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Matrix And Tensor Decomposition

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Matrix and Tensor Factorization Techniques for Recommender Systems

Matrix and Tensor Factorization Techniques for Recommender Systems Book
Author : Panagiotis Symeonidis,Andreas Zioupos
Publisher : Springer
Release : 2016-09-25
ISBN : 9783319413563
Language : En, Es, Fr & De

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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.

Matrix and Tensor Decompositions in Signal Processing

Matrix and Tensor Decompositions in Signal Processing Book
Author : Gérard Favier
Publisher : John Wiley & Sons
Release : 2021-08-31
ISBN : 1786301555
Language : En, Es, Fr & De

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Book Description :

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 Factorization Techniques for Recommender Systems

Matrix and Tensor Factorization Techniques for Recommender Systems Book
Author : Panagiotis Symeonidis,Andreas Zioupos
Publisher : Springer
Release : 2017-01-29
ISBN : 3319413570
Language : En, Es, Fr & De

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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.

Matrix and Tensor Decompositions in Signal Processing

Matrix and Tensor Decompositions in Signal Processing Book
Author : Gérard Favier
Publisher : John Wiley & Sons
Release : 2021-08-17
ISBN : 1119700965
Language : En, Es, Fr & De

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Book Description :

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

Nonnegative Matrix and Tensor Factorizations Book
Author : Andrzej Cichocki,Rafal Zdunek,Anh Huy Phan,Shun-ichi Amari
Publisher : John Wiley & Sons
Release : 2009-07-10
ISBN : 9780470747285
Language : En, Es, Fr & De

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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.

Matrix and Tensor Factorization Techniques for Recommender Systems

Matrix and Tensor Factorization Techniques for Recommender Systems Book
Author : Panagiotis Symeonidis
Publisher : Unknown
Release : 2016
ISBN : 9783319413587
Language : En, Es, Fr & De

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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.

Tensor Computation for Data Analysis

Tensor Computation for Data Analysis Book
Author : Yipeng Liu
Publisher : Springer Nature
Release : 2022
ISBN : 3030743861
Language : En, Es, Fr & De

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Book Description :

Tensor is a natural representation for multi-dimensional data, and tensor computation can avoid possible multi-linear data structure loss in classical matrix computation-based data analysis. This book is intended to provide non-specialists an overall understanding of tensor computation and its applications in data analysis, and benefits researchers, engineers, and students with theoretical, computational, technical and experimental details. It presents a systematic and up-to-date overview of tensor decompositions from the engineer's point of view, and comprehensive coverage of tensor computation based data analysis techniques. In addition, some practical examples in machine learning, signal processing, data mining, computer vision, remote sensing, and biomedical engineering are also presented for easy understanding and implementation. These data analysis techniques may be further applied in other applications on neuroscience, communication, psychometrics, chemometrics, biometrics, quantum physics, quantum chemistry, etc. The discussion begins with basic coverage of notations, preliminary operations in tensor computations, main tensor decompositions and their properties. Based on them, a series of tensor-based data analysis techniques are presented as the tensor extensions of their classical matrix counterparts, including tensor dictionary learning, low rank tensor recovery, tensor completion, coupled tensor analysis, robust principal tensor component analysis, tensor regression, logistical tensor regression, support tensor machine, multilinear discriminate analysis, tensor subspace clustering, tensor-based deep learning, tensor graphical model and tensor sketch. The discussion also includes a number of typical applications with experimental results, such as image reconstruction, image enhancement, data fusion, signal recovery, recommendation system, knowledge graph acquisition, traffic flow prediction, link prediction, environmental prediction, weather forecasting, background extraction, human pose estimation, cognitive state classification from fMRI, infrared small target detection, heterogeneous information networks clustering, multi-view image clustering, and deep neural network compression.

