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Simplicial and minimal-variance distances in multivariate data analysis

Gillard, Jonathan, O'Riordan, Emily and Zhigljavsky, Anatoly 2022. Simplicial and minimal-variance distances in multivariate data analysis. Journal of Statistical Theory and Practice 16 , 9. 10.1007/s42519-021-00227-7

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Abstract

In this paper, we study the behaviour of the so-called k-simplicial distances and k-minimal-variance distances between a point and a sample. The family of k-simplicial distances includes the Euclidean distance, the Mahalanobis distance, Oja’s simplex distance and many others. We give recommendations about the choice of parameters used to calculate the distances, including the size of the sub-sample of simplices used to improve computation time, if needed. We introduce a new family of distances which we call k-minimal-variance distances. Each of these distances is constructed using polynomials in the sample covariance matrix, with the aim of providing an alternative to the inverse covariance matrix, that is applicable when data is degenerate. We explore some applications of the considered distances, including outlier detection and clustering, and compare how the behaviour of the distances is affected for different parameter choices.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Additional Information: This article is licensed under a Creative Commons Attribution 4.0 International License
Publisher: Taylor and Francis
ISSN: 1559-8616
Date of First Compliant Deposit: 13 January 2022
Date of Acceptance: 24 December 2021
Last Modified: 28 Feb 2022 12:01
URI: https://orca.cardiff.ac.uk/id/eprint/146545

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