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Depth functions and mutidimensional medians on minimal spanning trees
Mengta Yang1, Reza Modarres1, Lingzhe Guo1
1Department of Statistics, The George Washington University, Washington, D.C., USA.
Abstract:
Based on the minimal spanning tree (MST) of the observed data set, the paper introduces new notions of data depth and medians for multivariate data. The MST of a data set of size n is the MST of the complete weighted undirected graph on n vertices, where the edge weights are the pairwise distances of the data points. We study several properties of the MST-based depth functions. We consider the corresponding multidimensional medians, investigate their robustness and computational complexity. An example illustrates the use of the MST-based depth functions.
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