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A Study of the Neighborhood Counting Similarity
April 2008 (vol. 20 no. 4)
pp. 449-461
ASCII Text
x 
 
Hui Wang, Fionn Murtagh, "A Study of the Neighborhood Counting Similarity," IEEE Transactions on Knowledge and Data Engineering, vol. 20, no. 4, pp. 449-461, April, 2008.
 
 
BibTex
x
 
@article{ 10.1109/TKDE.2007.190721,
author = {Hui Wang and Fionn Murtagh},
title = {A Study of the Neighborhood Counting Similarity},
journal ={IEEE Transactions on Knowledge and Data Engineering},
volume = {20},
number = {4},
issn = {1041-4347},
year = {2008},
pages = {449-461},
doi = {http://doi.ieeecomputersociety.org/10.1109/TKDE.2007.190721},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Knowledge and Data Engineering
TI - A Study of the Neighborhood Counting Similarity
IS - 4
SN - 1041-4347
SP449
EP461
EPD - 449-461
A1 - Hui Wang,
A1 - Fionn Murtagh,
PY - 2008
KW - Decision support
KW - Clustering
KW - classification
KW - and association rules
VL - 20
JA - IEEE Transactions on Knowledge and Data Engineering
ER -
 
A novel similarity, neighborhood counting measure, was recently proposed which counts the number of neighborhoods of a pair of data points. This similarity can handle numerical and categorical attributes in a conceptually uniform way, can be calculated efficiently through a simple formula, and gives good performance when tested in the framework of k-nearest neighbor classifier. In particular it consistently outperforms a combination of the classical Euclidean distance and Hamming distance. This measure was also shown to be related to a probability formalism, G probability, which is induced from a target probability function P. It was however unclear how G is related to P, especially for classification. Therefore it was not possible to explain some characteristic features of the neighborhood counting measure. In this paper we show that G is a linear function of P, and G-based Bayes classification is equivalent to P-based Bayes classification. We also show that the k-nearest neighbor classifier, when weighted by the neighborhood counting measure, is in fact an approximation of the G-based Bayes classifier, and furthermore, the P-based Bayes classifier. Additionally we show that the neighborhood counting measure remains unchanged when binary attributes are treated as categorical or numerical data. This is a feature that is not shared by other distance measures, to the best of our knowledge. This study provides a theoretical insight into the neighborhood counting measure.

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Index Terms:
Decision support, Clustering, classification, and association rules
Citation:
Hui Wang, Fionn Murtagh, "A Study of the Neighborhood Counting Similarity," IEEE Transactions on Knowledge and Data Engineering, vol. 20, no. 4, pp. 449-461, April 2008, doi:10.1109/TKDE.2007.190721
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