### Abstract

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.

Original language | English (US) |
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Title of host publication | Applied Computational Geometry |

Subtitle of host publication | Towards Geometric Engineering - FCRC 1996 Workshop, WACG 1996, Selected Papers |

Publisher | Springer Verlag |

Pages | 121-132 |

Number of pages | 12 |

ISBN (Print) | 354061785X, 9783540617853 |

State | Published - Jan 1 1995 |

Event | 1st ACM Workshop on Applied Computational Geometry, WACG 1996 held as part of 2nd Federated Computing Research Conference, FCRC 1996 - Philadelphia, United States Duration: May 27 1996 → May 28 1996 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1148 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 1st ACM Workshop on Applied Computational Geometry, WACG 1996 held as part of 2nd Federated Computing Research Conference, FCRC 1996 |
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Country | United States |

City | Philadelphia |

Period | 5/27/96 → 5/28/96 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Applied Computational Geometry: Towards Geometric Engineering - FCRC 1996 Workshop, WACG 1996, Selected Papers*(pp. 121-132). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1148). Springer Verlag.