Elliptically Symmetric Distributions in Signal Processing and Machine Learning, 1st ed. 2024

This book constitutes a review of recent developments in the theory and practical exploitation of the elliptical model for measured data in both classical and emerging areas of signal processing. It develops techniques usable in (among other areas): graph learning, robust clustering, linear shrinkage, information geometry, subspace-based algorithm design, and semiparametric and misspecified estimation.

The various contributions combine to show how the goal of inferring information from a set of acquired data, recurrent in statistical signal processing, can be achieved, even when the common practical assumption of Gaussian distribution in the data is not valid. The elliptical model propounded maintains the performance of its inference procedures even when that assumption fails. The elliptical distribution, being fully characterized by its location vector, its scatter/covariance matrix and its so-called density generator, used to describe the impulsiveness of the data, is sufficiently flexible to model heterogeneous applications.

This book is of interest to any graduate students and academic researchers wishing to acquaint themselves with the latest research in an area of rising consequence. It is also of assistance to practitioners working in data analysis, wireless communications, radar, and image processing.

1. Background on real and complex elliptically symmetric distributions.- Part I: Theoretical developments.- 2.The Fisher-Rao geometry of CES distributions.- 3. Linear shrinkage of sample covariance matrix or matrices under elliptical distributions: a review.- 4. Robust estimation with missing values for elliptical distributions.- Part II: Performance analysis.- 5. Semiparametric estimation in elliptical distributions.- 6. Estimation and Detection Under Misspecification and Complex Elliptically Symmetric Distributions.- 7. Performance analysis of subspace-based algorithms in CES data models.- Part III: Applications to machine learning.- 8. Robust Bayesian Cluster Enumeration for RES Distributions.- 9. FEMDA: a unified framework for discriminant analysis.- 10. Learning Graphs from Heavy-tailed Data.

Jean-Pierre Delmas received the engineering degree from Ecole Centrale de Lyon, France in 1973, the Certificat d'Etudes Supérieures from Ecole Nationale Supérieure des Télécommunications, Paris, France in 1982 and the Habilitation à diriger des recherches degree from the University of Paris XI, Orsay, France in 2001. Since 1980, he has been with Telecom SudParis where he is currently a Professor with the CITI department. He was the deputy director (2005–2010) and the director (2011–2014) of UMR 5157 (CNRS laboratory). His teaching and research interest lie in statistical methods for signal processing with emphasis on asymptotic performance analysis and array processing applied to multi-sensor systems in the context of communications. He is author or co-author of more than 140 publications (journal, conference and chapter of book, book). He was an Associate Editor for the IEEE Transactions on Signal Processing (2002–2006) and (2010–2014) for Signal Processing (Elsevier) (2009–2020), and currently for IEEE Signal Processing Letters. From 2011 to 2016, he was a member of the IEEE Sensor Array and Multichannel Technical Committee.

Mohammed Nabil El Korso received the M.Sc. in Electrical Engineering from the National Polytechnic School, Algeria in 2007. He obtained the Master Research degree in Signal and Image Processing from ParisSud XI University, France in 2008. In 2011, he obtained his Ph.D. degree from Paris-Sud XI University. From 2011 to 2012, he was a research scientist in the Communication Systems Group at Technische Universitat Darmstadt, Germany. He was Assistant Professor at Ecole Normale Supérieure de Cachan from 2012 to 2013, and Assistant Professor at University of Paris Nanterre from 2013 to 2022. Currently, he is Professor at Paris Saclay University. His research interests include robust statistical signal processing, statistical analysis with missing values, estimation with mixed effects models with appli