Applied Matrix And Tensor Variate Data Analysis

Author : Toshio Sakata
Publisher : Springer
Page : 136 pages
File Size : 43,7 Mb
Release : 2016-02-02
Category : Computers
ISBN : 9784431553878

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Applied Matrix and Tensor Variate Data Analysis by Toshio Sakata Pdf

This book provides comprehensive reviews of recent progress in matrix variate and tensor variate data analysis from applied points of view. Matrix and tensor approaches for data analysis are known to be extremely useful for recently emerging complex and high-dimensional data in various applied fields. The reviews contained herein cover recent applications of these methods in psychology (Chap. 1), audio signals (Chap. 2) , image analysis from tensor principal component analysis (Chap. 3), and image analysis from decomposition (Chap. 4), and genetic data (Chap. 5) . Readers will be able to understand the present status of these techniques as applicable to their own fields. In Chapter 5 especially, a theory of tensor normal distributions, which is a basic in statistical inference, is developed, and multi-way regression, classification, clustering, and principal component analysis are exemplified under tensor normal distributions. Chapter 6 treats one-sided tests under matrix variate and tensor variate normal distributions, whose theory under multivariate normal distributions has been a popular topic in statistics since the books of Barlow et al. (1972) and Robertson et al. (1988). Chapters 1, 5, and 6 distinguish this book from ordinary engineering books on these topics.

Author : John A. Eisele,Robert M. Mason
Publisher : John Wiley & Sons
Page : 360 pages
File Size : 47,7 Mb
Release : 1970
Category : Mathematics
ISBN : UOM:39015015623088

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Applied Matrix and Tensor Analysis by John A. Eisele,Robert M. Mason Pdf

Author : Kohei Adachi
Publisher : Springer
Page : 298 pages
File Size : 53,7 Mb
Release : 2016-10-11
Category : Mathematics
ISBN : 9789811023415

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Matrix-Based Introduction to Multivariate Data Analysis by Kohei Adachi Pdf

This book enables readers who may not be familiar with matrices to understand a variety of multivariate analysis procedures in matrix forms. Another feature of the book is that it emphasizes what model underlies a procedure and what objective function is optimized for fitting the model to data. The author believes that the matrix-based learning of such models and objective functions is the fastest way to comprehend multivariate data analysis. The text is arranged so that readers can intuitively capture the purposes for which multivariate analysis procedures are utilized: plain explanations of the purposes with numerical examples precede mathematical descriptions in almost every chapter. This volume is appropriate for undergraduate students who already have studied introductory statistics. Graduate students and researchers who are not familiar with matrix-intensive formulations of multivariate data analysis will also find the book useful, as it is based on modern matrix formulations with a special emphasis on singular value decomposition among theorems in matrix algebra. The book begins with an explanation of fundamental matrix operations and the matrix expressions of elementary statistics, followed by the introduction of popular multivariate procedures with advancing levels of matrix algebra chapter by chapter. This organization of the book allows readers without knowledge of matrices to deepen their understanding of multivariate data analysis.

Author : Yipeng Liu,Jiani Liu,Zhen Long,Ce Zhu
Publisher : Springer Nature
Page : 347 pages
File Size : 45,9 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.

Author : Qi Zhang,Yingwei Wang,Liang-Jie Zhang
Publisher : Springer Nature
Page : 308 pages
File Size : 53,9 Mb
Release : 2020-09-17
Category : Computers
ISBN : 9783030596354

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Cloud Computing – CLOUD 2020 by Qi Zhang,Yingwei Wang,Liang-Jie Zhang Pdf

This book constitutes the proceedings of the 13th International Conference on Cloud Computing, CLOUD 2020, held as part of SCF 2020, during September 18-20, 2020. The conference was planned to take place in Honolulu, HI, USA and was changed to a virtual format due to the COVID-19 pandemic. The 16 full and 6 short papers presented were carefully reviewed and selected from 49 submissions. They deal with the latest fundamental advances in the state of the art and practice of cloud computing, identify emerging research topics, and define the future of cloud computing.

Author : Andrzej Cichocki,Rafal Zdunek,Anh Huy Phan,Shun-ichi Amari
Publisher : John Wiley & Sons
Page : 500 pages
File Size : 48,9 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.