Matrix and Tensor Decomposition

Matrix and Tensor Decomposition Book
Author : Christian Jutten
Publisher : Unknown
Release : 2022-06-27
ISBN : 9780128157602
Language : En, Es, Fr & De

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Book Description :

Download Matrix and Tensor Decomposition book written by Christian Jutten, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Advances in Knowledge Discovery and Data Mining

Advances in Knowledge Discovery and Data Mining Book
Author : Qiang Yang,Zhi-Hua Zhou,Zhiguo Gong,Min-Ling Zhang,Sheng-Jun Huang
Publisher : Springer
Release : 2019-04-03
ISBN : 303016148X
Language : En, Es, Fr & De

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Book Description :

The three-volume set LNAI 11439, 11440, and 11441 constitutes the thoroughly refereed proceedings of the 23rd Pacific-Asia Conference on Knowledge Discovery and Data Mining, PAKDD 2019, held in Macau, China, in April 2019. The 137 full papers presented were carefully reviewed and selected from 542 submissions. The papers present new ideas, original research results, and practical development experiences from all KDD related areas, including data mining, data warehousing, machine learning, artificial intelligence, databases, statistics, knowledge engineering, visualization, decision-making systems, and the emerging applications. They are organized in the following topical sections: classification and supervised learning; text and opinion mining; spatio-temporal and stream data mining; factor and tensor analysis; healthcare, bioinformatics and related topics; clustering and anomaly detection; deep learning models and applications; sequential pattern mining; weakly supervised learning; recommender system; social network and graph mining; data pre-processing and feature selection; representation learning and embedding; mining unstructured and semi-structured data; behavioral data mining; visual data mining; and knowledge graph and interpretable data mining.

Robust Statistics for Signal Processing

Robust Statistics for Signal Processing Book
Author : Abdelhak M. Zoubir,Visa Koivunen,Esa Ollila,Michael Muma
Publisher : Cambridge University Press
Release : 2018-10-31
ISBN : 1107017416
Language : En, Es, Fr & De

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Book Description :

Understand the benefits of robust statistics for signal processing using this unique and authoritative text.

Decomposability of Tensors

Decomposability of Tensors Book
Author : Luca Chiantini
Publisher : MDPI
Release : 2019-02-15
ISBN : 3038975907
Language : En, Es, Fr & De

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Book Description :

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

Human Interface and the Management of Information Information in Intelligent Systems

Human Interface and the Management of Information  Information in Intelligent Systems Book
Author : Sakae Yamamoto,Hirohiko Mori
Publisher : Springer
Release : 2019-07-10
ISBN : 3030226492
Language : En, Es, Fr & De

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Book Description :

This two-volume set LNCS 11569 and 11570 constitutes the refereed proceedings of the Thematic Area on Human Interface and the Management of Information, HIMI 2019, held as part of HCI International 2019 in Orlando, FL, USA. HCII 2019 received a total of 5029 submissions, of which 1275 papers and 209 posters were accepted for publication after a careful reviewing process. The 91 papers presented in the two volumes were organized in topical sections named: Visual information; Data visualization and analytics; Information, cognition and learning; Information, empathy and persuasion; Knowledge management and sharing; Haptic and tactile interaction; Information in virtual and augmented reality; Machine learning and intelligent systems; Human motion and expression recognition and tracking; Medicine, healthcare and quality of life applications.

Brain Informatics and Health

Brain Informatics and Health Book
Author : Dominik Slezak,Ah-Hwee Tan,James F. Peters,Lars Schwabe
Publisher : Springer
Release : 2014-07-14
ISBN : 3319098918
Language : En, Es, Fr & De

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Book Description :

This book constitutes the proceedings of the International Conference on Brain Informatics and Health, BIH 2014, held in Warsaw, Poland, in August 2014, as part of 2014 Web Intelligence Congress, WIC 2014. The 29 full papers presented together with 23 special session papers were carefully reviewed and selected from 101 submissions. The papers are organized in topical sections on brain understanding; cognitive modelling; brain data analytics; health data analytics; brain informatics and data management; semantic aspects of biomedical analytics; healthcare technologies and systems; analysis of complex medical data; understanding of information processing in brain; neuroimaging data processing strategies; advanced methods of interactive data mining for personalized medicine.

