matrix and tensor decomposition

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Matrix and Tensor Factorization Techniques for Recommender Systems
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Publisher : Springer
Release Date :
ISBN 10 : 3319413570
Pages : 102 pages
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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.

Matrix and Tensor Factorization Techniques for Recommender Systems

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

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Matrix and Tensor Decomposition

Download or read online Matrix and Tensor Decomposition written by Christian Jutten, published by Unknown which was released on . Get Matrix and Tensor Decomposition Books now! Available in PDF, ePub and Kindle.

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Algorithmic Aspects of Machine Learning

Introduces cutting-edge research on machine learning theory and practice, providing an accessible, modern algorithmic toolkit.

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Spectral Learning on Matrices and Tensors

The authors of this monograph survey recent progress in using spectral methods including matrix and tensor decomposition techniques to learn many popular latent variable models. With careful implementation, tensor-based methods can run efficiently in practice, and in many cases they are the only algorithms with provable guarantees on running time

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Tensor Decomposition Meets Approximation Theory

This thesis studies three different subjects, namely tensors and tensor decomposition, sparse interpolation and Pad\'e or rational approximation theory. These problems find their origin in various fields within mathematics: on the one hand tensors originate from algebra and are of importance in computer science and knowledge technology, while on

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Tensors in Image Processing and Computer Vision

Tensor signal processing is an emerging field with important applications to computer vision and image processing. This book presents the state of the art in this new branch of signal processing, offering a great deal of research and discussions by leading experts in the area. The wide-ranging volume offers an

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Sketching as a Tool for Numerical Linear Algebra

Sketching as a Tool for Numerical Linear Algebra highlights the recent advances in algorithms for numerical linear algebra that have come from the technique of linear sketching, whereby given a matrix, one first compressed it to a much smaller matrix by multiplying it by a (usually) random matrix with certain

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Low Rank Tensor Decomposition for Feature Extraction and Tensor Recovery

Feature extraction and tensor recovery problems are important yet challenging, particularly for multi-dimensional data with missing values and/or noise. Low-rank tensor decomposition approaches are widely used for solving these problems. This thesis focuses on three common tensor decompositions (CP, Tucker and t-SVD) and develops a set of decomposition-based approaches.

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Tensors

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

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Decomposability of Tensors

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

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Tensor Network Contractions

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

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Higher order Kronecker Products and Tensor Decompositions

The second problem in this dissertation involves solving shifted linear systems of the form (A - lambdaI) x = b when A is a Kronecker product of matrices. The Schur decomposition is used to reduce the shifted Kronecker product system to a Kronecker product of quasi-triangular matrices. The system is solved

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Three mode Principal Component Analysis

Download or read online Three mode Principal Component Analysis written by Pieter M. Kroonenberg, published by Unknown which was released on 1983. Get Three mode Principal Component Analysis Books now! Available in PDF, ePub and Kindle.

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New Frontiers in Applied Data Mining

This book constitutes the thoroughly refereed post-conference proceedings of five international workshops held in conjunction with PAKDD 2011 in Shenzhen, China, in May 2011: the International Workshop on Behavior Informatics (BI 2011), the Workshop on Quality Issues, Measures of Interestingness and Evaluation of Data Mining Models (QIMIE 2011), the Workshop on Biologically Inspired Techniques

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Adaptive Blind Signal and Image Processing

This book is a unification and extension of the theories behind adaptive blind signal and image processing, providing practical and efficient algorithms for many different and novel applications, including the latest developments and additional material not included in the first edition. This includes new material on multiway analysis, sparse representation

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