Tensors For Data Processing

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Tensors for Data Processing

Author : Yipeng Liu
Publisher : Academic Press
ISBN 13 : 0323859658
Total Pages : 598 pages
Book Rating : 4.3/5 (238 download)

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Book Synopsis Tensors for Data Processing by : Yipeng Liu

Download or read book Tensors for Data Processing written by Yipeng Liu and published by Academic Press. This book was released on 2021-10-21 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensors for Data Processing: Theory, Methods and Applications presents both classical and state-of-the-art methods on tensor computation for data processing, covering computation theories, processing methods, computing and engineering applications, with an emphasis on techniques for data processing. This reference is ideal for students, researchers and industry developers who want to understand and use tensor-based data processing theories and methods. As a higher-order generalization of a matrix, tensor-based processing can avoid multi-linear data structure loss that occurs in classical matrix-based data processing methods. This move from matrix to tensors is beneficial for many diverse application areas, including signal processing, computer science, acoustics, neuroscience, communication, medical engineering, seismology, psychometric, chemometrics, biometric, quantum physics and quantum chemistry. Provides a complete reference on classical and state-of-the-art tensor-based methods for data processing Includes a wide range of applications from different disciplines Gives guidance for their application

Tensor Computation for Data Analysis

Author : Yipeng Liu
Publisher : Springer Nature
ISBN 13 : 3030743861
Total Pages : 347 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Tensor Computation for Data Analysis by : Yipeng Liu

Download or read book Tensor Computation for Data Analysis written by Yipeng Liu and published by Springer Nature. This book was released on 2021-08-31 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor is a natural representation for multi-dimensional data, and tensor computation can avoid possible multi-linear data structure loss in classical matrix computation-based data analysis. This book is intended to provide non-specialists an overall understanding of tensor computation and its applications in data analysis, and benefits researchers, engineers, and students with theoretical, computational, technical and experimental details. It presents a systematic and up-to-date overview of tensor decompositions from the engineer's point of view, and comprehensive coverage of tensor computation based data analysis techniques. In addition, some practical examples in machine learning, signal processing, data mining, computer vision, remote sensing, and biomedical engineering are also presented for easy understanding and implementation. These data analysis techniques may be further applied in other applications on neuroscience, communication, psychometrics, chemometrics, biometrics, quantum physics, quantum chemistry, etc. The discussion begins with basic coverage of notations, preliminary operations in tensor computations, main tensor decompositions and their properties. Based on them, a series of tensor-based data analysis techniques are presented as the tensor extensions of their classical matrix counterparts, including tensor dictionary learning, low rank tensor recovery, tensor completion, coupled tensor analysis, robust principal tensor component analysis, tensor regression, logistical tensor regression, support tensor machine, multilinear discriminate analysis, tensor subspace clustering, tensor-based deep learning, tensor graphical model and tensor sketch. The discussion also includes a number of typical applications with experimental results, such as image reconstruction, image enhancement, data fusion, signal recovery, recommendation system, knowledge graph acquisition, traffic flow prediction, link prediction, environmental prediction, weather forecasting, background extraction, human pose estimation, cognitive state classification from fMRI, infrared small target detection, heterogeneous information networks clustering, multi-view image clustering, and deep neural network compression.

Matrix and Tensor Decompositions in Signal Processing, Volume 2

Author : Gérard Favier
Publisher : John Wiley & Sons
ISBN 13 : 1119700965
Total Pages : 386 pages
Book Rating : 4.1/5 (197 download)

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Book Synopsis Matrix and Tensor Decompositions in Signal Processing, Volume 2 by : Gérard Favier

Download or read book Matrix and Tensor Decompositions in Signal Processing, Volume 2 written by Gérard Favier and published by John Wiley & Sons. This book was released on 2021-08-17 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second volume will deal with a presentation of the main matrix and tensor decompositions and their properties of uniqueness, as well as very useful tensor networks for the analysis of massive data. Parametric estimation algorithms will be presented for the identification of the main tensor decompositions. After a brief historical review of the compressed sampling methods, an overview of the main methods of retrieving matrices and tensors with missing data will be performed under the low rank hypothesis. Illustrative examples will be provided.