Tensor Analysis

Tensor Analysis Book
Author : Liqun Qi,Ziyan Luo
Publisher : SIAM
Release : 2017-04-19
ISBN : 1611974755
Language : En, Es, Fr & De

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Book Description :

Tensors, or hypermatrices, are multi-arrays with more than two indices. In the last decade or so, many concepts and results in matrix theory?some of which are nontrivial?have been extended to tensors and have a wide range of applications (for example, spectral hypergraph theory, higher order Markov chains, polynomial optimization, magnetic resonance imaging, automatic control, and quantum entanglement problems). The authors provide a comprehensive discussion of this new theory of tensors. Tensor Analysis: Spectral Theory and Special Tensors is unique in that it is the first book on these three subject areas: spectral theory of tensors; the theory of special tensors, including nonnegative tensors, positive semidefinite tensors, completely positive tensors, and copositive tensors; and the spectral hypergraph theory via tensors.

Artificial Intelligence Algorithms and Applications

Artificial Intelligence Algorithms and Applications Book
Author : Kangshun Li,Wei Li,Hui Wang,Yong Liu
Publisher : Springer Nature
Release : 2020-05-25
ISBN : 981155577X
Language : En, Es, Fr & De

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Book Description :

This book constitutes the thoroughly refereed proceedings of the 11th International Symposium on Intelligence Computation and Applications, ISICA 2019, held in Guangzhou, China, in November 2019. The 65 papers presented were carefully reviewed and selected from the total of 112 submissions. This volume features the most up-to-date research in evolutionary algorithms, parallel computing and quantum computing, evolutionary multi-objective and dynamic optimization, intelligent multimedia systems, virtualization and AI applications, smart scheduling, intelligent control, big data and cloud computing, deep learning, and hybrid machine learning systems.The papers are organized according to the following topical sections: new frontier in evolutionary algorithms; evolutionary multi-objective and dynamic optimization; intelligent multimedia systems; virtualization and AI applications; smart scheduling; intelligent control; big data and cloud computing; statistical learning.

Signal Processing and Networking for Big Data Applications

Signal Processing and Networking for Big Data Applications Book
Author : Zhu Han,Mingyi Hong,Dan Wang
Publisher : Cambridge University Press
Release : 2017-04-27
ISBN : 1107124387
Language : En, Es, Fr & De

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Book Description :

This unique text helps make sense of big data using signal processing techniques, in applications including machine learning, networking, and energy systems.

Advanced Signal Processing on Brain Event Related Potentials

Advanced Signal Processing on Brain Event Related Potentials Book
Author : Fengyu Cong,Tapani Ristaniemi,Heikki Lyytinen
Publisher : World Scientific
Release : 2015-04-08
ISBN : 9814623105
Language : En, Es, Fr & De

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Book Description :

This book is devoted to the application of advanced signal processing on event-related potentials (ERPs) in the context of electroencephalography (EEG) for the cognitive neuroscience. ERPs are usually produced through averaging single-trials of preprocessed EEG, and then, the interpretation of underlying brain activities is based on the ordinarily averaged EEG. We find that randomly fluctuating activities and artifacts can still present in the averaged EEG data, and that constant brain activities over single trials can overlap with each other in time, frequency and spatial domains. Therefore, before interpretation, it will be beneficial to further separate the averaged EEG into individual brain activities. The book proposes systematic approaches pre-process wavelet transform (WT), independent component analysis (ICA), and nonnegative tensor factorization (NTF) to filter averaged EEG in time, frequency and space domains to sequentially and simultaneously obtain the pure ERP of interest. Software of the proposed approaches will be open-accessed. Contents:IntroductionWavelet Filter Design Based on Frequency Responses for Filtering ERP Data With Duration of One EpochIndividual-Level ICA to Extract the ERP Components from the Averaged EEG DataMulti-Domain Feature of the ERP Extracted by NTF: New Approach for Group-Level Analysis of ERPsAnalysis of Ongoing EEG by NTF During Real-World Music ExperiencesAppendix: Introduction to Basic Knowledge of Mismatch Negativity Readership: Undergraduate, graduate, researchers and professionals in the field of neurology/neuroscience, medical imaging, psychology, biomedical engineering and computer science. Key Features:Advanced signal processing approaches can be applied on averaged EEG to extract ERPs' componentsFiltering ERPs in time, frequency and space domains sequentially and simultaneouslyDemo of ERP data and MATLAB codes are open-access for the advanced signal processing approaches on ERPsKeywords:Event-Related Potentials (ERPs);Digital Filter;Wavelet Filter;Independent Component Analysis;Tensor Decomposition;Nonnegative Tensor Factorization;Time-Frequency Representation

