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Tensor Networks for Dimensionality Reduction and Large-scale Optimization - Part 1 Low-Rank Tensor Decompositions (Paperback)
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Tensor Networks for Dimensionality Reduction and Large-scale Optimization - Part 1 Low-Rank Tensor Decompositions (Paperback)
Series: Foundations and Trends (R) in Machine Learning
Expected to ship within 10 - 15 working days
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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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