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Abstract:
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An approach for the exploration of the shape of multivariate data is presented. For each pair of data points (X_i,X_j) in d-dimensional Euclidean space a real-valued function d_{ij}(alpha), 0 < alpha < 1, is constructed, the shapes of which reflect certain information about the geometry of the data. By design these functions contain information about both density (alpha near zero), and global depth (alpha near one). Intermediate values of alpha represent scales that perhaps contain the most useful information, in particular for large dimension d. The usefulness of this approach is illustrated by an application to classification.
We will also discuss connections of the presented approach to related concepts from the literature, including local depth, mass estimation, and the shorth plot, and present some supporting theory.
This is joint work with G. Chandler, Pomona College.
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