Handbook of Robust Low-Rank and Sparse Matrix Decomposition
Handbook of Robust Low-Rank and Sparse Matrix Decomposition

Author: Thierry Bouwmans

Publisher: CRC Press

Published: 2016-05-27

Total Pages: 553

ISBN-13: 1498724639

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Handbook of Robust Low-Rank and Sparse Matrix Decomposition: Applications in Image and Video Processing shows you how robust subspace learning and tracking by decomposition into low-rank and sparse matrices provide a suitable framework for computer vision applications. Incorporating both existing and new ideas, the book conveniently gives you one-stop access to a number of different decompositions, algorithms, implementations, and benchmarking techniques. Divided into five parts, the book begins with an overall introduction to robust principal component analysis (PCA) via decomposition into low-rank and sparse matrices. The second part addresses robust matrix factorization/completion problems while the third part focuses on robust online subspace estimation, learning, and tracking. Covering applications in image and video processing, the fourth part discusses image analysis, image denoising, motion saliency detection, video coding, key frame extraction, and hyperspectral video processing. The final part presents resources and applications in background/foreground separation for video surveillance. With contributions from leading teams around the world, this handbook provides a complete overview of the concepts, theories, algorithms, and applications related to robust low-rank and sparse matrix decompositions. It is designed for researchers, developers, and graduate students in computer vision, image and video processing, real-time architecture, machine learning, and data mining.

Nonnegative Matrix Factorization
Nonnegative Matrix Factorization

Author: Nicolas Gillis

Publisher: SIAM

Published: 2020-12-18

Total Pages: 376

ISBN-13: 1611976413

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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.

Matrix and Tensor Factorization Techniques for Recommender Systems
Matrix and Tensor Factorization Techniques for Recommender Systems

Author: Panagiotis Symeonidis

Publisher: Springer

Published: 2017-01-29

Total Pages: 101

ISBN-13: 3319413570

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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.

Large-Scale Scientific Computing
Large-Scale Scientific Computing

Author: Ivan Lirkov

Publisher: Springer Science & Business Media

Published: 2010-04-23

Total Pages: 855

ISBN-13: 3642125344

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The 7th International Conference on Large-Scale Scienti?c Computations (LSSC 2009) was held in Sozopol, Bulgaria, June 4–8, 2009. The conference was organized and sponsored by the Institute for Parallel Processing at the B- garian Academy of Sciences. The conference was devoted to the 70th birthday anniversary of Professor Zahari Zlatev. The Bulgarian Academy of Sciences awarded him the Marin Drinov medal on ribbon for his outstanding results in environmental mat- matics and for his contributions to the Bulgarian mathematical society and the Academy of Sciences. The plenary invited speakers and lectures were: – P. Arbenz, “?Finite Element Analysis of Human Bone Structures” – Y. Efendiev, “Mixed Multiscale Finite Element Methods Using Limited Global Information” – U. Langer, “Fast Solvers for Non-Linear Time-Harmonic Problems” – T. Manteu?el, “First-Order System Least-Squares Approach to Resistive Magnetohydrodynamic Equations” – K. Sabelfeld, “Stochastic Simulation for Solving Random Boundary Value Problems and Some Applications” – F. Tro ¨ltzsch,“OnFinite ElementErrorEstimatesforOptimalControlPr- lems with Elliptic PDEs” – Z. Zlatev, “On Some Stability Properties of the Richardson Extrapolation Applied Together with the ?-method” The success of the conference and the present volume in particular are an outcome of the joint e?orts of many partnersfrom various institutions and or- nizations. Firstwe wouldlike to thank allthe membersofthe Scienti?c Comm- tee for their valuable contribution forming the scienti?c face of the conference, as well as for their help in reviewing contributed papers. We especially thank the organizers of the special sessions.

Source Separation and Machine Learning
Source Separation and Machine Learning

Author: Jen-Tzung Chien

Publisher: Academic Press

Published: 2018-10-16

Total Pages: 386

ISBN-13: 0128045779

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Source Separation and Machine Learning presents the fundamentals in adaptive learning algorithms for Blind Source Separation (BSS) and emphasizes the importance of machine learning perspectives. It illustrates how BSS problems are tackled through adaptive learning algorithms and model-based approaches using the latest information on mixture signals to build a BSS model that is seen as a statistical model for a whole system. Looking at different models, including independent component analysis (ICA), nonnegative matrix factorization (NMF), nonnegative tensor factorization (NTF), and deep neural network (DNN), the book addresses how they have evolved to deal with multichannel and single-channel source separation. - Emphasizes the modern model-based Blind Source Separation (BSS) which closely connects the latest research topics of BSS and Machine Learning - Includes coverage of Bayesian learning, sparse learning, online learning, discriminative learning and deep learning - Presents a number of case studies of model-based BSS (categorizing them into four modern models - ICA, NMF, NTF and DNN), using a variety of learning algorithms that provide solutions for the construction of BSS systems

Nonnegative Matrix and Tensor Factorizations
Nonnegative Matrix and Tensor Factorizations

Author: Andrzej Cichocki

Publisher: John Wiley & Sons

Published: 2009-07-10

Total Pages: 500

ISBN-13: 9780470747285

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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.

Proceedings of the Future Technologies Conference (FTC) 2021, Volume 1
Proceedings of the Future Technologies Conference (FTC) 2021, Volume 1

Author: Kohei Arai

Publisher: Springer Nature

Published: 2021-10-23

Total Pages: 1020

ISBN-13: 3030899063

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This book covers a wide range of important topics including but not limited to Technology Trends, Computing, Artificial Intelligence, Machine Vision, Communication, Security, e-Learning, and Ambient Intelligence and their applications to the real world. The sixth Future Technologies Conference 2021 was organized virtually and received a total of 531 submissions from academic pioneering researchers, scientists, industrial engineers, and students from all over the world.. After a double-blind peer review process, 191 submissions have been selected to be included in these proceedings. One of the meaningful and valuable dimensions of this conference is the way it brings together a large group of technology geniuses in one venue to not only present breakthrough research in future technologies, but also to promote discussions and debate of relevant issues, challenges, opportunities and research findings. We hope that readers find the book interesting, exciting, and inspiring; it provides the state-of-the-art intelligent methods and techniques for solving real-world problems along with a vision of the future research.