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Titlebook: Elliptically Symmetric Distributions in Signal Processing and Machine Learning; Jean-Pierre Delmas,Mohammed Nabil El Korso,Frédéri Book 20

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书目名称Elliptically Symmetric Distributions in Signal Processing and Machine Learning
编辑Jean-Pierre Delmas,Mohammed Nabil El Korso,Frédéri
视频video
概述Avoids the need to make assumptions about Gaussian distributions in data.Provides a general, flexible method of signal processing analysis.Is helpful in a variety of practical applications
图书封面Titlebook: Elliptically Symmetric Distributions in Signal Processing and Machine Learning;  Jean-Pierre Delmas,Mohammed Nabil El Korso,Frédéri Book 20
描述.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 risi
出版日期Book 2024
关键词Graph Learning; Linear Shrinkage; Missing Data; Robust Statistics; Elliptical Distribution; Information G
版次1
doihttps://doi.org/10.1007/978-3-031-52116-4
isbn_softcover978-3-031-52118-8
isbn_ebook978-3-031-52116-4
copyrightThe Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl
The information of publication is updating

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Linear Shrinkage of Sample Covariance Matrix or Matrices Under Elliptical Distributions: A Reviewand multiple populations settings, respectively. In the single sample setting a popular linear shrinkage estimator is defined as a linear combination of the sample covariance matrix (SCM) with a scaled identity matrix. The optimal shrinkage coefficients minimizing the mean-squared error (MSE) under
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Semiparametric Estimation in Elliptical Distributionsowing how it can be fruitfully applied to the joint estimation of the . and the . (or .) matrix of a set of elliptically distributed observations in the presence of an unknown density generator. A semiparametric model is a set of probablity density functions (pdfs) parameterized by a finite-dimensio
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Performance Analysis of Subspace-Based Algorithms in CES Data Modelsapplications in signal processing. The statistical performance of these subspace-based algorithms depends on the deterministic and stochastic statistical model of the noisy linear mixture of the data, the estimate of the projector associated with different estimates of the scatter/covariance of the
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Robust Bayesian Cluster Enumeration for RES Distributionslustering methods are highly useful in a variety of applications. For example, in the medical sciences, identifying clusters may allow for a comprehensive characterization of subgroups of individuals. However, in real-world data, the true cluster structure is often obscured by heavy-tailed noise, ar
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FEMDA: A Unified Framework for Discriminant Analysisth non-Gaussian distributions or contaminated datasets. This is primarily due to their reliance on the Gaussian assumption, which lacks robustness. We first explain and review the classical methods to address this limitation and then present a novel approach that overcomes these issues. In this new
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Learning Graphs from Heavy-Tailed Dataultivariate Student’s .-distribution as a Laplacian matrix associated to a graph whose node features (or signals) are observable. We design numerical algorithms, via the alternating direction method of multipliers, to learn connected, .-component, bipartite, and .-component bipartite graphs suitable
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