Tensors For Data Processing

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Tensors for Data Processing

Yipeng Liu
Tensors for Data Processing Book PDF

Author : Yipeng Liu
Publisher : Academic Press
Page : 598 pages
File Size : 45,7 Mb
Release : 2021-10-21
Category : Technology & Engineering
ISBN : 9780323859653

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Tensors for Data Processing by Yipeng Liu Pdf

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

Yipeng Liu,Jiani Liu,Zhen Long,Ce Zhu
Tensor Computation for Data Analysis Book PDF

Author : Yipeng Liu,Jiani Liu,Zhen Long,Ce Zhu
Publisher : Springer Nature
Page : 347 pages
File Size : 40,7 Mb
Release : 2021-08-31
Category : Technology & Engineering
ISBN : 9783030743864

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Tensor Computation for Data Analysis by Yipeng Liu,Jiani Liu,Zhen Long,Ce Zhu Pdf

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

Gérard Favier
Matrix and Tensor Decompositions in Signal Processing Volume 2 Book PDF

Author : Gérard Favier
Publisher : John Wiley & Sons
Page : 386 pages
File Size : 55,7 Mb
Release : 2021-08-17
Category : Technology & Engineering
ISBN : 9781119700968

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Matrix and Tensor Decompositions in Signal Processing, Volume 2 by Gérard Favier Pdf

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.

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

Carl-Fredrik Westin,Anna Vilanova,Bernhard Burgeth
Visualization and Processing of Tensors and Higher Order Descriptors for Multi Valued Data Book PDF

Author : Carl-Fredrik Westin,Anna Vilanova,Bernhard Burgeth
Publisher : Springer
Page : 343 pages
File Size : 55,7 Mb
Release : 2014-07-17
Category : Mathematics
ISBN : 9783642543012

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Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data by Carl-Fredrik Westin,Anna Vilanova,Bernhard Burgeth Pdf

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 Regression

Jiani Liu,Ce Zhu,Zhen Long,Yipeng Liu
Tensor Regression Book PDF

Author : Jiani Liu,Ce Zhu,Zhen Long,Yipeng Liu
Publisher : Unknown
Page : 128 pages
File Size : 42,8 Mb
Release : 2021-09-27
Category : Electronic
ISBN : 1680838865

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Tensor Regression by Jiani Liu,Ce Zhu,Zhen Long,Yipeng Liu Pdf

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

Joachim Weickert,Hans Hagen
Visualization and Processing of Tensor Fields Book PDF

Author : Joachim Weickert,Hans Hagen
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 55,8 Mb
Release : 2007-06-25
Category : Mathematics
ISBN : 9783540312727

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Visualization and Processing of Tensor Fields by Joachim Weickert,Hans Hagen Pdf

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

Santiago Aja-Fernández,Rodrigo de Luis Garcia,Dacheng Tao,Xuelong Li
Tensors in Image Processing and Computer Vision Book PDF

Author : Santiago Aja-Fernández,Rodrigo de Luis Garcia,Dacheng Tao,Xuelong Li
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 43,6 Mb
Release : 2009-05-21
Category : Computers
ISBN : 9781848822993

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Tensors in Image Processing and Computer Vision by Santiago Aja-Fernández,Rodrigo de Luis Garcia,Dacheng Tao,Xuelong Li Pdf

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.

User-Defined Tensor Data Analysis

Bin Dong,Kesheng Wu,Suren Byna
User Defined Tensor Data Analysis Book PDF

Author : Bin Dong,Kesheng Wu,Suren Byna
Publisher : Springer
Page : 101 pages
File Size : 52,5 Mb
Release : 2021-10-31
Category : Computers
ISBN : 3030707490

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User-Defined Tensor Data Analysis by Bin Dong,Kesheng Wu,Suren Byna Pdf

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

Abdelhak M. Zoubir,Visa Koivunen,Esa Ollila,Michael Muma
Robust Statistics for Signal Processing Book PDF

Author : Abdelhak M. Zoubir,Visa Koivunen,Esa Ollila,Michael Muma
Publisher : Cambridge University Press
Page : 315 pages
File Size : 53,7 Mb
Release : 2018-11-08
Category : Mathematics
ISBN : 9781107017412

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Robust Statistics for Signal Processing by Abdelhak M. Zoubir,Visa Koivunen,Esa Ollila,Michael Muma Pdf

Understand the benefits of robust statistics for signal processing using this unique and authoritative text.

