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The Reduced Parzen Classifier
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/34.19040April 1989 (vol. 11 no. 4) pp. 423-425
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K. Fukunaga, R.R. Hayes, "The Reduced Parzen Classifier," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 4, pp. 423-425, April, 1989.
 
 
BibTex
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@article{ 10.1109/34.19040,
author = {K. Fukunaga and R.R. Hayes},
title = {The Reduced Parzen Classifier},
journal ={IEEE Transactions on Pattern Analysis and Machine Intelligence},
volume = {11},
number = {4},
issn = {0162-8828},
year = {1989},
pages = {423-425},
doi = {http://doi.ieeecomputersociety.org/10.1109/34.19040},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Pattern Analysis and Machine Intelligence
TI - The Reduced Parzen Classifier
IS - 4
SN - 0162-8828
SP423
EP425
EPD - 423-425
A1 - K. Fukunaga,
A1 - R.R. Hayes,
PY - 1989
KW - pattern recognition; Parzen classifier; Parzen density estimate; Bayes error; representative samples; piecewise quadratic classifier; Bayes methods; error analysis; estimation theory; pattern recognition
VL - 11
JA - IEEE Transactions on Pattern Analysis and Machine Intelligence
ER -
 

The Parzen density estimate is known to be an effective tool for estimating the Bayes error, given a set of training samples from the class distributions. An algorithm is developed to select a given number of representative samples whose Parzen density estimate closely matches that of the entire sample set. Using this reduced representative set, a piecewise quadratic classifier which provides nearly optimal performance is designed.

[1] 423E. Parzen, "An estimation of a probability density function and mode,"Ann. Math. Statist., vol. 33, pp. 1065-1076, 1962.
[2] D. J. Hand,Kernel Discriminant Analysis. Chichester, England: Research Studies, 1982.
[3] P. A. Devijver and J. Kittler, "On the edited nearest neighbor rule," inProc. 5th Int. Conf. Pattern Recognition, 1980, pp. 72-80.
[4] G. W. Gates, "The reduced nearest neighbor rule,"IEEE Trans. Inform. Theory, vol. IT-18, pp. 431-433, 1972.
[5] P. E. Hart, "The condensed nearest neighbor rule,"IEEE Trans. Inform. Theory, vol. IT-14, pp. 515-516, 1968.
[6] S. Geman and C. R. Hwang, "Nonparametric maximum likelihood estimation by the method of series,"Ann. Statist., vol. 10, pp. 401- 414, 1982.
[7] B. S. Everitt and D. J. Hand,Finite Mixture Distributions. London:Chapman and Hall, 1981.
[8] D. M. Titterington, A. F. M. Smith, and U. E. Markov,Statistical Analysis of Finite Mixture Distributions. New York: Wiley, 1985.
[9] K. Fukunaga and J. M. Mantock, "Nonparametric data reduction,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-6, pp. 115- 118, 1984.
[10] K. Fukunaga and D. Hummels, "Bayes error estimation using Parzen andk-NN procedure,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI- 9, pp. 634-643, 1987.

Index Terms:
pattern recognition; Parzen classifier; Parzen density estimate; Bayes error; representative samples; piecewise quadratic classifier; Bayes methods; error analysis; estimation theory; pattern recognition
Citation:
K. Fukunaga, R.R. Hayes, "The Reduced Parzen Classifier," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 4, pp. 423-425, Apr. 1989, doi:10.1109/34.19040
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