Author : Nickolay Trendafilov,Michele Gallo
Publisher : Springer Nature
Page : 467 pages
File Size : 48,9 Mb
Release : 2021-09-15
Category : Mathematics
ISBN : 9783030769741

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Multivariate Data Analysis on Matrix Manifolds by Nickolay Trendafilov,Michele Gallo Pdf

This graduate-level textbook aims to give a unified presentation and solution of several commonly used techniques for multivariate data analysis (MDA). Unlike similar texts, it treats the MDA problems as optimization problems on matrix manifolds defined by the MDA model parameters, allowing them to be solved using (free) optimization software Manopt. The book includes numerous in-text examples as well as Manopt codes and software guides, which can be applied directly or used as templates for solving similar and new problems. The first two chapters provide an overview and essential background for studying MDA, giving basic information and notations. Next, it considers several sets of matrices routinely used in MDA as parameter spaces, along with their basic topological properties. A brief introduction to matrix (Riemannian) manifolds and optimization methods on them with Manopt complete the MDA prerequisite. The remaining chapters study individual MDA techniques in depth. The number of exercises complement the main text with additional information and occasionally involve open and/or challenging research questions. Suitable fields include computational statistics, data analysis, data mining and data science, as well as theoretical computer science, machine learning and optimization. It is assumed that the readers have some familiarity with MDA and some experience with matrix analysis, computing, and optimization.

Author : Peter McCullagh
Publisher : Courier Dover Publications
Page : 308 pages
File Size : 53,8 Mb
Release : 2018-07-18
Category : Mathematics
ISBN : 9780486832692

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Tensor Methods in Statistics by Peter McCullagh Pdf

A pioneering monograph on tensor methods applied to distributional problems arising in statistics, this work begins with the study of multivariate moments and cumulants. An invaluable reference for graduate students and professional statisticians. 1987 edition.

Author : Reşat Ulusay
Publisher : CRC Press
Page : 2044 pages
File Size : 40,5 Mb
Release : 2016-11-18
Category : Technology & Engineering
ISBN : 9781315388489

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Rock Mechanics and Rock Engineering: From the Past to the Future by Reşat Ulusay Pdf

Rock Mechanics and Rock Engineering: From the Past to the Future contains the contributions presented at EUROCK2016, the 2016 International Symposium of the International Society for Rock Mechanics (ISRM 2016, Ürgüp, Cappadocia Region, Turkey, 29-31 August 2016). The contributions cover almost all aspects of rock mechanics and rock engineering from theories to engineering practices, emphasizing the future direction of rock engineering technologies. The 204 accepted papers and eight keynote papers, are grouped into several main sections: - Fundamental rock mechanics - Rock properties and experimental rock mechanics - Analytical and numerical methods in rock engineering - Stability of slopes in civil and mining engineering - Design methodologies and analysis - Rock dynamics, rock mechanics and rock engineering at historical sites and monuments - Underground excavations in civil and mining engineering - Coupled processes in rock mass for underground storage and waste disposal - Rock mass characterization - Petroleum geomechanics - Carbon dioxide sequestration - Instrumentation-monitoring in rock engineering and back analysis - Risk management, and - the 2016 Rocha Medal Lecture and the 2016 Franklin Lecture Rock Mechanics and Rock Engineering: From the Past to the Future will be of interest to researchers and professionals involved in the various branches of rock mechanics and rock engineering. EUROCK 2016, organized by the Turkish National Society for Rock Mechanics, is a continuation of the successful series of ISRM symposia in Europe, which began in 1992 in Chester, UK.

Author : Panagiotis Symeonidis,Andreas Zioupos
Publisher : Springer
Page : 102 pages
File Size : 51,7 Mb
Release : 2017-01-29
Category : Computers
ISBN : 9783319413570

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Matrix and Tensor Factorization Techniques for Recommender Systems by Panagiotis Symeonidis,Andreas Zioupos Pdf

This book presents the algorithms used to provide recommendations by exploiting matrix factorization and tensor decomposition techniques. It highlights well-known decomposition methods for recommender systems, such as Singular Value Decomposition (SVD), UV-decomposition, Non-negative Matrix Factorization (NMF), etc. and describes in detail the pros and cons of each method for matrices and tensors. This book provides a detailed theoretical mathematical background of matrix/tensor factorization techniques and a step-by-step analysis of each method on the basis of an integrated toy example that runs throughout all its chapters and helps the reader to understand the key differences among methods. It also contains two chapters, where different matrix and tensor methods are compared experimentally on real data sets, such as Epinions, GeoSocialRec, Last.fm, BibSonomy, etc. and provides further insights into the advantages and disadvantages of each method. The book offers a rich blend of theory and practice, making it suitable for students, researchers and practitioners interested in both recommenders and factorization methods. Lecturers can also use it for classes on data mining, recommender systems and dimensionality reduction methods.

