Matrix and Tensor Factorization Techniques for Recommender Systems

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Author :
Publisher : Springer
ISBN 13 : 3319413570
Total Pages : 101 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Matrix and Tensor Factorization Techniques for Recommender Systems by : Panagiotis Symeonidis

Download or read book Matrix and Tensor Factorization Techniques for Recommender Systems written by Panagiotis Symeonidis and published by Springer. This book was released on 2017-01-29 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Matrix and Tensor Decompositions in Signal Processing, Volume 2

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Author :
Publisher : John Wiley & Sons
ISBN 13 : 1119700965
Total Pages : 386 pages
Book Rating : 4.1/5 (197 download)

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Book Synopsis Matrix and Tensor Decompositions in Signal Processing, Volume 2 by : Gérard Favier

Download or read book Matrix and Tensor Decompositions in Signal Processing, Volume 2 written by Gérard Favier and published by John Wiley & Sons. This book was released on 2021-08-17 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second volume will deal with a presentation of the main matrix and tensor decompositions and their properties of uniqueness, as well as very useful tensor networks for the analysis of massive data. Parametric estimation algorithms will be presented for the identification of the main tensor decompositions. After a brief historical review of the compressed sampling methods, an overview of the main methods of retrieving matrices and tensors with missing data will be performed under the low rank hypothesis. Illustrative examples will be provided.

Nonnegative Matrix and Tensor Factorizations

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Author :
Publisher : John Wiley & Sons
ISBN 13 : 9780470747285
Total Pages : 500 pages
Book Rating : 4.7/5 (472 download)

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Book Synopsis Nonnegative Matrix and Tensor Factorizations by : Andrzej Cichocki

Download or read book Nonnegative Matrix and Tensor Factorizations written by Andrzej Cichocki and published by John Wiley & Sons. This book was released on 2009-07-10 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Decompositions in Signal Processing, Volume 2

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Author :
Publisher : John Wiley & Sons
ISBN 13 : 1786301555
Total Pages : 386 pages
Book Rating : 4.7/5 (863 download)

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Book Synopsis Matrix and Tensor Decompositions in Signal Processing, Volume 2 by : Gérard Favier

Download or read book Matrix and Tensor Decompositions in Signal Processing, Volume 2 written by Gérard Favier and published by John Wiley & Sons. This book was released on 2021-08-31 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second volume will deal with a presentation of the main matrix and tensor decompositions and their properties of uniqueness, as well as very useful tensor networks for the analysis of massive data. Parametric estimation algorithms will be presented for the identification of the main tensor decompositions. After a brief historical review of the compressed sampling methods, an overview of the main methods of retrieving matrices and tensors with missing data will be performed under the low rank hypothesis. Illustrative examples will be provided.

Matrix and Tensor Decomposition

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Author :
Publisher :
ISBN 13 : 9780128157602
Total Pages : pages
Book Rating : 4.1/5 (576 download)

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Book Synopsis Matrix and Tensor Decomposition by : Christian Jutten

Download or read book Matrix and Tensor Decomposition written by Christian Jutten and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Matrix and Tensor Factorization Techniques for Recommender Systems

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Author :
Publisher :
ISBN 13 : 9783319413587
Total Pages : pages
Book Rating : 4.4/5 (135 download)

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Book Synopsis Matrix and Tensor Factorization Techniques for Recommender Systems by : Panagiotis Symeonidis

Download or read book Matrix and Tensor Factorization Techniques for Recommender Systems written by Panagiotis Symeonidis and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Anisotropy Across Fields and Scales

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Author :
Publisher : Springer Nature
ISBN 13 : 3030562158
Total Pages : 284 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Anisotropy Across Fields and Scales by : Evren Özarslan

