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Selection: Rizzo:ML [6 articles] 

Publications by author Rizzo:ML.
 

K-groups: a generalization of K-means clustering

  
(12 Nov 2017)

Abstract

We propose a new class of distribution-based clustering algorithms, called k-groups, based on energy distance between samples. The energy distance clustering criterion assigns observations to clusters according to a multi-sample energy statistic that measures the distance between distributions. The energy distance determines a consistent test for equality of distributions, and it is based on a population distance that characterizes equality of distributions. The k-groups procedure therefore generalizes the k-means method, which separates clusters that have different means. We propose two k-groups algorithms: k-groups by first variation; and k-groups by ...

 

Partial distance correlation with methods for dissimilarities

  
The Annals of Statistics, Vol. 42, No. 6. (December 2014), pp. 2382-2412, https://doi.org/10.1214/14-aos1255

Abstract

Distance covariance and distance correlation are scalar coefficients that characterize independence of random vectors in arbitrary dimension. Properties, extensions and applications of distance correlation have been discussed in the recent literature, but the problem of defining the partial distance correlation has remained an open question of considerable interest. The problem of partial distance correlation is more complex than partial correlation partly because the squared distance covariance is not an inner product in the usual linear space. For the definition of partial ...

 

Energy distance

  
Wiley Interdisciplinary Reviews: Computational Statistics, Vol. 8, No. 1. (January 2016), pp. 27-38, https://doi.org/10.1002/wics.1375

Abstract

Energy distance is a metric that measures the distance between the distributions of random vectors. Energy distance is zero if and only if the distributions are identical, thus it characterizes equality of distributions and provides a theoretical foundation for statistical inference and analysis. Energy statistics are functions of distances between observations in metric spaces. As a statistic, energy distance can be applied to measure the difference between a sample and a hypothesized distribution or the difference between two or more samples ...

 

Measuring and testing dependence by correlation of distances

  
The Annals of Statistics, Vol. 35, No. 6. (28 December 2007), pp. 2769-2794, https://doi.org/10.1214/009053607000000505

Abstract

Distance correlation is a new measure of dependence between random vectors. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but unlike the classical definition of correlation, distance correlation is zero only if the random vectors are independent. The empirical distance dependence measures are based on certain Euclidean distances between sample elements rather than sample moments, yet have a compact representation analogous to the classical covariance and correlation. Asymptotic properties and applications in testing independence are discussed. Implementation of the test and Monte Carlo results are ...

 

Brownian distance covariance

  
The Annals of Applied Statistics, Vol. 3, No. 4. (6 Oct 2010), pp. 1236-1265, https://doi.org/10.1214/09-aoas312

Abstract

Distance correlation is a new class of multivariate dependence coefficients applicable to random vectors of arbitrary and not necessarily equal dimension. Distance covariance and distance correlation are analogous to product-moment covariance and correlation, but generalize and extend these classical bivariate measures of dependence. Distance correlation characterizes independence: it is zero if and only if the random vectors are independent. The notion of covariance with respect to a stochastic process is introduced, and it is shown that population distance covariance coincides with the covariance with respect to Brownian motion; thus, ...

 

Rejoinder: brownian distance covariance

  
The Annals of Applied Statistics, Vol. 3, No. 4. (5 Oct 2010), pp. 1303-1308, https://doi.org/10.1214/09-aoas312rej

Abstract

Rejoinder to "Brownian distance covariance" by Gábor J. Székely and Maria L. Rizzo [arXiv:1010.0297] ...

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