Tensor Regression

Author : Jiani Liu
Publisher :
ISBN 13 : 9781680838862
Total Pages : pages
Book Rating : 4.8/5 (388 download)

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Book Synopsis Tensor Regression by : Jiani Liu

Download or read book Tensor Regression written by Jiani Liu and published by . This book was released on 2021-09-27 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor Regression is the first thorough overview of the fundamentals, motivations, popular algorithms, strategies for efficient implementation, related applications, available datasets, and software resources for tensor-based regression analysis.

Visualization and Processing of Tensor Fields

Author : Joachim Weickert
Publisher : Springer Science & Business Media
ISBN 13 : 3540312722
Total Pages : 481 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Visualization and Processing of Tensor Fields by : Joachim Weickert

Download or read book Visualization and Processing of Tensor Fields written by Joachim Weickert and published by Springer Science & Business Media. This book was released on 2007-06-25 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix-valued data sets – so-called second order tensor fields – have gained significant importance in scientific visualization and image processing due to recent developments such as diffusion tensor imaging. This book is the first edited volume that presents the state of the art in the visualization and processing of tensor fields. It contains some longer chapters dedicated to surveys and tutorials of specific topics, as well as a great deal of original work by leading experts that has not been published before. It serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as as a textbook for specialized classes and seminars for graduate and doctoral students.

Tensors in Image Processing and Computer Vision

Author : Santiago Aja-Fernández
Publisher : Springer Science & Business Media
ISBN 13 : 1848822995
Total Pages : 468 pages
Book Rating : 4.8/5 (488 download)

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Book Synopsis Tensors in Image Processing and Computer Vision by : Santiago Aja-Fernández

Download or read book Tensors in Image Processing and Computer Vision written by Santiago Aja-Fernández and published by Springer Science & Business Media. This book was released on 2009-05-21 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor signal processing is an emerging field with important applications to computer vision and image processing. This book presents the state of the art in this new branch of signal processing, offering a great deal of research and discussions by leading experts in the area. The wide-ranging volume offers an overview into cutting-edge research into the newest tensor processing techniques and their application to different domains related to computer vision and image processing. This comprehensive text will prove to be an invaluable reference and resource for researchers, practitioners and advanced students working in the area of computer vision and image processing.

Vector and Tensor Analysis with Applications

Author : A. I. Borisenko
Publisher : Courier Corporation
ISBN 13 : 0486131904
Total Pages : 288 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Vector and Tensor Analysis with Applications by : A. I. Borisenko

Download or read book Vector and Tensor Analysis with Applications written by A. I. Borisenko and published by Courier Corporation. This book was released on 2012-08-28 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise, readable text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. Worked-out problems and solutions. 1968 edition.

Introduction to Tensor Analysis and the Calculus of Moving Surfaces

Author : Pavel Grinfeld
Publisher : Springer Science & Business Media
ISBN 13 : 1461478677
Total Pages : 302 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Introduction to Tensor Analysis and the Calculus of Moving Surfaces by : Pavel Grinfeld

Download or read book Introduction to Tensor Analysis and the Calculus of Moving Surfaces written by Pavel Grinfeld and published by Springer Science & Business Media. This book was released on 2013-09-24 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations. The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author’s skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 – when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject. The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem.

Tensor Algebra and Tensor Analysis for Engineers

Author : Mikhail Itskov
Publisher : Springer Science & Business Media
ISBN 13 : 3540939075
Total Pages : 253 pages
Book Rating : 4.5/5 (49 download)

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Book Synopsis Tensor Algebra and Tensor Analysis for Engineers by : Mikhail Itskov

Download or read book Tensor Algebra and Tensor Analysis for Engineers written by Mikhail Itskov and published by Springer Science & Business Media. This book was released on 2009-04-30 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is a large gap between engineering courses in tensor algebra on one hand, and the treatment of linear transformations within classical linear algebra on the other. This book addresses primarily engineering students with some initial knowledge of matrix algebra. Thereby, mathematical formalism is applied as far as it is absolutely necessary. Numerous exercises provided in the book are accompanied by solutions enabling autonomous study. The last chapters deal with modern developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics and might therefore be of high interest for PhD-students and scientists working in this area.

