Tensor Networks For Dimensionality Reduction And Large Scale Optimization

Author : Andrzej Cichocki
Publisher :
ISBN 13 : 9781680832761
Total Pages : 262 pages
Book Rating : 4.6X/5 ( download)

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Download or read book Tensor Networks for Dimensionality Reduction and Large-Scale Optimization written by Andrzej Cichocki and published by . This book was released on 2017-05-28 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Andrzej Cichocki
Publisher :
ISBN 13 : 9781680832235
Total Pages : 180 pages
Book Rating : 4.39/5 ( download)

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Download or read book Tensor Networks for Dimensionality Reduction and Large-scale Optimization written by Andrzej Cichocki and published by . This book was released on 2016 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 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 large-scale, multi-modal and multi-relational datasets. Given that such data are often efficiently represented as multiway arrays or tensors, it is therefore timely and valuable for the multidisciplinary machine learning and data analytic communities to review low-rank tensor decompositions and tensor networks as emerging tools for dimensionality reduction and large scale optimization problems. Our particular emphasis is on elucidating that, by virtue of the underlying low-rank approximations, tensor networks have the ability to alleviate the curse of dimensionality in a number of applied areas. In Part 1 of this monograph we provide innovative solutions to low-rank tensor network decompositions and easy to interpret graphical representations of the mathematical operations on tensor networks. Such a conceptual insight allows for seamless migration of ideas from the flat-view matrices to tensor network operations and vice versa, and provides a platform for further developments, practical applications, and non-Euclidean extensions. It also permits the introduction of various tensor network operations without an explicit notion of mathematical expressions, which may be beneficial for many research communities that do not directly rely on multilinear algebra. Our focus is on the Tucker and tensor train (TT) decompositions and their extensions, and on demonstrating the ability of tensor networks to provide linearly or even super-linearly (e.g., logarithmically) scalable solutions, as illustrated in detail in Part 2 of this monograph.

Author : Andrzej Cichocki
Publisher :
ISBN 13 : 9781680832228
Total Pages : 196 pages
Book Rating : 4.20/5 ( download)

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Download or read book Tensor Networks for Dimensionality Reduction and Large-Scale Optimization written by Andrzej Cichocki and published by . This book was released on 2016-12-19 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Shi-Ju Ran
Publisher : Springer Nature
ISBN 13 : 3030344894
Total Pages : 160 pages
Book Rating : 4.94/5 ( download)

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Download or read book Tensor Network Contractions written by Shi-Ju Ran and published by Springer Nature. This book was released on 2020-01-27 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.

Author : Kohei Arai
Publisher : Springer Nature
ISBN 13 : 3030551806
Total Pages : 815 pages
Book Rating : 4.03/5 ( download)

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Download or read book Intelligent Systems and Applications written by Kohei Arai and published by Springer Nature. This book was released on 2020-08-25 with total page 815 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book Intelligent Systems and Applications - Proceedings of the 2020 Intelligent Systems Conference is a remarkable collection of chapters covering a wider range of topics in areas of intelligent systems and artificial intelligence and their applications to the real world. The Conference attracted a total of 545 submissions from many academic pioneering researchers, scientists, industrial engineers, students from all around the world. These submissions underwent a double-blind peer review process. Of those 545 submissions, 177 submissions have been selected to be included in these proceedings. As intelligent systems continue to replace and sometimes outperform human intelligence in decision-making processes, they have enabled a larger number of problems to be tackled more effectively.This branching out of computational intelligence in several directions and use of intelligent systems in everyday applications have created the need for such an international conference which serves as a venue to report on up-to-the-minute innovations and developments. This book collects both theory and application based chapters on all aspects of artificial intelligence, from classical to intelligent scope. We hope that readers find the volume interesting and valuable; it provides the state of the art intelligent methods and techniques for solving real world problems along with a vision of the future research.

