Nonnegative Matrix and Tensor Factorizations PDF Download

Author: Andrzej Cichocki
Publisher: John Wiley & Sons
ISBN: 9780470747285
Category : Science
Languages : en
Pages : 500

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Book Description
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.

Author: Panagiotis Symeonidis
Publisher: Springer
ISBN: 3319413570
Category : Computers
Languages : en
Pages : 101

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Book Description
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.

Author: Nicolas Gillis
Publisher: SIAM
ISBN: 1611976413
Category : Mathematics
Languages : en
Pages : 376

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Book Description
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.

Author: Lars Elden
Publisher: SIAM
ISBN: 0898716268
Category : Computers
Languages : en
Pages : 226

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Book Description
Several very powerful numerical linear algebra techniques are available for solving problems in data mining and pattern recognition. This application-oriented book describes how modern matrix methods can be used to solve these problems, gives an introduction to matrix theory and decompositions, and provides students with a set of tools that can be modified for a particular application.Matrix Methods in Data Mining and Pattern Recognition is divided into three parts. Part I gives a short introduction to a few application areas before presenting linear algebra concepts and matrix decompositions that students can use in problem-solving environments such as MATLAB®. Some mathematical proofs that emphasize the existence and properties of the matrix decompositions are included. In Part II, linear algebra techniques are applied to data mining problems. Part III is a brief introduction to eigenvalue and singular value algorithms. The applications discussed by the author are: classification of handwritten digits, text mining, text summarization, pagerank computations related to the GoogleÔ search engine, and face recognition. Exercises and computer assignments are available on a Web page that supplements the book.Audience The book is intended for undergraduate students who have previously taken an introductory scientific computing/numerical analysis course. Graduate students in various data mining and pattern recognition areas who need an introduction to linear algebra techniques will also find the book useful.Contents Preface; Part I: Linear Algebra Concepts and Matrix Decompositions. Chapter 1: Vectors and Matrices in Data Mining and Pattern Recognition; Chapter 2: Vectors and Matrices; Chapter 3: Linear Systems and Least Squares; Chapter 4: Orthogonality; Chapter 5: QR Decomposition; Chapter 6: Singular Value Decomposition; Chapter 7: Reduced-Rank Least Squares Models; Chapter 8: Tensor Decomposition; Chapter 9: Clustering and Nonnegative Matrix Factorization; Part II: Data Mining Applications. Chapter 10: Classification of Handwritten Digits; Chapter 11: Text Mining; Chapter 12: Page Ranking for a Web Search Engine; Chapter 13: Automatic Key Word and Key Sentence Extraction; Chapter 14: Face Recognition Using Tensor SVD. Part III: Computing the Matrix Decompositions. Chapter 15: Computing Eigenvalues and Singular Values; Bibliography; Index.

Author: Mike E. Davies
Publisher: Springer Science & Business Media
ISBN: 3540744932
Category : Computers
Languages : en
Pages : 864

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Book Description
This book constitutes the refereed proceedings of the 7th International Conference on Independent Component Analysis and Blind Source Separation, ICA 2007, held in London, UK, in September 2007. It covers algorithms and architectures, applications, medical applications, speech and signal processing, theory, and visual and sensory processing.

Author: Alessandro Villa
Publisher: Springer
ISBN: 3642332668
Category : Computers
Languages : en
Pages : 612

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Book Description
The two-volume set LNCS 7552 + 7553 constitutes the proceedings of the 22nd International Conference on Artificial Neural Networks, ICANN 2012, held in Lausanne, Switzerland, in September 2012. The 162 papers included in the proceedings were carefully reviewed and selected from 247 submissions. They are organized in topical sections named: theoretical neural computation; information and optimization; from neurons to neuromorphism; spiking dynamics; from single neurons to networks; complex firing patterns; movement and motion; from sensation to perception; object and face recognition; reinforcement learning; bayesian and echo state networks; recurrent neural networks and reservoir computing; coding architectures; interacting with the brain; swarm intelligence and decision-making; mulitlayer perceptrons and kernel networks; training and learning; inference and recognition; support vector machines; self-organizing maps and clustering; clustering, mining and exploratory analysis; bioinformatics; and time weries and forecasting.

Author: Michael Gertz
Publisher: Springer
ISBN: 3319643673
Category : Computers
Languages : en
Pages : 454

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Book Description
This book constitutes the refereed proceedings of the 15th International Symposium on Spatial and Temporal Databases, SSTD 2017, held in Arlington, VA, USA, in August 2017.The 19 full papers presented together with 8 demo papers and 5 vision papers were carefully reviewed and selected from 90 submissions. The papers are organized around the current research on concepts, tools, and techniques related to spatial and temporal databases.

Author: Shoji Makino
Publisher: Springer
ISBN: 3319730312
Category : Technology & Engineering
Languages : en
Pages : 389

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Book Description
This book provides the first comprehensive overview of the fascinating topic of audio source separation based on non-negative matrix factorization, deep neural networks, and sparse component analysis. The first section of the book covers single channel source separation based on non-negative matrix factorization (NMF). After an introduction to the technique, two further chapters describe separation of known sources using non-negative spectrogram factorization, and temporal NMF models. In section two, NMF methods are extended to multi-channel source separation. Section three introduces deep neural network (DNN) techniques, with chapters on multichannel and single channel separation, and a further chapter on DNN based mask estimation for monaural speech separation. In section four, sparse component analysis (SCA) is discussed, with chapters on source separation using audio directional statistics modelling, multi-microphone MMSE-based techniques and diffusion map methods. The book brings together leading researchers to provide tutorial-like and in-depth treatments on major audio source separation topics, with the objective of becoming the definitive source for a comprehensive, authoritative, and accessible treatment. This book is written for graduate students and researchers who are interested in audio source separation techniques based on NMF, DNN and SCA.

Author: Fengyu Cong
Publisher: Springer
ISBN: 3319590812
Category : Computers
Languages : en
Pages : 614

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Book Description
This book constitutes the refereed proceedings of the 14th International Symposium on Neural Networks, ISNN 2017, held in Sapporo, Hakodate, and Muroran, Hokkaido, Japan, in June 2017. The 135 revised full papers presented in this two-volume set were carefully reviewed and selected from 259 submissions. The papers cover topics like perception, emotion and development, action and motor control, attractor and associative memory, neurodynamics, complex systems, and chaos.

Author: Michael W. Berry
Publisher: Springer Science & Business Media
ISBN: 1447124367
Category : Computers
Languages : en
Pages : 351

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Book Description
This book presents the state of the art in parallel numerical algorithms, applications, architectures, and system software. The book examines various solutions for issues of concurrency, scale, energy efficiency, and programmability, which are discussed in the context of a diverse range of applications. Features: includes contributions from an international selection of world-class authorities; examines parallel algorithm-architecture interaction through issues of computational capacity-based codesign and automatic restructuring of programs using compilation techniques; reviews emerging applications of numerical methods in information retrieval and data mining; discusses the latest issues in dense and sparse matrix computations for modern high-performance systems, multicores, manycores and GPUs, and several perspectives on the Spike family of algorithms for solving linear systems; presents outstanding challenges and developing technologies, and puts these in their historical context.