Anisotropy Across Fields and Scales

Author : Evren Özarslan
Publisher : Springer Nature
ISBN 13 : 3030562158
Total Pages : 284 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Anisotropy Across Fields and Scales by : Evren Özarslan

Download or read book Anisotropy Across Fields and Scales written by Evren Özarslan and published by Springer Nature. This book was released on 2021 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book focuses on processing, modeling, and visualization of anisotropy information, which are often addressed by employing sophisticated mathematical constructs such as tensors and other higher-order descriptors. It also discusses adaptations of such constructs to problems encountered in seemingly dissimilar areas of medical imaging, physical sciences, and engineering. Featuring original research contributions as well as insightful reviews for scientists interested in handling anisotropy information, it covers topics such as pertinent geometric and algebraic properties of tensors and tensor fields, challenges faced in processing and visualizing different types of data, statistical techniques for data processing, and specific applications like mapping white-matter fiber tracts in the brain. The book helps readers grasp the current challenges in the field and provides information on the techniques devised to address them. Further, it facilitates the transfer of knowledge between different disciplines in order to advance the research frontiers in these areas. This multidisciplinary book presents, in part, the outcomes of the seventh in a series of Dagstuhl seminars devoted to visualization and processing of tensor fields and higher-order descriptors, which was held in Dagstuhl, Germany, on October 28-November 2, 2018.

Tensors: Geometry and Applications

Author : J. M. Landsberg
Publisher : American Mathematical Soc.
ISBN 13 : 0821869078
Total Pages : 464 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Tensors: Geometry and Applications by : J. M. Landsberg

Download or read book Tensors: Geometry and Applications written by J. M. Landsberg and published by American Mathematical Soc.. This book was released on 2011-12-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.

Nonnegative Matrix and Tensor Factorizations

Author : Andrzej Cichocki
Publisher : John Wiley & Sons
ISBN 13 : 9780470747285
Total Pages : 500 pages
Book Rating : 4.7/5 (472 download)

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Book Synopsis Nonnegative Matrix and Tensor Factorizations by : Andrzej Cichocki

Download or read book Nonnegative Matrix and Tensor Factorizations written by Andrzej Cichocki and published by John Wiley & Sons. This book was released on 2009-07-10 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a broad survey of models and efficient algorithms for Nonnegative Matrix Factorization (NMF). This includes NMF’s various extensions and modifications, especially Nonnegative Tensor Factorizations (NTF) and Nonnegative Tucker Decompositions (NTD). NMF/NTF and their extensions are increasingly used as tools in signal and image processing, and data analysis, having garnered interest due to their capability to provide new insights and relevant information about the complex latent relationships in experimental data sets. It is suggested that NMF can provide meaningful components with physical interpretations; for example, in bioinformatics, NMF and its extensions have been successfully applied to gene expression, sequence analysis, the functional characterization of genes, clustering and text mining. As such, the authors focus on the algorithms that are most useful in practice, looking at the fastest, most robust, and suitable for large-scale models. Key features: Acts as a single source reference guide to NMF, collating information that is widely dispersed in current literature, including the authors’ own recently developed techniques in the subject area. Uses generalized cost functions such as Bregman, Alpha and Beta divergences, to present practical implementations of several types of robust algorithms, in particular Multiplicative, Alternating Least Squares, Projected Gradient and Quasi Newton algorithms. Provides a comparative analysis of the different methods in order to identify approximation error and complexity. Includes pseudo codes and optimized MATLAB source codes for almost all algorithms presented in the book. The increasing interest in nonnegative matrix and tensor factorizations, as well as decompositions and sparse representation of data, will ensure that this book is essential reading for engineers, scientists, researchers, industry practitioners and graduate students across signal and image processing; neuroscience; data mining and data analysis; computer science; bioinformatics; speech processing; biomedical engineering; and multimedia.

Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data

Author : Carl-Fredrik Westin
Publisher : Springer
ISBN 13 : 3642543014
Total Pages : 346 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data by : Carl-Fredrik Westin

