Nonnegative Matrix And Tensor Factorizations

Author : Andrzej Cichocki,Rafal Zdunek,Anh Huy Phan,Shun-ichi Amari
Publisher : John Wiley & Sons
Page : 500 pages
File Size : 40,7 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 : Andrzej Cichocki,Morten Mrup,Paris Smaragdis
Publisher : Unknown
Page : 120 pages
File Size : 48,5 Mb
Release : 2008
Category : Electronic
ISBN : 977454045X

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Advances in Nonnegative Matrix and Tensor Factorization by Andrzej Cichocki,Morten Mrup,Paris Smaragdis Pdf

Author : Panagiotis Symeonidis,Andreas Zioupos
Publisher : Springer
Page : 102 pages
File Size : 48,5 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 : Nicolas Gillis
Publisher : SIAM
Page : 376 pages
File Size : 44,5 Mb
Release : 2020-12-18
Category : Mathematics
ISBN : 9781611976410

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Nonnegative Matrix Factorization by Nicolas Gillis Pdf

Nonnegative matrix factorization (NMF) in its modern form has become a standard tool in the analysis of high-dimensional data sets. This book provides a comprehensive and up-to-date account of the most important aspects of the NMF problem and is the first to detail its theoretical aspects, including geometric interpretation, nonnegative rank, complexity, and uniqueness. It explains why understanding these theoretical insights is key to using this computational tool effectively and meaningfully. Nonnegative Matrix Factorization is accessible to a wide audience and is ideal for anyone interested in the workings of NMF. It discusses some new results on the nonnegative rank and the identifiability of NMF and makes available MATLAB codes for readers to run the numerical examples presented in the book. Graduate students starting to work on NMF and researchers interested in better understanding the NMF problem and how they can use it will find this book useful. It can be used in advanced undergraduate and graduate-level courses on numerical linear algebra and on advanced topics in numerical linear algebra and requires only a basic knowledge of linear algebra and optimization.

Author : Emmanuel Vincent,Tuomas Virtanen,Sharon Gannot
Publisher : John Wiley & Sons
Page : 517 pages
File Size : 46,6 Mb
Release : 2018-10-22
Category : Technology & Engineering
ISBN : 9781119279891

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Audio Source Separation and Speech Enhancement by Emmanuel Vincent,Tuomas Virtanen,Sharon Gannot Pdf

Learn the technology behind hearing aids, Siri, and Echo Audio source separation and speech enhancement aim to extract one or more source signals of interest from an audio recording involving several sound sources. These technologies are among the most studied in audio signal processing today and bear a critical role in the success of hearing aids, hands-free phones, voice command and other noise-robust audio analysis systems, and music post-production software. Research on this topic has followed three convergent paths, starting with sensor array processing, computational auditory scene analysis, and machine learning based approaches such as independent component analysis, respectively. This book is the first one to provide a comprehensive overview by presenting the common foundations and the differences between these techniques in a unified setting. Key features: Consolidated perspective on audio source separation and speech enhancement. Both historical perspective and latest advances in the field, e.g. deep neural networks. Diverse disciplines: array processing, machine learning, and statistical signal processing. Covers the most important techniques for both single-channel and multichannel processing. This book provides both introductory and advanced material suitable for people with basic knowledge of signal processing and machine learning. Thanks to its comprehensiveness, it will help students select a promising research track, researchers leverage the acquired cross-domain knowledge to design improved techniques, and engineers and developers choose the right technology for their target application scenario. It will also be useful for practitioners from other fields (e.g., acoustics, multimedia, phonetics, and musicology) willing to exploit audio source separation or speech enhancement as pre-processing tools for their own needs.

Author : Pierre Comon,Christian Jutten
Publisher : Academic Press
Page : 856 pages
File Size : 54,8 Mb
Release : 2010-02-17
Category : Technology & Engineering
ISBN : 9780080884943

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Handbook of Blind Source Separation by Pierre Comon,Christian Jutten Pdf

Edited by the people who were forerunners in creating the field, together with contributions from 34 leading international experts, this handbook provides the definitive reference on Blind Source Separation, giving a broad and comprehensive description of all the core principles and methods, numerical algorithms and major applications in the fields of telecommunications, biomedical engineering and audio, acoustic and speech processing. Going beyond a machine learning perspective, the book reflects recent results in signal processing and numerical analysis, and includes topics such as optimization criteria, mathematical tools, the design of numerical algorithms, convolutive mixtures, and time frequency approaches. This Handbook is an ideal reference for university researchers, R&D engineers and graduates wishing to learn the core principles, methods, algorithms, and applications of Blind Source Separation. Covers the principles and major techniques and methods in one book Edited by the pioneers in the field with contributions from 34 of the world’s experts Describes the main existing numerical algorithms and gives practical advice on their design Covers the latest cutting edge topics: second order methods; algebraic identification of under-determined mixtures, time-frequency methods, Bayesian approaches, blind identification under non negativity approaches, semi-blind methods for communications Shows the applications of the methods to key application areas such as telecommunications, biomedical engineering, speech, acoustic, audio and music processing, while also giving a general method for developing applications

