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  "Description": "We provide three distance metrics for measuring the\nseparation between two clusters in high-dimensional spaces. The\nfirst metric is the centroid distance, which calculates the\nEuclidean distance between the centers of the two groups. The\nsecond is a ridge Mahalanobis distance, which incorporates a\nridge correction constant, alpha, to ensure that the covariance\nmatrix is invertible. The third metric is the maximal data\npiling distance, which computes the orthogonal distance between\nthe affine spaces spanned by each class. These three distances\nare asymptotically interconnected and are applicable in tasks\nsuch as discrimination, clustering, and outlier detection in\nhigh-dimensional settings.",
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