A polynomial time computable metric between point sets

J. Ramon and M. Bruynooghe. Acta Informatica, 37(10):765--780, August 2001. More behind this link.

Abstract

Measuring the similarity or distance between sets of points in a metric space is an important problem in machine learning and has also applications in other disciplines e.g. in computational geometry, philosophy of science, methods for updating or changing theories, $\ldots$. Recently Eiter and Mannila have proposed a new measure which is computable in polynomial time. However, it is not a distance function in the mathematical sense because it does not satisfy the trian gle inequality. We introduce a new measure which is a metric while being computable in polynomial time. We also present a variant which computes a normalised metric and a variant which can associate different weights with the points in the set.

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J Ramon, janr@cs.kuleuven.ac.be,