Delaunay-weighted two-sample test uses geometric direction information to detect principal-direction covariance differences in high-dimensional manifold data
The authors propose a Delaunay-weighted two-sample test: under a low-dimensional manifold assumption they define a Delaunay weight from the Delaunay triangulation that captures both geodesic distance and relative direction, use the average within-group Delaunay weight as the test statistic with a permutation p-value, prove asymptotic normality under the null and consistency under the alternative, and show in simulations substantially higher power than k-NN, k-MST, kernel, e-distance, covariance, and regression tests when the two distributions differ in the principal directions of their covariance matrices, while detecting a treatment-group difference with p=0.011 in a mice protein expression dataset.