Matrix and Tensor Decomposition: Application to Data Fusion and Analysis introduces the main theoretical concepts for data fusion using matrix and tensor decompositions, beginning 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 rich diagrams to help communicate the main ideas and relationships among models and methods, this book presents 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 decomposition
- Provides a unifying framework for basic matrix and tensor decompositions, considering both algebraic and statistical points-of-view and discussing their relationships
- Addresses key questions in implementation, most importantly, that of model order selection and other parameters
- Provides tools for model order selection so that the signal subspace can be identified
Tulay Adali received the Ph.D. degree in Electrical Engineering from North Carolina State University, Raleigh, NC, USA, in 1992 and joined the faculty at the University of Maryland Baltimore County (UMBC), Baltimore, MD, the same year. She is currently a Distinguished University Professor in the Department of Computer Science and Electrical Engineering at UMBC and is the director of the Machine Learning for Signal Processing Lab (MLSP Lab). Dana Lahat received the BSc, MSc and PhD degrees in electrical and electronics engineering from Tel Aviv University, Israel, in 1998, 2004 and 2013, respectively. She is currently a postdoctoral researcher in GIPSA-Lab, Grenoble, France. She has been awarded the Chateaubriand Fellowship of the French Government for the academic year 2007-2008. Her main research interests are statistical signal processing and source separation Christian Jutten received a PhD degree in 1981 and the Docteur es Sciences degree in 1987 from the Institut National Polytechnique of Grenoble (France). He is currently deputy director of Institute for Information Sciences and Technologies of CNRS. He has been deputy director of the Grenoble images, speech, signal and control laboratory (GIPSA) and director of the Department Images-Signal (DIS from 2007 to 2010. For 30 years, his research interests have been blind source separation, independent component analysis and learning in neural networks, including theoretical aspects (separability, source separation in nonlinear mixtures, sparsity) and applications in signal processing (biomedical, seismic, hyperspectral imaging, speech). He is author or co-author of more than 75 papers in international journals, four books, 25 invited plenary talks and 170 communications in international conferences. He received the Medal Blondel in 1997 from SEE (French Electrical Engineering society) for his contributions in source separation and independent component analysis, and has been elevated as a Fellow IEEE and a senior Member of Institut Universitaire de France in 2008. In 2012, he was awarded by an ERC Advanced Grant CHESS. In 2013, he has been elevated as EURASIP Fellow and reconducted for five years as a senior member of Institut Universitaire de France.
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
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