Author : Michael R. Berthold,David J Hand
Publisher : Springer
Page : 515 pages
File Size : 46,8 Mb
Release : 2007-06-07
Category : Computers
ISBN : 9783540486251

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Intelligent Data Analysis by Michael R. Berthold,David J Hand Pdf

This second and revised edition contains a detailed introduction to the key classes of intelligent data analysis methods. The twelve coherently written chapters by leading experts provide complete coverage of the core issues. The first half of the book is devoted to the discussion of classical statistical issues. The following chapters concentrate on machine learning and artificial intelligence, rule induction methods, neural networks, fuzzy logic, and stochastic search methods. The book concludes with a chapter on visualization and an advanced overview of IDA processes.

Author : Ganesh R. Naik
Publisher : Springer
Page : 194 pages
File Size : 52,5 Mb
Release : 2015-09-25
Category : Technology & Engineering
ISBN : 9783662483312

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Non-negative Matrix Factorization Techniques by Ganesh R. Naik Pdf

This book collects new results, concepts and further developments of NMF. The open problems discussed include, e.g. in bioinformatics: NMF and its extensions applied to gene expression, sequence analysis, the functional characterization of genes, clustering and text mining etc. The research results previously scattered in different scientific journals and conference proceedings are methodically collected and presented in a unified form. While readers can read the book chapters sequentially, each chapter is also self-contained. This book can be a good reference work for researchers and engineers interested in NMF, and can also be used as a handbook for students and professionals seeking to gain a better understanding of the latest applications of NMF.

Author : Luca Chiantini
Publisher : MDPI
Page : 161 pages
File Size : 47,8 Mb
Release : 2019-02-15
Category : Mathematics
ISBN : 9783038975908

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Decomposability of Tensors by Luca Chiantini Pdf

This book is a printed edition of the Special Issue "Decomposability of Tensors" that was published in Mathematics

Author : Derong Liu,Shumin Fei,Zeng-Guang Hou,Huaguang Zhang,Changyin Sun
Publisher : Springer Science & Business Media
Page : 1210 pages
File Size : 43,6 Mb
Release : 2007-07-16
Category : Computers
ISBN : 9783540723950

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Advances in Neural Networks - ISNN 2007 by Derong Liu,Shumin Fei,Zeng-Guang Hou,Huaguang Zhang,Changyin Sun Pdf

This book is part of a three volume set that constitutes the refereed proceedings of the 4th International Symposium on Neural Networks, ISNN 2007, held in Nanjing, China in June 2007. Coverage includes neural networks for control applications, robotics, data mining and feature extraction, chaos and synchronization, support vector machines, fault diagnosis/detection, image/video processing, and applications of neural networks.

Author : Vincent Vigneron,Vicente Zarzoso,Eric Moreau,Rémi Gribonval,Emmanuel Vincent
Publisher : Springer Science & Business Media
Page : 672 pages
File Size : 48,6 Mb
Release : 2010-09-27
Category : Computers
ISBN : 9783642159947

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Latent Variable Analysis and Signal Separation by Vincent Vigneron,Vicente Zarzoso,Eric Moreau,Rémi Gribonval,Emmanuel Vincent Pdf

Thisvolumecollectsthepaperspresentedatthe9thInternationalConferenceon Latent Variable Analysis and Signal Separation,LVA/ICA 2010. The conference was organized by INRIA, the French National Institute for Computer Science and Control,and was held in Saint-Malo, France, September 27–30,2010,at the Palais du Grand Large. Tenyearsafterthe?rstworkshoponIndependent Component Analysis(ICA) in Aussois, France, the series of ICA conferences has shown the liveliness of the community of theoreticians and practitioners working in this ?eld. While ICA and blind signal separation have become mainstream topics, new approaches have emerged to solve problems involving signal mixtures or various other types of latent variables: semi-blind models, matrix factorization using sparse com- nent analysis, non-negative matrix factorization, probabilistic latent semantic indexing, tensor decompositions, independent vector analysis, independent s- space analysis, and so on. To re?ect this evolution towards more general latent variable analysis problems in signal processing, the ICA International Steering Committee decided to rename the 9th instance of the conference LVA/ICA. From more than a hundred submitted papers, 25 were accepted as oral p- sentationsand53 asposter presentations. Thecontent ofthis volumefollowsthe conference schedule, resulting in 14 chapters. The papers collected in this v- ume demonstrate that the research activity in the ?eld continues to range from abstract concepts to the most concrete and applicable questions and consid- ations. Speech and audio, as well as biomedical applications, continue to carry the mass of the applications considered.

