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Abstract:
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Spanning trees are efficient but often overlooked alternative tools for the analysis of large, multivariate metric datasets. They are easy to compute and can reduce high-dimensional correlated, clustered, and arbitrarily shaped data clouds to easily visualizable distributions of arc lengths, node degrees, and topological distances. These distributions reflect the inherent structure and characteristics of the dataset. For example, these properties of the spanning tree can be used to deduce the implicit dimension of a dataset, to differentiate between data generating distributions, to find outlying observations, and to detect the presence of clustering or clumping. We report computational experiments in high dimensions on (1) tests for normality and stable laws (2) resistant estimates of location (3) detection of clustering (4) tests of implicit dimension.
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