Data Exploration by Representative Region Selection: Axioms and Convergence

44 Pages Posted: 9 Sep 2019

See all articles by Alexander Estes

Alexander Estes

University of Minnesota - Institute for Mathematics and its Applications

Michael O. Ball

University of Maryland - Decision and Information Technologies Department

David Lovell

University of Maryland

Date Written: September 6, 2019

Abstract

We present a new type of unsupervised learning problem in which we find a small set of representative regions that approximates a larger dataset. These regions may be presented to a practitioner along with additional information in order to help the practitioner explore the data set. An advantage of this approach is that it does not rely on cluster structure of the data. We formally define this problem, and we present axioms that should be satisfied by functions that measure the quality of representatives. We provide a quality function that satisfies all of these axioms. Using this quality function, we formulate two optimization problems for finding representatives. We provide convergence results for a general class of methods, and we show that these results apply to several specific methods, including methods derived from the solution of the optimization problems formulated in this paper. We provide an example of how representative regions may be used to explore a data set.

Keywords: Representative Region Selection, Unsupervised learning, Data exploration, Density estimation, Consistency

JEL Classification: C02, C13, C44, C55

Suggested Citation

Estes, Alexander and Ball, Michael O. and Lovell, David, Data Exploration by Representative Region Selection: Axioms and Convergence (September 6, 2019). Available at SSRN: https://ssrn.com/abstract=3005997 or http://dx.doi.org/10.2139/ssrn.3005997

Alexander Estes (Contact Author)

University of Minnesota - Institute for Mathematics and its Applications ( email )

425 Lind Hall
207 Church St SE
Minneapolis, MN 55455
United States

HOME PAGE: http://asestes1.github.io

Michael O. Ball

University of Maryland - Decision and Information Technologies Department ( email )

Robert H. Smith School of Business
4313 Van Munching Hall
College Park, MD 20815
United States
301-405-2227 (Phone)
301-405-8655 (Fax)

David Lovell

University of Maryland ( email )

College Park
College Park, MD 20742
United States

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