Download or read book Anisotropy Across Fields and Scales written by Evren Özarslan and published by Springer Nature. This book was released on 2021 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book focuses on processing, modeling, and visualization of anisotropy information, which are often addressed by employing sophisticated mathematical constructs such as tensors and other higher-order descriptors. It also discusses adaptations of such constructs to problems encountered in seemingly dissimilar areas of medical imaging, physical sciences, and engineering. Featuring original research contributions as well as insightful reviews for scientists interested in handling anisotropy information, it covers topics such as pertinent geometric and algebraic properties of tensors and tensor fields, challenges faced in processing and visualizing different types of data, statistical techniques for data processing, and specific applications like mapping white-matter fiber tracts in the brain. The book helps readers grasp the current challenges in the field and provides information on the techniques devised to address them. Further, it facilitates the transfer of knowledge between different disciplines in order to advance the research frontiers in these areas. This multidisciplinary book presents, in part, the outcomes of the seventh in a series of Dagstuhl seminars devoted to visualization and processing of tensor fields and higher-order descriptors, which was held in Dagstuhl, Germany, on October 28-November 2, 2018.

Tensors: Geometry and Applications

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Publisher : American Mathematical Soc.
ISBN 13 : 0821869078
Total Pages : 464 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Tensors: Geometry and Applications by : J. M. Landsberg

Download or read book Tensors: Geometry and Applications written by J. M. Landsberg and published by American Mathematical Soc.. This book was released on 2011-12-14 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensors are ubiquitous in the sciences. The geometry of tensors is both a powerful tool for extracting information from data sets, and a beautiful subject in its own right. This book has three intended uses: a classroom textbook, a reference work for researchers in the sciences, and an account of classical and modern results in (aspects of) the theory that will be of interest to researchers in geometry. For classroom use, there is a modern introduction to multilinear algebra and to the geometry and representation theory needed to study tensors, including a large number of exercises. For researchers in the sciences, there is information on tensors in table format for easy reference and a summary of the state of the art in elementary language. This is the first book containing many classical results regarding tensors. Particular applications treated in the book include the complexity of matrix multiplication, P versus NP, signal processing, phylogenetics, and algebraic statistics. For geometers, there is material on secant varieties, G-varieties, spaces with finitely many orbits and how these objects arise in applications, discussions of numerous open questions in geometry arising in applications, and expositions of advanced topics such as the proof of the Alexander-Hirschowitz theorem and of the Weyman-Kempf method for computing syzygies.

Tensor Network Contractions

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Publisher : Springer Nature
ISBN 13 : 3030344894
Total Pages : 160 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Tensor Network Contractions by : Shi-Ju Ran

Download or read book Tensor Network Contractions written by Shi-Ju Ran and published by Springer Nature. This book was released on 2020-01-27 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.

Unsupervised Feature Extraction Applied to Bioinformatics

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Publisher : Springer Nature
ISBN 13 : 3030224562
Total Pages : 321 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Unsupervised Feature Extraction Applied to Bioinformatics by : Y-h. Taguchi

Download or read book Unsupervised Feature Extraction Applied to Bioinformatics written by Y-h. Taguchi and published by Springer Nature. This book was released on 2019-08-23 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book proposes applications of tensor decomposition to unsupervised feature extraction and feature selection. The author posits that although supervised methods including deep learning have become popular, unsupervised methods have their own advantages. He argues that this is the case because unsupervised methods are easy to learn since tensor decomposition is a conventional linear methodology. This book starts from very basic linear algebra and reaches the cutting edge methodologies applied to difficult situations when there are many features (variables) while only small number of samples are available. The author includes advanced descriptions about tensor decomposition including Tucker decomposition using high order singular value decomposition as well as higher order orthogonal iteration, and train tenor decomposition. The author concludes by showing unsupervised methods and their application to a wide range of topics. Allows readers to analyze data sets with small samples and many features; Provides a fast algorithm, based upon linear algebra, to analyze big data; Includes several applications to multi-view data analyses, with a focus on bioinformatics.

Handbook of Variational Methods for Nonlinear Geometric Data

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Publisher : Springer Nature
ISBN 13 : 3030313514
Total Pages : 701 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Handbook of Variational Methods for Nonlinear Geometric Data by : Philipp Grohs

Download or read book Handbook of Variational Methods for Nonlinear Geometric Data written by Philipp Grohs and published by Springer Nature. This book was released on 2020-04-03 with total page 701 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art. Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance. Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.

