DocumentCode :
327691
Title :
Reference set thinning for the k-nearest neighbor decision rule
Author :
Bhattacharya, Binay ; Kaller, Damon
Author_Institution :
Sch. of Comput. Sci., Simon Fraser Univ., Burnaby, BC, Canada
Volume :
1
fYear :
1998
fDate :
16-20 Aug 1998
Firstpage :
238
Abstract :
The k-nearest neighbor decision rule (or k-NNR) is used to classify a point in d-space according to the dominant class among its k nearest neighbors in some reference set (in which each point has a known class). It is useful to find a small subset S´ of S that can be used as the reference set instead. If the k-NNR always makes the same decision using either S or S´ as the reference set, then S´ is called an exact thinning of S for the k-NNR. We show that such an exact thinning can be determined easily from the k-Delaunay graph of S (which is dual to the order-k Voronoi diagram of S). This graph “encodes” a particular subset of S that must be included within any exact thinning for the k-NNR, and it also provides information on how this subset can be augmented into an exact thinning (although perhaps not a minimum one). In addition, we investigate how the k-Gabriel graph (which is a subgraph of the k-Delaunay graph) can be used to derive an inexact thinning of S that performs well in practice for the k-NNR. It is advantageous to use the k-Gabriel graph instead of the k-Delaunay graph, because the k-Gabriel graph is smaller and much easier to compute from the point set S
Keywords :
computational geometry; image classification; d-space; duality; exact thinning; image classification; k-Delaunay graph; k-Gabriel graph; k-NN rule; k-NNR; k-nearest neighbor decision rule; order-k Voronoi diagram; reference set; reference set thinning; Costs; Error analysis; Extraterrestrial measurements; Genetic algorithms; Nearest neighbor searches; Postal services; Read only memory;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Pattern Recognition, 1998. Proceedings. Fourteenth International Conference on
Conference_Location :
Brisbane, Qld.
ISSN :
1051-4651
Print_ISBN :
0-8186-8512-3
Type :
conf
DOI :
10.1109/ICPR.1998.711125
Filename :
711125
Link To Document :
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