Title :
The Nearest Neighbor and the Bayes Error Rates
Author :
Loizou, George ; Maybank, Stephen J.
Author_Institution :
Department of Computer Science, Birkbeck College, University of London, Malet Street, London WC1E 7HX, England.
fDate :
3/1/1987 12:00:00 AM
Abstract :
The (k, l) nearest neighbor method of pattern classification is compared to the Bayes method. If the two acceptance rates are equal then the asymptotic error rates satisfy the inequalities Ek,l + 1 ¿ E*(¿) ¿ Ek,l dE*(¿), where d is a function of k, l, and the number of pattern classes, and ¿ is the reject threshold for the Bayes method. An explicit expression for d is given which is optimal in the sense that for some probability distributions Ek,l and dE* (¿) are equal.
Keywords :
Computer science; Distributed computing; Educational institutions; Error analysis; Extraterrestrial measurements; Nearest neighbor searches; Pattern classification; Pattern recognition; Probability density function; Probability distribution; Asymptotic error rates; Bayes method; Lebesgue integration; nearest neighbor method; statistical pattern recognition;
Journal_Title :
Pattern Analysis and Machine Intelligence, IEEE Transactions on
DOI :
10.1109/TPAMI.1987.4767899