Multimodal Analytics for Next Generation Big Data Technologies and Applications

Multimodal Analytics for Next Generation Big Data Technologies and Applications Book
Author : Kah Phooi Seng,Li-minn Ang,Alan Wee-Chung Liew,Junbin Gao
Publisher : Springer
Release : 2019-07-18
ISBN : 3319975986
Language : En, Es, Fr & De

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Book Description :

This edited book will serve as a source of reference for technologies and applications for multimodality data analytics in big data environments. After an introduction, the editors organize the book into four main parts on sentiment, affect and emotion analytics for big multimodal data; unsupervised learning strategies for big multimodal data; supervised learning strategies for big multimodal data; and multimodal big data processing and applications. The book will be of value to researchers, professionals and students in engineering and computer science, particularly those engaged with image and speech processing, multimodal information processing, data science, and artificial intelligence.

Data Fusion Methodology and Applications

Data Fusion Methodology and Applications Book
Author : Marina Cocchi
Publisher : Elsevier
Release : 2019-05-11
ISBN : 0444639853
Language : En, Es, Fr & De

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Book Description :

Data Fusion Methodology and Applications explores the data-driven discovery paradigm in science and the need to handle large amounts of diverse data. Drivers of this change include the increased availability and accessibility of hyphenated analytical platforms, imaging techniques, the explosion of omics data, and the development of information technology. As data-driven research deals with an inductive attitude that aims to extract information and build models capable of inferring the underlying phenomena from the data itself, this book explores the challenges and methodologies used to integrate data from multiple sources, analytical platforms, different modalities, and varying timescales. Presents the first comprehensive textbook on data fusion, focusing on all aspects of data-driven discovery Includes comprehensible, theoretical chapters written for large and diverse audiences Provides a wealth of selected application to the topics included

Latent Variable Analysis and Signal Separation

Latent Variable Analysis and Signal Separation Book
Author : Vincent Vigneron,Vicente Zarzoso,Eric Moreau,Rémi Gribonval,Emmanuel Vincent
Publisher : Springer Science & Business Media
Release : 2010-09-27
ISBN : 364215994X
Language : En, Es, Fr & De

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Book Description :

Thisvolumecollectsthepaperspresentedatthe9thInternationalConferenceon Latent Variable Analysis and Signal Separation,LVA/ICA 2010. The conference was organized by INRIA, the French National Institute for Computer Science and Control,and was held in Saint-Malo, France, September 27–30,2010,at the Palais du Grand Large. Tenyearsafterthe?rstworkshoponIndependent Component Analysis(ICA) in Aussois, France, the series of ICA conferences has shown the liveliness of the community of theoreticians and practitioners working in this ?eld. While ICA and blind signal separation have become mainstream topics, new approaches have emerged to solve problems involving signal mixtures or various other types of latent variables: semi-blind models, matrix factorization using sparse com- nent analysis, non-negative matrix factorization, probabilistic latent semantic indexing, tensor decompositions, independent vector analysis, independent s- space analysis, and so on. To re?ect this evolution towards more general latent variable analysis problems in signal processing, the ICA International Steering Committee decided to rename the 9th instance of the conference LVA/ICA. From more than a hundred submitted papers, 25 were accepted as oral p- sentationsand53 asposter presentations. Thecontent ofthis volumefollowsthe conference schedule, resulting in 14 chapters. The papers collected in this v- ume demonstrate that the research activity in the ?eld continues to range from abstract concepts to the most concrete and applicable questions and consid- ations. Speech and audio, as well as biomedical applications, continue to carry the mass of the applications considered.