Author : Michael W. Berry,Kyle A. Gallivan,Efstratios Gallopoulos,Ananth Grama,Bernard Philippe,Yousef Saad,Faisal Saied
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 42,6 Mb
Release : 2012-01-18
Category : Computers
ISBN : 9781447124368

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High-Performance Scientific Computing by Michael W. Berry,Kyle A. Gallivan,Efstratios Gallopoulos,Ananth Grama,Bernard Philippe,Yousef Saad,Faisal Saied Pdf

This book presents the state of the art in parallel numerical algorithms, applications, architectures, and system software. The book examines various solutions for issues of concurrency, scale, energy efficiency, and programmability, which are discussed in the context of a diverse range of applications. Features: includes contributions from an international selection of world-class authorities; examines parallel algorithm-architecture interaction through issues of computational capacity-based codesign and automatic restructuring of programs using compilation techniques; reviews emerging applications of numerical methods in information retrieval and data mining; discusses the latest issues in dense and sparse matrix computations for modern high-performance systems, multicores, manycores and GPUs, and several perspectives on the Spike family of algorithms for solving linear systems; presents outstanding challenges and developing technologies, and puts these in their historical context.

Author : M. Emre Celebi
Publisher : Springer
Page : 415 pages
File Size : 47,6 Mb
Release : 2014-11-07
Category : Technology & Engineering
ISBN : 9783319092591

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Partitional Clustering Algorithms by M. Emre Celebi Pdf

This book focuses on partitional clustering algorithms, which are commonly used in engineering and computer scientific applications. The goal of this volume is to summarize the state-of-the-art in partitional clustering. The book includes such topics as center-based clustering, competitive learning clustering and density-based clustering. Each chapter is contributed by a leading expert in the field.

Author : Ireneusz Czarnowski,Robert J. Howlett,Lakhmi C. Jain
Publisher : Springer Nature
Page : 525 pages
File Size : 51,6 Mb
Release : 2020-06-11
Category : Technology & Engineering
ISBN : 9789811559259

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Intelligent Decision Technologies by Ireneusz Czarnowski,Robert J. Howlett,Lakhmi C. Jain Pdf

This book gathers selected papers from the KES-IDT-2020 Conference, held as a Virtual Conference on June 17–19, 2020. The aim of the annual conference was to present and discuss the latest research results, and to generate new ideas in the field of intelligent decision-making. However, the range of topics discussed during the conference was definitely broader and covered methods in e.g. classification, prediction, data analysis, big data, data science, decision support, knowledge engineering, and modeling in such diverse areas as finance, cybersecurity, economics, health, management and transportation. The Problems in Industry 4.0 and IoT are also addressed. The book contains several sections devoted to specific topics, such as Intelligent Data Processing and its Applications High-Dimensional Data Analysis and its Applications Multi-Criteria Decision Analysis – Theory and Applications Large-Scale Systems for Intelligent Decision-Making and Knowledge Engineering Decision Technologies and Related Topics in Big Data Analysis of Social and Financial Issues Decision-Making Theory for Economics

Author : Lars Elden
Publisher : SIAM
Page : 226 pages
File Size : 40,9 Mb
Release : 2007-07-12
Category : Computers
ISBN : 9780898716269

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

Several very powerful numerical linear algebra techniques are available for solving problems in data mining and pattern recognition. This application-oriented book describes how modern matrix methods can be used to solve these problems, gives an introduction to matrix theory and decompositions, and provides students with a set of tools that can be modified for a particular application.Matrix Methods in Data Mining and Pattern Recognition is divided into three parts. Part I gives a short introduction to a few application areas before presenting linear algebra concepts and matrix decompositions that students can use in problem-solving environments such as MATLAB®. Some mathematical proofs that emphasize the existence and properties of the matrix decompositions are included. In Part II, linear algebra techniques are applied to data mining problems. Part III is a brief introduction to eigenvalue and singular value algorithms. The applications discussed by the author are: classification of handwritten digits, text mining, text summarization, pagerank computations related to the GoogleÔ search engine, and face recognition. Exercises and computer assignments are available on a Web page that supplements the book.Audience The book is intended for undergraduate students who have previously taken an introductory scientific computing/numerical analysis course. Graduate students in various data mining and pattern recognition areas who need an introduction to linear algebra techniques will also find the book useful.Contents Preface; Part I: Linear Algebra Concepts and Matrix Decompositions. Chapter 1: Vectors and Matrices in Data Mining and Pattern Recognition; Chapter 2: Vectors and Matrices; Chapter 3: Linear Systems and Least Squares; Chapter 4: Orthogonality; Chapter 5: QR Decomposition; Chapter 6: Singular Value Decomposition; Chapter 7: Reduced-Rank Least Squares Models; Chapter 8: Tensor Decomposition; Chapter 9: Clustering and Nonnegative Matrix Factorization; Part II: Data Mining Applications. Chapter 10: Classification of Handwritten Digits; Chapter 11: Text Mining; Chapter 12: Page Ranking for a Web Search Engine; Chapter 13: Automatic Key Word and Key Sentence Extraction; Chapter 14: Face Recognition Using Tensor SVD. Part III: Computing the Matrix Decompositions. Chapter 15: Computing Eigenvalues and Singular Values; Bibliography; Index.