### Abstract

Oja depth (Oja 1983) is a generalization of the median to multivariate data that measures the centrality of a point x with respect to a set S of points in such a way that points with smaller Oja depth are more central with respect to S. Two relationships involving Oja depth and centers of mass are presented. The first is a form of Centerpoint Theorem which shows that the center of mass of the convex hull of a point set has low Oja depth. The second is an approximation result which shows that the center of mass of a point set approximates a point of minimum Oja depth.

Original language | English (US) |
---|---|

Pages (from-to) | 140-147 |

Number of pages | 8 |

Journal | Computational Geometry: Theory and Applications |

Volume | 46 |

Issue number | 2 |

DOIs | |

State | Published - Feb 2013 |

### Fingerprint

### Keywords

- Centerpoint theorem
- Data depth
- Oja depth

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Computer Science Applications
- Computational Mathematics
- Control and Optimization
- Geometry and Topology

### Cite this

*Computational Geometry: Theory and Applications*,

*46*(2), 140-147. https://doi.org/10.1016/j.comgeo.2012.04.004

**Oja centers and centers of gravity.** / Chen, Dan; Devillers, Olivier; Iacono, John; Langerman, Stefan; Morin, Pat.

Research output: Contribution to journal › Article

*Computational Geometry: Theory and Applications*, vol. 46, no. 2, pp. 140-147. https://doi.org/10.1016/j.comgeo.2012.04.004

}

TY - JOUR

T1 - Oja centers and centers of gravity

AU - Chen, Dan

AU - Devillers, Olivier

AU - Iacono, John

AU - Langerman, Stefan

AU - Morin, Pat

PY - 2013/2

Y1 - 2013/2

N2 - Oja depth (Oja 1983) is a generalization of the median to multivariate data that measures the centrality of a point x with respect to a set S of points in such a way that points with smaller Oja depth are more central with respect to S. Two relationships involving Oja depth and centers of mass are presented. The first is a form of Centerpoint Theorem which shows that the center of mass of the convex hull of a point set has low Oja depth. The second is an approximation result which shows that the center of mass of a point set approximates a point of minimum Oja depth.

AB - Oja depth (Oja 1983) is a generalization of the median to multivariate data that measures the centrality of a point x with respect to a set S of points in such a way that points with smaller Oja depth are more central with respect to S. Two relationships involving Oja depth and centers of mass are presented. The first is a form of Centerpoint Theorem which shows that the center of mass of the convex hull of a point set has low Oja depth. The second is an approximation result which shows that the center of mass of a point set approximates a point of minimum Oja depth.

KW - Centerpoint theorem

KW - Data depth

KW - Oja depth

UR - http://www.scopus.com/inward/record.url?scp=84867576102&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867576102&partnerID=8YFLogxK

U2 - 10.1016/j.comgeo.2012.04.004

DO - 10.1016/j.comgeo.2012.04.004

M3 - Article

VL - 46

SP - 140

EP - 147

JO - Computational Geometry: Theory and Applications

JF - Computational Geometry: Theory and Applications

SN - 0925-7721

IS - 2

ER -