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.

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: Deuflhard

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 390

ISBN-13: 1468467549

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In this book, the new and rapidly expanding field of scientific computing is understood in a double sense: as computing for scientific and engineering problems and as the science of doing such computations. Thus scientific computing touches at one side mathematical modelling (in the various fields of applications) and at the other side computer science. As soon as the mathematical models de scribe the features of real life processes in sufficient detail, the associated computations tend to be large scale. As a consequence, interest more and more focusses on such numerical methods that can be expected to cope with large scale computational problems. Moreover, given the algorithms which are known to be efficient on a tradi tional computer, the question of implementation on modern supercomputers may get crucial. The present book is the proceedings of a meeting on "Large Scale Scientific Computing" , that was held a t the Oberwolfach Mathematical Institute (July 14-19, 1985) under the auspices of the Sonderforschungsbereich 123 of the University of Heidelberg. Participants included applied scientists with computational interests, numerical analysts, and experts on modern parallel computers. 'l'he purpose of the meeting was to establish a common under standing of recent issues in scientific computing, especially in view of large scale problems. Fields of applications, which have been covered, included semi-conductor design, chemical combustion, flow through porous media, climatology, seismology, fluid dynami. cs, tomography, rheology, hydro power plant optimization, subwil. y control, space technology.

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

Non-negative Matrix Factorization Techniques
Non-negative Matrix Factorization Techniques

Author: Ganesh R. Naik

Publisher: Springer

Published: 2015-09-25

Total Pages: 200

ISBN-13: 3662483319

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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.

Computer Vision – ECCV 2012
Computer Vision – ECCV 2012

Author: Andrew Fitzgibbon

Publisher: Springer

Published: 2012-09-26

Total Pages: 508

ISBN-13: 3642337864

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The seven-volume set comprising LNCS volumes 7572-7578 constitutes the refereed proceedings of the 12th European Conference on Computer Vision, ECCV 2012, held in Florence, Italy, in October 2012. The 408 revised papers presented were carefully reviewed and selected from 1437 submissions. The papers are organized in topical sections on geometry, 2D and 3D shapes, 3D reconstruction, visual recognition and classification, visual features and image matching, visual monitoring: action and activities, models, optimisation, learning, visual tracking and image registration, photometry: lighting and colour, and image segmentation.

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.

Machine Learning for Data Science Handbook
Machine Learning for Data Science Handbook

Author: Lior Rokach

Publisher: Springer Nature

Published: 2023-08-17

Total Pages: 975

ISBN-13: 3031246284

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This book organizes key concepts, theories, standards, methodologies, trends, challenges and applications of data mining and knowledge discovery in databases. It first surveys, then provides comprehensive yet concise algorithmic descriptions of methods, including classic methods plus the extensions and novel methods developed recently. It also gives in-depth descriptions of data mining applications in various interdisciplinary industries.

Context-Aware Ranking with Factorization Models
Context-Aware Ranking with Factorization Models

Author: Steffen Rendle

Publisher: Springer Science & Business Media

Published: 2010-11-11

Total Pages: 183

ISBN-13: 3642168973

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Context-aware ranking is an important task with many applications. E.g. in recommender systems items (products, movies, ...) and for search engines webpages should be ranked. In all these applications, the ranking is not global (i.e. always the same) but depends on the context. Simple examples for context are the user for recommender systems and the query for search engines. More complicated context includes time, last actions, etc. The major problem is that typically the variable domains (e.g. customers, products) are categorical and huge, the observations are very sparse and only positive events are observed. In this book, a generic method for context-aware ranking as well as its application are presented. For modelling a new factorization based on pairwise interactions is proposed and compared to other tensor factorization approaches. For learning, the `Bayesian Context-aware Ranking' framework consisting of an optimization criterion and algorithm is developed. The second main part of the book applies this general theory to the three scenarios of item, tag and sequential-set recommendation. Furthermore extensions of time-variant factors and one-class problems are studied. This book generalizes and builds on work that has received the `WWW 2010 Best Paper Award', the `WSDM 2010 Best Student Paper Award' and the `ECML/PKDD 2009 Best Discovery Challenge Award'.