Matrix and Tensor Decomposition: Application to Data Fusion and Analysis

In data fusion, where there are multiple sets of data, very little is often known about the relationship of the underlying processes that give rise to such data. It is therefore desirable to minimize the underlying modeling assumptions and, at the same time, to fully exploit the interactions within and across the multiple sets of data. Matrix and tensor decompositions have emerged as attractive means of enabling a complete and symmetric interaction across datasets, while also making use of the complete available information within each dataset. This book introduces the main theoretical concepts for data fusion using matrix and tensor decompositions, starting with the concept of diversity, which facilitates identifiability. It provides the link between theoretical results and practice by addressing key implementation issues such as model choice for a given problem, identification of sources of diversity, parameter selection and performance evaluation. Using a rich use of diagrams to help communicate the main ideas and relationships among models and methods, Matrix and Tensor Decompositions: Application to Data Fusion and Analysis is a readily accessible reference for researchers on the methods and application of matrix and tensor decompositions. Introduces basic theory and practice of data fusion along with the concept of diversity as a key concept for interpretability and identifiability of a given decompositionProvides a unifying framework for basic matrix and tensor decompositions considering both algebraic and statistical points of view, discussing their relationshipsAddresses key questions in implementation, most importantly, that of model order selection as well as other parametersIntroduce tools for model order selection so that the signal subspace can be identified and consideration given to the more convenient noiseless case in implementationAddresses interpretability of the final analysis/fusion results and introduces objective tools of performance assessment to enable comparison among candidate modelsApplications from multiple domains, including medical image fusion, video analysis, remote sensing, and chemometrics INDICE: 1. Introduction 2. ICA and IVA: A Bottom-up Approach 3. ICA and IVA: A Top-down Approach 4. Sparse Decompositions 5. Nonnegative Decompositions 6. Tensor Decompositions 7. Data Fusion and Analysis Through 8. Data Fusion and Analysis Using General 9. Implementation Issues and Open

• ISBN: 978-0-12-815760-2
• Editorial: Academic Press
• Encuadernacion: Rústica
• Páginas: 225
• Fecha Publicación: 01/07/2020
• Nº Volúmenes: 1
• Idioma: Inglés