 in or 234 x 156 mm (Royal 8vo) Perfect Bound on White w/Gloss Lam
ISBN
9781680832228

Tensor Networks for Dimensionality Reduction and Large-scale Optimization

Part 1 Low-Rank Tensor Decompositions

Häftad,  Engelska, 2016-12-19
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Modern applications in engineering and data science are increasingly based on multidimensional data of exceedingly high volume, variety, and structural richness. However, standard machine learning and data mining algorithms typically scale exponentially with data volume and complexity of cross-modal couplings - the so called curse of dimensionality - which is prohibitive to the analysis of such large-scale, multi-modal and multi-relational datasets. Given that such data are often conveniently represented as multiway arrays or tensors, it is therefore timely and valuable for the multidisciplinary machine learning and data analytic communities to review tensor decompositions and tensor networks as emerging tools for dimensionality reduction and large scale optimization. This monograph provides a systematic and example-rich guide to the basic properties and applications of tensor network methodologies, and demonstrates their promise as a tool for the analysis of extreme-scale multidimensional data. It demonstrates the ability of tensor networks to provide linearly or even super-linearly, scalable solutions. The low-rank tensor network framework of analysis presented in this monograph is intended to both help demystify tensor decompositions for educational purposes and further empower practitioners with enhanced intuition and freedom in algorithmic design for the manifold applications. In addition, the material may be useful in lecture courses on large-scale machine learning and big data analytics, or indeed, as interesting reading for the intellectually curious and generally knowledgeable reader.
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Innehållsförteckning

1: Introduction and Motivation 2: Tensor Operations and Tensor Network Diagrams 3: Constrained Tensor Decompositions: From Two-way to Multiway Component Analysis 4: Tensor Train Decompositions: Graphical Interpretations and Algorithms 5: Discussion and Conclusions References