Elliptically Symmetric Distributions In Signal Processing And Machine Learning
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Elliptically Symmetric Distributions In Signal Processing And Machine Learning
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Author : Jean-Pierre Delmas
language : en
Publisher: Springer
Release Date : 2024-04-03
Elliptically Symmetric Distributions In Signal Processing And Machine Learning written by Jean-Pierre Delmas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-04-03 with Technology & Engineering categories.
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.
Elliptically Symmetric Distributions In Signal Processing And Machine Learning
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Author : Jean-Pierre Delmas
language : en
Publisher: Springer Nature
Release Date : 2024
Elliptically Symmetric Distributions In Signal Processing And Machine Learning written by Jean-Pierre Delmas and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024 with Electronic books categories.
Zusammenfassung: 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
Blind Identification And Separation Of Complex Valued Signals
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Author : Eric Moreau
language : en
Publisher: John Wiley & Sons
Release Date : 2013-10-07
Blind Identification And Separation Of Complex Valued Signals written by Eric Moreau and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-07 with Technology & Engineering categories.
Blind identification consists of estimating a multi-dimensional system only through the use of its output, and source separation, the blind estimation of the inverse of the system. Estimation is generally carried out using different statistics of the output. The authors of this book consider the blind identification and source separation problem in the complex-domain, where the available statistical properties are richer and include non-circularity of the sources – underlying components. They define identifiability conditions and present state-of-the-art algorithms that are based on algebraic methods as well as iterative algorithms based on maximum likelihood theory. Contents 1. Mathematical Preliminaries. 2. Estimation by Joint Diagonalization. 3. Maximum Likelihood ICA. About the Authors Eric Moreau is Professor of Electrical Engineering at the University of Toulon, France. His research interests concern statistical signal processing, high order statistics and matrix/tensor decompositions with applications to data analysis, telecommunications and radar. Tülay Adali is Professor of Electrical Engineering and Director of the Machine Learning for Signal Processing Laboratory at the University of Maryland, Baltimore County, USA. Her research interests concern statistical and adaptive signal processing, with an emphasis on nonlinear and complex-valued signal processing, and applications in biomedical data analysis and communications. Blind identification consists of estimating a multidimensional system through the use of only its output. Source separation is concerned with the blind estimation of the inverse of the system. The estimation is generally performed by using different statistics of the outputs. The authors consider the blind estimation of a multiple input/multiple output (MIMO) system that mixes a number of underlying signals of interest called sources. They also consider the case of direct estimation of the inverse system for the purpose of source separation. They then describe the estimation theory associated with the identifiability conditions and dedicated algebraic algorithms. The algorithms depend critically on (statistical and/or time frequency) properties of complex sources that will be precisely described.
Algorithmic Advances In Riemannian Geometry And Applications
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Author : Hà Quang Minh
language : en
Publisher: Springer
Release Date : 2016-10-05
Algorithmic Advances In Riemannian Geometry And Applications written by Hà Quang Minh and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-05 with Computers categories.
This book presents a selection of the most recent algorithmic advances in Riemannian geometry in the context of machine learning, statistics, optimization, computer vision, and related fields. The unifying theme of the different chapters in the book is the exploitation of the geometry of data using the mathematical machinery of Riemannian geometry. As demonstrated by all the chapters in the book, when the data is intrinsically non-Euclidean, the utilization of this geometrical information can lead to better algorithms that can capture more accurately the structures inherent in the data, leading ultimately to better empirical performance. This book is not intended to be an encyclopedic compilation of the applications of Riemannian geometry. Instead, it focuses on several important research directions that are currently actively pursued by researchers in the field. These include statistical modeling and analysis on manifolds,optimization on manifolds, Riemannian manifolds and kernel methods, and dictionary learning and sparse coding on manifolds. Examples of applications include novel algorithms for Monte Carlo sampling and Gaussian Mixture Model fitting, 3D brain image analysis,image classification, action recognition, and motion tracking.
Coherence
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Author : David Ramírez
language : en
Publisher: Springer Nature
Release Date : 2023-01-01
Coherence written by David Ramírez and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Technology & Engineering categories.
