The k-step spatial sign covariance matrix

Croux, Christophe; Dehon, Catherine; Yadine, Abdelilah

doi:10.1007/s11634-010-0062-7

Cited by 20 publications

(18 citation statements)

References 19 publications

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“…Median, given by the middle value of the ordered univariate sample (unique only for odd numbers of points [17]), can, like the mean, be estimated from the marginal distribution being inherently univariate. The spatial median, on the other hand, is truly a multivariate, orthogonally equivariant location estimate [18]. These location estimates and their intrinsic properties are illustrated and more thoroughly discussed in [17,19].…”

Section: Introductionmentioning

confidence: 99%

Comparison of Internal Clustering Validation Indices for Prototype-Based Clustering

2017

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Abstract:Clustering is an unsupervised machine learning and pattern recognition method. In general, in addition to revealing hidden groups of similar observations and clusters, their number needs to be determined. Internal clustering validation indices estimate this number without any external information. The purpose of this article is to evaluate, empirically, characteristics of a representative set of internal clustering validation indices with many datasets. The prototype-based clustering framework includes multiple, classical and robust, statistical estimates of cluster location so that the overall setting of the paper is novel. General observations on the quality of validation indices and on the behavior of different variants of clustering algorithms will be given.

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Section: Introductionmentioning

confidence: 99%

Comparison of Internal Clustering Validation Indices for Prototype-Based Clustering

2017

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“…≥ δ p ≥ 0 those of S(X). Explicit formulae that relate the δ i to the λ i are only known for p = 2 (see Vogel, Köllmann, and Fried 2008;Croux, Dehon, and Yadine 2010), namely…”

Section: Eigenvalues Of the Sscmmentioning

confidence: 99%

The Spatial Sign Covariance Matrix and Its Application for Robust Correlation Estimation

Dürre

Fried

Vogel

2017

AJS

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We summarize properties of the spatial sign covariance matrix and especially consider the relationship between its eigenvalues and those of the shape matrix of an elliptical distribution. The explicit relationship known in the bivariate case was used to construct the spatial sign correlation coefficient, which is a non-parametric and robust estimator for the correlation coefficient within the elliptical model. We consider a multivariate generalization, which we call the multivariate spatial sign correlation matrix. A small simulation study indicates that the new estimator is very efficient under various elliptical distributions if the dimension is large. We furthermore derive its influence function under certain conditions which indicates that the multivariate spatial sign correlation becomes more sensitive to outliers as the dimension increases.

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“…covariance matrix in adaptive radar detection problems, especially due to its good robustness properties. The SSCM has the highest possible breakdown point of 1 with fixed location [7] and breakdown point of 1/2 when using the spatial median [8] to estimate the location [9]. The best possible breakdown point of M-estimators is 1/p and obtained by Tyler's M-estimator [10].…”

Section: Introductionmentioning

confidence: 99%

Bias Adjusted Sign Covariance Matrix

Raninen

Ollila

2022

IEEE Signal Process. Lett.

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The spatial sign covariance matrix (SSCM), also known as the normalized sample covariance matrix (NSCM), has been widely used in signal processing as a robust alternative to the sample covariance matrix (SCM). It is well-known that the SSCM does not provide consistent estimates of the eigenvalues of the shape matrix (normalized scatter matrix). To alleviate this problem, we propose BASIC (Bias Adjusted SIgn Covariance), which performs an approximate bias correction to the eigenvalues of the SSCM under the assumption that the samples are generated from zero mean unspecified complex elliptically symmetric distributions (the real-valued case is also addressed). We then use the bias correction in order to develop a robust regularized SSCM based estimator, BASIC Shrinkage estimator (BASICS), which is suitable for high dimensional problems, where the dimension can be larger than the sample size. We assess the proposed estimator with several numerical examples as well as in a linear discriminant analysis (LDA) classification problem with real data sets. The simulations show that the proposed estimator compares well to competing robust covariance matrix estimators but has the advantage of being significantly faster to compute.

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The k-step spatial sign covariance matrix

Cited by 20 publications

References 19 publications

Comparison of Internal Clustering Validation Indices for Prototype-Based Clustering

Comparison of Internal Clustering Validation Indices for Prototype-Based Clustering

The Spatial Sign Covariance Matrix and Its Application for Robust Correlation Estimation

Bias Adjusted Sign Covariance Matrix

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