Analysis of distance matrices

The relationships between eigenvalues of the distance matrices and outliers are largely unexplored. We show a discrepancy in the sizes of eigenvalues of the distance matrix that is contaminated with outliers. We present test statistics to determine when a distance matrix has a constant structure. We relate the eigenvalues of the two-sample distance matrix to the tests of equality of distributions, study dissimilarity matrices and their eigenvalues in high dimensional and low sample size setting.(c) 2022 Elsevier B.V. All rights reserved.