This book organizes principles and methods of signal processing and machine learning into the framework of coherence. The book contains a wealth of classical and modern methods of inference, some reported here for the first time. General results are applied to problems in communications, cognitive radio, passive and active radar and sonar, multi-sensor array processing, spectrum analysis, hyperspectral imaging, subspace clustering, and related. The reader will find new results for model fitting; for dimension reduction in models and ambient spaces; for detection, estimation, and space-time series analysis; for subspace averaging; and for uncertainty quantification. Throughout, the transformation invariances of statistics are clarified, geometries are illuminated, and null distributions are given where tractable. Stochastic representations are emphasized, as these are central to Monte Carlo simulations. The appendices contain a comprehensive account of matrix theory, the SVD, the multivariate normal distribution, and many of the important distributions for coherence statistics. The book begins with a review of classical results in the physical and engineering sciences where coherence plays a fundamental role. Then least squares theory and the theory of minimum mean-squared error estimation are developed, with special attention paid to statistics that may be interpreted as coherence statistics. A chapter on classical hypothesis tests for covariance structure introduces the next three chapters on matched and adaptive subspace detectors. These detectors are derived from likelihood reasoning, but it is their geometries and invariances that qualify them as coherence statistics. A chapter on independence testing in space-time data sets leads to a definition of broadband coherence, and contains novel applications to cognitive radio and the analysis of cyclostationarity. The chapter on subspace averaging reviews basic results and derives an order-fitting rule for determining the dimension of an average subspace. These results are used to enumerate sources of acoustic and electromagnetic radiation and to cluster subspaces into similarity classes. The chapter on performance bounds and uncertainty quantification emphasizes the geometry of the Cramèr-Rao bound and its related information geometry.
Machine Learning For Signal Processing
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Author : Max A. Little
language : en
Publisher: Oxford University Press, USA
Release Date : 2019
Machine Learning For Signal Processing written by Max A. Little and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Computers categories.
Describes in detail the fundamental mathematics and algorithms of machine learning (an example of artificial intelligence) and signal processing, two of the most important and exciting technologies in the modern information economy. Builds up concepts gradually so that the ideas and algorithms can be implemented in practical software applications.
Pattern Recognition And Machine Intelligence
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Author : Bhabesh Deka
language : en
Publisher: Springer Nature
Release Date : 2019-11-25
Pattern Recognition And Machine Intelligence written by Bhabesh Deka and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-25 with Computers categories.
The two-volume set of LNCS 11941 and 11942 constitutes the refereed proceedings of the 8th International Conference on Pattern Recognition and Machine Intelligence, PReMI 2019, held in Tezpur, India, in December 2019. The 131 revised full papers presented were carefully reviewed and selected from 341 submissions. They are organized in topical sections named: Pattern Recognition; Machine Learning; Deep Learning; Soft and Evolutionary Computing; Image Processing; Medical Image Processing; Bioinformatics and Biomedical Signal Processing; Information Retrieval; Remote Sensing; Signal and Video Processing; and Smart and Intelligent Sensors.
Robust And Multivariate Statistical Methods
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Author : Mengxi Yi
language : en
Publisher: Springer Nature
Release Date : 2023-04-19
Robust And Multivariate Statistical Methods written by Mengxi Yi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-19 with Mathematics categories.
This book presents recent developments in multivariate and robust statistical methods. Featuring contributions by leading experts in the field it covers various topics, including multivariate and high-dimensional methods, time series, graphical models, robust estimation, supervised learning and normal extremes. It will appeal to statistics and data science researchers, PhD students and practitioners who are interested in modern multivariate and robust statistics. The book is dedicated to David E. Tyler on the occasion of his pending retirement and also includes a review contribution on the popular Tyler’s shape matrix.
Cumulative Index To Entire Ieee Group Transactions Journals 1951 1971 Subject
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Author : Nichigai Asoshiētsu
language : en
Publisher:
Release Date : 1973
Cumulative Index To Entire Ieee Group Transactions Journals 1951 1971 Subject written by Nichigai Asoshiētsu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Electric engineering categories.
Shrinkage Estimation
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Author : Dominique Fourdrinier
language : en
Publisher: Springer
Release Date : 2018-12-06
Shrinkage Estimation written by Dominique Fourdrinier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-06 with Mathematics categories.
This book provides a coherent framework for understanding shrinkage estimation in statistics. The term refers to modifying a classical estimator by moving it closer to a target which could be known a priori or arise from a model. The goal is to construct estimators with improved statistical properties. The book focuses primarily on point and loss estimation of the mean vector of multivariate normal and spherically symmetric distributions. Chapter 1 reviews the statistical and decision theoretic terminology and results that will be used throughout the book. Chapter 2 is concerned with estimating the mean vector of a multivariate normal distribution under quadratic loss from a frequentist perspective. In Chapter 3 the authors take a Bayesian view of shrinkage estimation in the normal setting. Chapter 4 introduces the general classes of spherically and elliptically symmetric distributions. Point and loss estimation for these broad classes are studied in subsequent chapters. In particular, Chapter 5 extends many of the results from Chapters 2 and 3 to spherically and elliptically symmetric distributions. Chapter 6 considers the general linear model with spherically symmetric error distributions when a residual vector is available. Chapter 7 then considers the problem of estimating a location vector which is constrained to lie in a convex set. Much of the chapter is devoted to one of two types of constraint sets, balls and polyhedral cones. In Chapter 8 the authors focus on loss estimation and data-dependent evidence reports. Appendices cover a number of technical topics including weakly differentiable functions; examples where Stein’s identity doesn’t hold; Stein’s lemma and Stokes’ theorem for smooth boundaries; harmonic, superharmonic and subharmonic functions; and modified Bessel functions.