Author : Adam E Gawęda
Publisher : Springer
ISBN 13 : 3319679465
Total Pages : 412 pages
Book Rating : 4.64/5 ( download)

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Download or read book Advances in Data Analysis with Computational Intelligence Methods written by Adam E Gawęda and published by Springer. This book was released on 2017-09-21 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a tribute to Professor Jacek Żurada, who is best known for his contributions to computational intelligence and knowledge-based neurocomputing. It is dedicated to Professor Jacek Żurada, Full Professor at the Computational Intelligence Laboratory, Department of Electrical and Computer Engineering, J.B. Speed School of Engineering, University of Louisville, Kentucky, USA, as a token of appreciation for his scientific and scholarly achievements, and for his longstanding service to many communities, notably the computational intelligence community, in particular neural networks, machine learning, data analyses and data mining, but also the fuzzy logic and evolutionary computation communities, to name but a few. At the same time, the book recognizes and honors Professor Żurada’s dedication and service to many scientific, scholarly and professional societies, especially the IEEE (Institute of Electrical and Electronics Engineers), the world’s largest professional technical professional organization dedicated to advancing science and technology in a broad spectrum of areas and fields. The volume is divided into five major parts, the first of which addresses theoretic, algorithmic and implementation problems related to the intelligent use of data in the sense of how to derive practically useful information and knowledge from data. In turn, Part 2 is devoted to various aspects of neural networks and connectionist systems. Part 3 deals with essential tools and techniques for intelligent technologies in systems modeling and Part 4 focuses on intelligent technologies in decision-making, optimization and control, while Part 5 explores the applications of intelligent technologies.

Author : Philipp Grohs
Publisher : Springer Nature
ISBN 13 : 3030313514
Total Pages : 701 pages
Book Rating : 4.17/5 ( download)

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Download or read book Handbook of Variational Methods for Nonlinear Geometric Data written by Philipp Grohs and published by Springer Nature. This book was released on 2020-04-03 with total page 701 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art. Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance. Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.

Author : Boris N. Khoromskij
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 311036591X
Total Pages : 379 pages
Book Rating : 4.17/5 ( download)

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Download or read book Tensor Numerical Methods in Scientific Computing written by Boris N. Khoromskij and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-06-11 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: The most difficult computational problems nowadays are those of higher dimensions. This research monograph offers an introduction to tensor numerical methods designed for the solution of the multidimensional problems in scientific computing. These methods are based on the rank-structured approximation of multivariate functions and operators by using the appropriate tensor formats. The old and new rank-structured tensor formats are investigated. We discuss in detail the novel quantized tensor approximation method (QTT) which provides function-operator calculus in higher dimensions in logarithmic complexity rendering super-fast convolution, FFT and wavelet transforms. This book suggests the constructive recipes and computational schemes for a number of real life problems described by the multidimensional partial differential equations. We present the theory and algorithms for the sinc-based separable approximation of the analytic radial basis functions including Green’s and Helmholtz kernels. The efficient tensor-based techniques for computational problems in electronic structure calculations and for the grid-based evaluation of long-range interaction potentials in multi-particle systems are considered. We also discuss the QTT numerical approach in many-particle dynamics, tensor techniques for stochastic/parametric PDEs as well as for the solution and homogenization of the elliptic equations with highly-oscillating coefficients. Contents Theory on separable approximation of multivariate functions Multilinear algebra and nonlinear tensor approximation Superfast computations via quantized tensor approximation Tensor approach to multidimensional integrodifferential equations

Author : Wil M.P. van der Aalst
Publisher : Springer
ISBN 13 : 3319730134
Total Pages : 430 pages
Book Rating : 4.34/5 ( download)

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Download or read book Analysis of Images, Social Networks and Texts written by Wil M.P. van der Aalst and published by Springer. This book was released on 2017-12-20 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 6th International Conference on Analysis of Images, Social Networks and Texts, AIST 2017, held in Moscow, Russia, in July 2017. The 29 full papers and 8 short papers were carefully reviewed and selected from 127 submissions. The papers are organized in topical sections on natural language processing; general topics of data analysis; analysis of images and video; optimization problems on graphs and network structures; analysis of dynamic behavior through event data; social network analysis.

Author : Simone Montangero
Publisher : Springer
ISBN 13 : 3030014096
Total Pages : 172 pages
Book Rating : 4.94/5 ( download)

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Download or read book Introduction to Tensor Network Methods written by Simone Montangero and published by Springer. This book was released on 2018-11-28 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of lecture notes briefly introduces the basic concepts needed in any computational physics course: software and hardware, programming skills, linear algebra, and differential calculus. It then presents more advanced numerical methods to tackle the quantum many-body problem: it reviews the numerical renormalization group and then focuses on tensor network methods, from basic concepts to gauge invariant ones. Finally, in the last part, the author presents some applications of tensor network methods to equilibrium and out-of-equilibrium correlated quantum matter. The book can be used for a graduate computational physics course. After successfully completing such a course, a student should be able to write a tensor network program and can begin to explore the physics of many-body quantum systems. The book can also serve as a reference for researchers working or starting out in the field.