Structured Matrices

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Publisher : Nova Biomedical Books
ISBN 13 :
Total Pages : 222 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Structured Matrices by : Dario Bini

Download or read book Structured Matrices written by Dario Bini and published by Nova Biomedical Books. This book was released on 2001 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematicians from various countries assemble computational techniques that have developed and described over the past two decades to analyze matrices with structure, which are encountered in a wide variety of problems in pure and applied mathematics and in engineering. The 16 studies are on asymptotical spectral properties; algorithm design and analysis; issues specifically relating to structures, algebras, and polynomials; and image processing and differential equations. c. Book News Inc.

Tensors for Data Processing

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Publisher : Academic Press
ISBN 13 : 0323859658
Total Pages : 598 pages
Book Rating : 4.3/5 (238 download)

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Book Synopsis Tensors for Data Processing by : Yipeng Liu

Download or read book Tensors for Data Processing written by Yipeng Liu and published by Academic Press. This book was released on 2021-10-21 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensors for Data Processing: Theory, Methods and Applications presents both classical and state-of-the-art methods on tensor computation for data processing, covering computation theories, processing methods, computing and engineering applications, with an emphasis on techniques for data processing. This reference is ideal for students, researchers and industry developers who want to understand and use tensor-based data processing theories and methods. As a higher-order generalization of a matrix, tensor-based processing can avoid multi-linear data structure loss that occurs in classical matrix-based data processing methods. This move from matrix to tensors is beneficial for many diverse application areas, including signal processing, computer science, acoustics, neuroscience, communication, medical engineering, seismology, psychometric, chemometrics, biometric, quantum physics and quantum chemistry. Provides a complete reference on classical and state-of-the-art tensor-based methods for data processing Includes a wide range of applications from different disciplines Gives guidance for their application

Algorithmic Aspects of Machine Learning

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Publisher : Cambridge University Press
ISBN 13 : 1107184584
Total Pages : 161 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Algorithmic Aspects of Machine Learning by : Ankur Moitra

Download or read book Algorithmic Aspects of Machine Learning written by Ankur Moitra and published by Cambridge University Press. This book was released on 2018-09-27 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces cutting-edge research on machine learning theory and practice, providing an accessible, modern algorithmic toolkit.

Advances in Nonnegative Matrix and Tensor Factorization

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Publisher :
ISBN 13 : 9789774540455
Total Pages : 120 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Advances in Nonnegative Matrix and Tensor Factorization by : Andrzej Cichocki

Download or read book Advances in Nonnegative Matrix and Tensor Factorization written by Andrzej Cichocki and published by . This book was released on 2008 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Theory and Computation of Complex Tensors and its Applications

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Publisher : Springer Nature
ISBN 13 : 9811520593
Total Pages : 250 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Theory and Computation of Complex Tensors and its Applications by : Maolin Che

Download or read book Theory and Computation of Complex Tensors and its Applications written by Maolin Che and published by Springer Nature. This book was released on 2020-04-01 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides an introduction of very recent results about the tensors and mainly focuses on the authors' work and perspective. A systematic description about how to extend the numerical linear algebra to the numerical multi-linear algebra is also delivered in this book. The authors design the neural network model for the computation of the rank-one approximation of real tensors, a normalization algorithm to convert some nonnegative tensors to plane stochastic tensors and a probabilistic algorithm for locating a positive diagonal in a nonnegative tensors, adaptive randomized algorithms for computing the approximate tensor decompositions, and the QR type method for computing U-eigenpairs of complex tensors. This book could be used for the Graduate course, such as Introduction to Tensor. Researchers may also find it helpful as a reference in tensor research.

Decomposability of Tensors

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Author :
Publisher : MDPI
ISBN 13 : 3038975907
Total Pages : 161 pages
Book Rating : 4.0/5 (389 download)

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Book Synopsis Decomposability of Tensors by : Luca Chiantini

Download or read book Decomposability of Tensors written by Luca Chiantini and published by MDPI. This book was released on 2019-02-15 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a printed edition of the Special Issue "Decomposability of Tensors" that was published in Mathematics