Geometrical pattern learning
In this paper we consider the problem of learning the positions of spheres in metric spaces, given as data randomly drawn points classified according to whether they are internal or external to an unknown sphere. The particular metrics under consideration are geometrical shape metrics, and the results are intended to be applicable to the problem of learning to identify a shape from related shapes classified according to whether they resemble it visually. While it is typically NP-hard to locate a central point for a hypothesis sphere, we find that it is however often possible to obtain a non-spherical hypothesis which can accurately predict whether further random points lie within the unknown sphere. We exhibit algorithms which achieve this, and in the process indicate useful general techniques for computational learning. Finally we exhibit a natural shape metric and show that it defines a class of spheres not predictable in this sense, subject to standard cryptographic assumptions.
- Research Organization:
- Sandia National Labs., Albuquerque, NM (United States)
- Sponsoring Organization:
- USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC04-76DP00789
- OSTI ID:
- 10178400
- Report Number(s):
- SAND-93-1283C; CONF-931167-2-Extd.Abst.; ON: DE93017641
- Resource Relation:
- Conference: 34. meeting of the Institute of Electrical and Electronics Engineers Foundation of Computer Science,Palo Alto, CA (United States),3-5 Nov 1993; Other Information: PBD: Apr 1993
- Country of Publication:
- United States
- Language:
- English
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