Geometric problems in machine learning

  • David Dobkin
  • Dimitrios Gunopulos
Submitted Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1148)


We present some problems with geometric characterizations that arise naturally in practical applications of machine learning. Our motivation comes from a well known machine learning problem, the problem of computing decision trees. Typically one is given a dataset of positive and negative points, and has to compute a decision tree that fits it. The points are in a low dimensional space, and the data are collected experimentally. Most practical solutions use heuristic algorithms.

To compute decision trees quickly, one has to solve optimization problems in one or more dimensions efficiently. In this paper we give geometric characterizations for these problems. We present a selection of algorithms for some of them. These algorithms are motivated from practice, and have been in many cases implemented and used as well. In addition, they are theoretically interesting, and typically employ sophisticated geometric techniques. Finally we present future research directions.


Decision Tree Greedy Algorithm Dynamic Algorithm Geometric Characterization Hypothesis Class 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • David Dobkin
    • 1
  • Dimitrios Gunopulos
    • 2
  1. 1.Computer Science Dept.Princeton UniversityPrincetonUSA
  2. 2.Max-Planck-Institute für InformatikIm StadtwaldSaarbrückenGermany

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