Robust M-Estimation Based Bayesian Cluster Enumeration for Real Elliptically Symmetric Distributions

Schroth, Christian A.; Muma, Michael

doi:10.1109/tsp.2021.3072482

Cited by 10 publications

(5 citation statements)

References 31 publications

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“…The SCRB for the joint estimation of location and shape in CES distributed data has been derived in [3] as the inverse of the SFIM in Eq. (30). We refer the reader to [3] for all the details about its calculation.…”

Section: The Semiparametric Cramér-rao Bound (Scrb)mentioning

confidence: 99%

“…Motivated by a wide range of experimental evidences and measurement campaigns, the (Real or Complex) Elliptically Symmetric (ES) model has been recently adopted to characterize the statistical data behavior. The RES and CES models in fact have been proved to be able to catch the data heavytailedness in a large variety of applications such us radar/sonar [23,29], hyperspectral imaging [8,17] and image/data classification [28,30] just to cite a few. From now on, in this paper, we will focus our attention only on complexvalued, CES distributed, datasets.…”

Section: Introductionmentioning

confidence: 99%

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Joint Estimation of Location and Scatter in Complex Elliptically Symmetric Distributions

Fortunati

Renaux

Pascal

2021

J Sign Process Syst

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The joint estimation of the location vector and the shape matrix of a set of independent and identically Complex Elliptically Symmetric (CES) distributed observations is investigated from both the theoretical and computational viewpoints. This joint estimation problem is framed in the original context of semiparametric models allowing us to handle the (generally unknown) density generator as an infinite-dimensional nuisance parameter. In the first part of the paper, a computationally efficient and memory saving implementation of the robust and semiparmaetric efficient R-estimator for shape matrices is derived. Building upon this result, in the second part, a joint estimator, relying on the Tyler's M -estimator of location and on the R-estimator of shape matrix, is proposed and its Mean Squared Error (MSE) performance compared with the Semiparametric Cramér-Rao Bound (SCRB).

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Section: The Semiparametric Cramér-rao Bound (Scrb)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Joint Estimation of Location and Scatter in Complex Elliptically Symmetric Distributions

Fortunati

Renaux

Pascal

2021

J Sign Process Syst

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“…There exist alternative criteria, e.g. [30], [60], [61], but in this paper the focus does not lie on cluster enumeration. Hence, we will only adapt the log-likelihood function to RESK distributions and apply the Schwarz BIC defined as…”

Section: Proposed Expectation Maximization Algorithm For a Mixture Of...mentioning

confidence: 99%

“…Recently, an EM algorithm has been derived that is applicable to any RES distribution [30]. An important member of the RES family, is the so-called Huber distribution, for which the popular Huber M-estimator is the MLE.…”

Section: Introductionmentioning

confidence: 99%

Real Elliptically Skewed Distributions and Their Application to Robust Cluster Analysis

Schroth,

Muma

2020

Preprint

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This article proposes a new class of Real Elliptically Skewed (RESK) distributions and associated clustering algorithms that allow for integrating robustness and skewness into a single unified cluster analysis framework. Non-symmetrically distributed and heavy-tailed data clusters have been reported in a variety of real-world applications. Robustness is essential because a few outlying observations can severely obscure the cluster structure. The RESK distributions are a generalization of the Real Elliptically Symmetric (RES) distributions. To estimate the cluster parameters and memberships, we derive an expectation maximization (EM) algorithm for arbitrary RESK distributions. Special attention is given to a new robust skew-Huber M-estimator, which is also the maximum likelihood estimator (MLE) for the skew-Huber distribution that belongs to the RESK class. Numerical experiments on simulated and real-world data confirm the usefulness of the proposed methods for skewed and heavy-tailed data sets.

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“…Motivated by a wide range of experimental evidences and measurement campaigns, the (Real or Complex) Elliptically Symmetric (ES) model has been recently adopted to characterize the statistical data behavior. The RES and CES models in fact have been proved to be able to catch the data heavytailedness in a large variety of applications such us radar/sonar [23,29], hyperspectral imaging [8,17] and clustering [28,30] just to cite a few. From now on, in this paper, we will focus our attention only on complex-valued, CES distributed, datasets.…”

Section: Introductionmentioning

confidence: 99%

Joint Estimation of Location and Scatter in Complex Elliptical Distributions: A robust semiparametric and computationally efficient $R$-estimator of the shape matrix

Fortunati¹,

Renaux²,

Pascal³

2021

Preprint

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Robust M-Estimation Based Bayesian Cluster Enumeration for Real Elliptically Symmetric Distributions

Cited by 10 publications

References 31 publications

Joint Estimation of Location and Scatter in Complex Elliptically Symmetric Distributions

Joint Estimation of Location and Scatter in Complex Elliptically Symmetric Distributions

Real Elliptically Skewed Distributions and Their Application to Robust Cluster Analysis

Joint Estimation of Location and Scatter in Complex Elliptical Distributions: A robust semiparametric and computationally efficient $R$-estimator of the shape matrix

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