Download or read book Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data written by Carl-Fredrik Westin and published by Springer. This book was released on 2014-07-17 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Arising from the fourth Dagstuhl conference entitled Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data (2011), this book offers a broad and vivid view of current work in this emerging field. Topics covered range from applications of the analysis of tensor fields to research on their mathematical and analytical properties. Part I, Tensor Data Visualization, surveys techniques for visualization of tensors and tensor fields in engineering, discusses the current state of the art and challenges, and examines tensor invariants and glyph design, including an overview of common glyphs. The second Part, Representation and Processing of Higher-order Descriptors, describes a matrix representation of local phase, outlines mathematical morphological operations techniques, extended for use in vector images, and generalizes erosion to the space of diffusion weighted MRI. Part III, Higher Order Tensors and Riemannian-Finsler Geometry, offers powerful mathematical language to model and analyze large and complex diffusion data such as High Angular Resolution Diffusion Imaging (HARDI) and Diffusion Kurtosis Imaging (DKI). A Part entitled Tensor Signal Processing presents new methods for processing tensor-valued data, including a novel perspective on performing voxel-wise morphometry of diffusion tensor data using kernel-based approach, explores the free-water diffusion model, and reviews proposed approaches for computing fabric tensors, emphasizing trabecular bone research. The last Part, Applications of Tensor Processing, discusses metric and curvature tensors, two of the most studied tensors in geometry processing. Also covered is a technique for diagnostic prediction of first-episode schizophrenia patients based on brain diffusion MRI data. The last chapter presents an interactive system integrating the visual analysis of diffusion MRI tractography with data from electroencephalography.

Tensor Analysis on Manifolds

Author : Richard L. Bishop
Publisher : Courier Corporation
ISBN 13 : 0486139239
Total Pages : 288 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Tensor Analysis on Manifolds by : Richard L. Bishop

Download or read book Tensor Analysis on Manifolds written by Richard L. Bishop and published by Courier Corporation. This book was released on 2012-04-26 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVProceeds from general to special, including chapters on vector analysis on manifolds and integration theory. /div

User-Defined Tensor Data Analysis

Author : Bin Dong
Publisher : Springer
ISBN 13 : 9783030707491
Total Pages : 101 pages
Book Rating : 4.7/5 (74 download)

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Book Synopsis User-Defined Tensor Data Analysis by : Bin Dong

Download or read book User-Defined Tensor Data Analysis written by Bin Dong and published by Springer. This book was released on 2021-10-31 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: The SpringerBrief introduces FasTensor, a powerful parallel data programming model developed for big data applications. This book also provides a user's guide for installing and using FasTensor. FasTensor enables users to easily express many data analysis operations, which may come from neural networks, scientific computing, or queries from traditional database management systems (DBMS). FasTensor frees users from all underlying and tedious data management tasks, such as data partitioning, communication, and parallel execution. This SpringerBrief gives a high-level overview of the state-of-the-art in parallel data programming model and a motivation for the design of FasTensor. It illustrates the FasTensor application programming interface (API) with an abundance of examples and two real use cases from cutting edge scientific applications. FasTensor can achieve multiple orders of magnitude speedup over Spark and other peer systems in executing big data analysis operations. FasTensor makes programming for data analysis operations at large scale on supercomputers as productively and efficiently as possible. A complete reference of FasTensor includes its theoretical foundations, C++ implementation, and usage in applications. Scientists in domains such as physical and geosciences, who analyze large amounts of data will want to purchase this SpringerBrief. Data engineers who design and develop data analysis software and data scientists, and who use Spark or TensorFlow to perform data analyses, such as training a deep neural network will also find this SpringerBrief useful as a reference tool.

Robust Statistics for Signal Processing

Author : Abdelhak M. Zoubir
Publisher : Cambridge University Press
ISBN 13 : 1107017416
Total Pages : 315 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Robust Statistics for Signal Processing by : Abdelhak M. Zoubir

Download or read book Robust Statistics for Signal Processing written by Abdelhak M. Zoubir and published by Cambridge University Press. This book was released on 2018-11-08 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understand the benefits of robust statistics for signal processing using this unique and authoritative text.

Tensor Analysis

Author : Liqun Qi
Publisher : SIAM
ISBN 13 : 1611974747
Total Pages : 313 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Tensor Analysis by : Liqun Qi

Download or read book Tensor Analysis written by Liqun Qi and published by SIAM. This book was released on 2017-04-19 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory?some of which are nontrivial?have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimization, magnetic resonance imaging, automatic control, and quantum entanglement problems). The authors provide a comprehensive discussion of this new theory of tensors. Tensor Analysis: Spectral Theory and Special Tensors is unique in that it is the first book on these three subject areas: spectral theory of tensors; the theory of special tensors, including nonnegative tensors, positive semidefinite tensors, completely positive tensors, and copositive tensors; and the spectral hypergraph theory via tensors. ?