Non-negative matrix and tensor factorizations : applications to exploratory multiway data analysis and blind source separation / / Andrzej Cichocki ... [et al.]

• Pubblicazione: Hoboken, NJ, : John Wiley, 2009
• Descrizione fisica: 1 online resource (501 p.)
• Disciplina: 005.1
• Soggetto topico: Computer algorithms; Data mining; Machine learning; Data structures (Computer science)
• Altri autori: CichockiAndrzej
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: NONNEGATIVE MATRIX AND TENSOR FACTORIZATIONS: APPLICATIONS TO EXPLORATORY MULTI-WAY DATA ANALYSIS AND BLIND SOURCE SEPARATION; Contents; Preface; Acknowledgments; Glossary of Symbols and Abbreviations; 1 Introduction - Problem Statements and Models; 1.1 Blind Source Separation and Linear Generalized Component Analysis; 1.2 Matrix Factorization Models with Nonnegativity and Sparsity Constraints; 1.2.1 Why Nonnegativity and Sparsity Constraints?; 1.2.2 Basic NMF Model; 1.2.3 Symmetric NMF; 1.2.4 Semi-Orthogonal NMF; 1.2.5 Semi-NMF and Nonnegative Factorization of Arbitrary Matrix ; 1.2.6 Three-factor NMF1.2.7 NMF with Offset (Affine NMF); 1.2.8 Multi-layer NMF; 1.2.9 Simultaneous NMF; 1.2.10 Projective and Convex NMF; 1.2.11 Kernel NMF; 1.2.12 Convolutive NMF; 1.2.13 Overlapping NMF; 1.3 Basic Approaches to Estimate Parameters of Standard NMF; 1.3.1 Large-scale NMF; 1.3.2 Non-uniqueness of NMF and Techniques to Alleviate the Ambiguity Problem; 1.3.3 Initialization of NMF; 1.3.4 Stopping Criteria; 1.4 Tensor Properties and Basis of Tensor Algebra; 1.4.1 Tensors (Multi-way Arrays) - Preliminaries; 1.4.2 Subarrays, Tubes and Slices; 1.4.3 Unfolding - Matricization ; 1.4.4 Vectorization1.4.5 Outer, Kronecker, Khatri-Rao and Hadamard Products; 1.4.6 Mode-n Multiplication of Tensor by Matrix and Tensor by Vector, Contracted Tensor Product; 1.4.7 Special Forms of Tensors; 1.5 Tensor Decompositions and Factorizations; 1.5.1 Why Multi-way Array Decompositions and Factorizations?; 1.5.2 PARAFAC and Nonnegative Tensor Factorization; 1.5.3 NTF1 Model; 1.5.4 NTF2 Model; 1.5.5 Individual Differences in Scaling (INDSCAL) and Implicit Slice Canonical Decomposition Model (IMCAND); 1.5.6 Shifted PARAFAC and Convolutive NTF; 1.5.7 Nonnegative Tucker Decompositions ; 1.5.8 Block Component Decompositions1.5.9 Block-Oriented Decompositions; 1.5.10 PARATUCK2 and DEDICOM Models; 1.5.11 Hierarchical Tensor Decomposition; 1.6 Discussion and Conclusions; Appendix 1.A: Uniqueness Conditions for Three-way Tensor Factorizations; Appendix 1.B: Singular Value Decomposition (SVD) and Principal Component Analysis (PCA) with Sparsity and/or Nonnegativity Constraints; 1.B.1 Standard SVD and PCA; 1.B.2 Sparse PCA; 1.B.3 Nonnegative PCA; Appendix 1.C: Determining a True Number of Components ; Appendix 1.D: Nonnegative Rank Factorization Using Wedderborn Theorem - Estimation of the Number of ComponentsReferences; 2 Similarity Measures and Generalized Divergences; 2.1 Error-induced Distance and Robust Regression Techniques; 2.2 Robust Estimation; 2.3 Csiszár Divergences; 2.4 Bregman Divergence; 2.4.1 Bregman Matrix Divergences; 2.5 Alpha-Divergences; 2.5.1 Asymmetric Alpha-Divergences; 2.5.2 Symmetric Alpha-Divergences; 2.6 Beta-Divergences; 2.7 Gamma-Divergences; 2.8 Divergences Derived from Tsallis and Rényi Entropy; 2.8.1 Concluding Remarks ; Appendix 2.A: Information Geometry, Canonical Divergence, and Projection
• Sommario/riassunto: 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
• Titolo autorizzato: Non-negative matrix and tensor factorizations
• ISBN: 9786612688331; 9781282688339; 1282688332; 9780470747278; 0470747277; 9780470747285; 0470747285
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9911019146803321
• Lo trovi qui: Univ. Federico II