Author : Fabian Theis,Andrzej Cichocki,Arie Yeredor,Michael Zibulevsky
Publisher : Springer
Page : 538 pages
File Size : 51,7 Mb
Release : 2012-02-09
Category : Computers
ISBN : 9783642285516

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Latent Variable Analysis and Signal Separation by Fabian Theis,Andrzej Cichocki,Arie Yeredor,Michael Zibulevsky Pdf

This book constitutes the proceedings of the 10th International Conference on Latent Variable Analysis and Signal Separation, LVA/ICA 2012, held in Tel Aviv, Israel, in March 2012. The 20 revised full papers presented together with 42 revised poster papers, 1 keynote lecture, and 2 overview papers for the regular, as well as for the special session were carefully reviewed and selected from numerous submissions. Topics addressed are ranging from theoretical issues such as causality analysis and measures, through novel methods for employing the well-established concepts of sparsity and non-negativity for matrix and tensor factorization, down to a variety of related applications ranging from audio and biomedical signals to precipitation analysis.

Author : Emmanuel Vincent,Arie Yeredor,Zbyněk Koldovský,Petr Tichavský
Publisher : Springer
Page : 532 pages
File Size : 50,7 Mb
Release : 2015-08-14
Category : Computers
ISBN : 9783319224824

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Latent Variable Analysis and Signal Separation by Emmanuel Vincent,Arie Yeredor,Zbyněk Koldovský,Petr Tichavský Pdf

This book constitutes the proceedings of the 12th International Conference on Latent Variable Analysis and Signal Separation, LVA/ICS 2015, held in Liberec, Czech Republic, in August 2015. The 61 revised full papers presented – 29 accepted as oral presentations and 32 accepted as poster presentations – were carefully reviewed and selected from numerous submissions. Five special topics are addressed: tensor-based methods for blind signal separation; deep neural networks for supervised speech separation/enhancement; joined analysis of multiple datasets, data fusion, and related topics; advances in nonlinear blind source separation; sparse and low rank modeling for acoustic signal processing.

Author : Petr Tichavský,Massoud Babaie-Zadeh,Olivier J.J. Michel,Nadège Thirion-Moreau
Publisher : Springer
Page : 578 pages
File Size : 44,7 Mb
Release : 2017-02-13
Category : Computers
ISBN : 9783319535470

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Latent Variable Analysis and Signal Separation by Petr Tichavský,Massoud Babaie-Zadeh,Olivier J.J. Michel,Nadège Thirion-Moreau Pdf

This book constitutes the proceedings of the 13th International Conference on Latent Variable Analysis and Signal Separation, LVA/ICA 2017, held in Grenoble, France, in Feburary 2017. The 53 papers presented in this volume were carefully reviewed and selected from 60 submissions. They were organized in topical sections named: tensor approaches; from source positions to room properties: learning methods for audio scene geometry estimation; tensors and audio; audio signal processing; theoretical developments; physics and bio signal processing; latent variable analysis in observation sciences; ICA theory and applications; and sparsity-aware signal processing.

Author : David Skillicorn
Publisher : CRC Press
Page : 268 pages
File Size : 54,6 Mb
Release : 2007-05-17
Category : Computers
ISBN : 9781584888338

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Understanding Complex Datasets by David Skillicorn Pdf

Making obscure knowledge about matrix decompositions widely available, Understanding Complex Datasets: Data Mining with Matrix Decompositions discusses the most common matrix decompositions and shows how they can be used to analyze large datasets in a broad range of application areas. Without having to understand every mathematical detail, the book

Author : Lars Elden
Publisher : SIAM
Page : 229 pages
File Size : 43,5 Mb
Release : 2019-08-30
Category : Mathematics
ISBN : 9781611975864

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Matrix Methods in Data Mining and Pattern Recognition, Second Edition by Lars Elden Pdf

This thoroughly revised second edition provides an updated treatment of numerical linear algebra techniques for solving problems in data mining and pattern recognition. Adopting an application-oriented approach, the author introduces matrix theory and decompositions, describes how modern matrix methods can be applied in real life scenarios, and provides a set of tools that students can modify for a particular application. Building on material from the first edition, the author discusses basic graph concepts and their matrix counterparts. He introduces the graph Laplacian and properties of its eigenvectors needed in spectral partitioning and describes spectral graph partitioning applied to social networks and text classification. Examples are included to help readers visualize the results. This new edition also presents matrix-based methods that underlie many of the algorithms used for big data. The book provides a solid foundation to further explore related topics and presents applications such as classification of handwritten digits, text mining, text summarization, PageRank computations related to the Google search engine, and facial recognition. Exercises and computer assignments are available on a Web page that supplements the book. This book is primarily for undergraduate students who have previously taken an introductory scientific computing/numerical analysis course and graduate students in data mining and pattern recognition areas who need an introduction to linear algebra techniques.