Tensor Algebra and Tensor Analysis for Engineers

Mikhail Itskov
Tensor Algebra and Tensor Analysis for Engineers Book PDF

Author : Mikhail Itskov
Publisher : Springer Science & Business Media
Page : 253 pages
File Size : 53,5 Mb
Release : 2009-04-30
Category : Technology & Engineering
ISBN : 9783540939078

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Tensor Algebra and Tensor Analysis for Engineers by Mikhail Itskov Pdf

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.

Tensor Eigenvalues and Their Applications

Liqun Qi,Haibin Chen,Yannan Chen
Tensor Eigenvalues and Their Applications Book PDF

Author : Liqun Qi,Haibin Chen,Yannan Chen
Publisher : Springer
Page : 329 pages
File Size : 40,6 Mb
Release : 2018-03-30
Category : Mathematics
ISBN : 9789811080586

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Tensor Eigenvalues and Their Applications by Liqun Qi,Haibin Chen,Yannan Chen Pdf

This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.

Advances in Data Analysis with Computational Intelligence Methods

Adam E Gawęda,Janusz Kacprzyk,Leszek Rutkowski,Gary G. Yen
Advances in Data Analysis with Computational Intelligence Methods Book PDF

Author : Adam E Gawęda,Janusz Kacprzyk,Leszek Rutkowski,Gary G. Yen
Publisher : Springer
Page : 412 pages
File Size : 52,9 Mb
Release : 2017-09-21
Category : Technology & Engineering
ISBN : 9783319679464

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Advances in Data Analysis with Computational Intelligence Methods by Adam E Gawęda,Janusz Kacprzyk,Leszek Rutkowski,Gary G. Yen Pdf

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.

Anisotropy Across Fields and Scales

Evren Özarslan,Thomas Schultz,Eugene Zhang,Andrea Fuster
Anisotropy Across Fields and Scales Book PDF

Author : Evren Özarslan,Thomas Schultz,Eugene Zhang,Andrea Fuster
Publisher : Springer Nature
Page : 284 pages
File Size : 50,8 Mb
Release : 2021
Category : Algebra
ISBN : 9783030562151

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Anisotropy Across Fields and Scales by Evren Özarslan,Thomas Schultz,Eugene Zhang,Andrea Fuster Pdf

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.

Proceedings of the Fifth Euro-China Conference on Intelligent Data Analysis and Applications

Pavel Krömer,Hong Zhang,Yongquan Liang,Jeng-Shyang Pan
Proceedings of the Fifth Euro China Conference on Intelligent Data Analysis and Applications Book PDF

Author : Pavel Krömer,Hong Zhang,Yongquan Liang,Jeng-Shyang Pan
Publisher : Springer
Page : 854 pages
File Size : 50,6 Mb
Release : 2018-12-24
Category : Technology & Engineering
ISBN : 9783030037666

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Proceedings of the Fifth Euro-China Conference on Intelligent Data Analysis and Applications by Pavel Krömer,Hong Zhang,Yongquan Liang,Jeng-Shyang Pan Pdf

This volume of Advances in Intelligent Systems and Computing highlights papers presented at the Fifth Euro-China Conference on Intelligent Data Analysis and Applications (ECC2018), held in Xi’an, China from October 12 to 14 2018. The conference was co-sponsored by Springer, Xi’an University of Posts and Telecommunications, VSB Technical University of Ostrava (Czech Republic), Fujian University of Technology, Fujian Provincial Key Laboratory of Digital Equipment, Fujian Provincial Key Lab of Big Data Mining and Applications, and Shandong University of Science and Technology in China. The conference was intended as an international forum for researchers and professionals engaged in all areas of computational intelligence, intelligent control, intelligent data analysis, pattern recognition, intelligent information processing, and applications.

Nonnegative Matrix and Tensor Factorizations

Andrzej Cichocki,Rafal Zdunek,Anh Huy Phan,Shun-ichi Amari
Nonnegative Matrix and Tensor Factorizations Book PDF

Author : Andrzej Cichocki,Rafal Zdunek,Anh Huy Phan,Shun-ichi Amari
Publisher : John Wiley & Sons
Page : 500 pages
File Size : 50,8 Mb
Release : 2009-07-10
Category : Science
ISBN : 0470747285

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Nonnegative Matrix and Tensor Factorizations by Andrzej Cichocki,Rafal Zdunek,Anh Huy Phan,Shun-ichi Amari Pdf

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.