Matrix and Tensor Decompositions in Signal Processing, Volume 2

2021-08-31 Technology & Engineering

Author : Gérard Favier
Release : 2021-08-31
Genre : Technology & Engineering
Kind : eBook
Book Rating : 555/5 ( reviews)

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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. This book was released on 2021-08-31. 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

2009-07-10 Science

Author : Andrzej Cichocki
Release : 2009-07-10
Genre : Science
Kind : eBook
Book Rating : 285/5 ( reviews)

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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. This book was released on 2009-07-10. 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.

From Algebraic Structures to Tensors

2020-01-02 Technology & Engineering

Author : Gérard Favier
Release : 2020-01-02
Genre : Technology & Engineering
Kind : eBook
Book Rating : 547/5 ( reviews)

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Book Synopsis From Algebraic Structures to Tensors by : Gérard Favier

Download or read book From Algebraic Structures to Tensors written by Gérard Favier. This book was released on 2020-01-02. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays, tensors play a central role for the representation, mining, analysis, and fusion of multidimensional, multimodal, and heterogeneous big data in numerous fields. This set on Matrices and Tensors in Signal Processing aims at giving a self-contained and comprehensive presentation of various concepts and methods, starting from fundamental algebraic structures to advanced tensor-based applications, including recently developed tensor models and efficient algorithms for dimensionality reduction and parameter estimation. Although its title suggests an orientation towards signal processing, the results presented in this set will also be of use to readers interested in other disciplines. This first book provides an introduction to matrices and tensors of higher-order based on the structures of vector space and tensor space. Some standard algebraic structures are first described, with a focus on the hilbertian approach for signal representation, and function approximation based on Fourier series and orthogonal polynomial series. Matrices and hypermatrices associated with linear, bilinear and multilinear maps are more particularly studied. Some basic results are presented for block matrices. The notions of decomposition, rank, eigenvalue, singular value, and unfolding of a tensor are introduced, by emphasizing similarities and differences between matrices and tensors of higher-order.

Tensors for Data Processing

2021-10-21 Technology & Engineering

Author : Yipeng Liu
Release : 2021-10-21
Genre : Technology & Engineering
Kind : eBook
Book Rating : 658/5 ( reviews)

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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. This book was released on 2021-10-21. 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

Tensors for Data Processing

2021-10-27 Technology & Engineering

Author : Yipeng Liu
Release : 2021-10-27
Genre : Technology & Engineering
Kind : eBook
Book Rating : 47X/5 ( reviews)

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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. This book was released on 2021-10-27. 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

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