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Data Exploration by Representative Region Selection: Axioms and Convergence

Author

Listed:
  • Alexander S. Estes

    (Department of Industrial and Systems Engineering, University of Minnesota, Minneapolis, Minnesota 55455)

  • Michael O. Ball

    (Robert H. Smith School of Business and Institute of Systems Research, University of Maryland, College Park, Maryland 20742)

  • David J. Lovell

    (Department of Civil and Environmental Engineering and Institute of Systems Research, University of Maryland, College Park, Maryland 20742)

Abstract

We present a new type of unsupervised learning problem in which we find a small set of representative regions that approximates a larger data set. 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.

Suggested Citation

  • Alexander S. Estes & Michael O. Ball & David J. Lovell, 2021. "Data Exploration by Representative Region Selection: Axioms and Convergence," Mathematics of Operations Research, INFORMS, vol. 46(3), pages 970-1007, August.
    • Handle: RePEc:inm:ormoor:v:46:y:2021:i:3:p:970-1007
    DOI: 10.1287/moor.2020.1115
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