Nonnegative Matrix And Tensor Factorizations Least Squares Problems And Applications
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Nonnegative Matrix And Tensor Factorizations
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Author : Andrzej Cichocki
language : en
Publisher: John Wiley & Sons
Release Date : 2009-07-10
Nonnegative Matrix And Tensor Factorizations written by Andrzej Cichocki and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-10 with Science categories.
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.
Nonnegative Matrix And Tensor Factorizations Least Squares Problems And Applications
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Author : Jingu Kim
language : en
Publisher:
Release Date : 2011
Nonnegative Matrix And Tensor Factorizations Least Squares Problems And Applications written by Jingu Kim and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Computer science categories.
Nonnegative matrix factorization (NMF) is a useful dimension reduction method that has been investigated and applied in various areas. NMF is considered for high-dimensional data in which each element has a nonnegative value, and it provides a low-rank approximation formed by factors whose elements are also nonnegative. The nonnegativity constraints imposed on the low-rank factors not only enable natural interpretation but also reveal the hidden structure of data. Extending the benefits of NMF to multidimensional arrays, nonnegative tensor factorization (NTF) has been shown to be successful in analyzing complicated data sets. Despite the success, NMF and NTF have been actively developed only in the recent decade, and algorithmic strategies for computing NMF and NTF have not been fully studied. In this thesis, computational challenges regarding NMF, NTF, and related least squares problems are addressed.
Nonnegative Matrix Factorization
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Author : Nicolas Gillis
language : en
Publisher: SIAM
Release Date : 2020-12-18
Nonnegative Matrix Factorization written by Nicolas Gillis and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-18 with Mathematics categories.
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.
The Birth Of Numerical Analysis
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Author : Adhemar Bultheel
language : en
Publisher: World Scientific
Release Date : 2010
The Birth Of Numerical Analysis written by Adhemar Bultheel and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
The 1947 paper by John von Neumann & Herman Goldstine, 'Numerical Inverting of Matrices of High Order', is considered as the birth certificate of numerical analysis. Since its publication, the evolution of this domain has been enormous. This book collects contributions by researchers who have lived through this evolution.
Optimization Algorithms
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Author : Mykhaylo Andriychuk
language : en
Publisher: BoD – Books on Demand
Release Date : 2024-07-10
Optimization Algorithms written by Mykhaylo Andriychuk and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-10 with Mathematics categories.
Optimization Algorithms - Classics and Last Advances is devoted to developing algorithm theory and exploring the use of different optimization algorithms for solving various problems in pure science, applied physics, and information technology. The book consists of two sections. The first focuses on developing abstract algorithms with subsequent applications to real-world optimization problems. It discusses optimization problems based on partial differential equations, canonical polyadic decomposition, variational approach, and ant colony optimization, which are discussed here. The second section presents problems related to optimization in information technologies. Chapters in this section address the utilization of optimization algorithms to solve problems of reducing computation time and computer memory, reducing kernel mechanism processing time in multimedia authoring tools, arranging access optimization for special applications, and minimizing resources for solving vehicle routing problems.
Advances In Neural Networks Isnn 2024
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Author : Xinyi Le
language : en
Publisher: Springer Nature
Release Date : 2024-07-06
Advances In Neural Networks Isnn 2024 written by Xinyi Le and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-06 with Computers categories.
This volume constitutes the refereed proceedings of the 18th International Symposium on Neural Networks, ISNN 2024, held in Weihai, China, during 11-14, July 2024. The 59 full papers were carefully reviewed and selected from 82 submission. They are categorized in the following sections: Optimization Algorithms; Adversarial Learning, Transfer Learning, and Deep Learning; Signal, Image, and Video Processing; Modeling, Analysis, and Implementation of Neural Networks; Control Systems, Robotics, and Autonomous Driving; Fault Diagnosis and Intelligent Industry & Bio-signal, Bioinformatics, and Biomedical Engineering.
Information Geometry And Its Applications
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Author : Shun-ichi Amari
language : en
Publisher: Springer
Release Date : 2016-02-02
Information Geometry And Its Applications written by Shun-ichi Amari and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-02 with Mathematics categories.
This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman–Scott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning, signal processing, optimization, and neural networks. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields.
Advances In Neural Networks Isnn 2007
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Author : Derong Liu
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-16
Advances In Neural Networks Isnn 2007 written by Derong Liu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-16 with Computers categories.
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.
Academic Press Library In Signal Processing
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Author : Paulo S.R. Diniz
language : en
Publisher: Academic Press
Release Date : 2013-09-21
Academic Press Library In Signal Processing written by Paulo S.R. Diniz and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-21 with Technology & Engineering categories.
This first volume, edited and authored by world leading experts, gives a review of the principles, methods and techniques of important and emerging research topics and technologies in machine learning and advanced signal processing theory. With this reference source you will: - Quickly grasp a new area of research - Understand the underlying principles of a topic and its application - Ascertain how a topic relates to other areas and learn of the research issues yet to be resolved - Quick tutorial reviews of important and emerging topics of research in machine learning - Presents core principles in signal processing theory and shows their applications - Reference content on core principles, technologies, algorithms and applications - Comprehensive references to journal articles and other literature on which to build further, more specific and detailed knowledge - Edited by leading people in the field who, through their reputation, have been able to commission experts to write on a particular topic
Artificial Intelligence Logic And Applications
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Author : Songmao Zhang
language : en
Publisher: Springer Nature
Release Date : 2025-01-30
Artificial Intelligence Logic And Applications written by Songmao Zhang and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-30 with Computers categories.
This book constitutes the proceedings of the 4th International Conference on Artificial Intelligence Logic and Applications, AILA 2024, held in Lanzhou, China, during August 10–11, 2024. The 16 full papers and the 11 short papers included in this volume were carefully reviewed and selected from 45 submissions. The papers cover the following topics: AI logic foundation; AI logic reasoning; AI logic applications.