DIMACS TR: 2006-20

Contour approximation of data and the harmonic mean



Author: Marina Arav

ABSTRACT

A contour approximation of data is a function capturing the data points in its lower level sets. Desirable properties of contour approximation are posited, and shown to be satisfied uniquely (up to a multiplicative constant) by the weighted harmonic mean of distances to the cluster centers. This harmonic mean is the joint distance function used in probabilistic clustering, expressing the uncertainty of classification.

Keywords: Harmonic mean, quasi-linear mean, clustering, contour approximation of data, distance functions.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/2006/2006-20.ps.gz

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