This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
On the Inequality of Cover and Hart in Nearest Neighbor Discrimination
January 1981 (vol. 3 no. 1)
pp. 75-78
Luc Devroye, School of Computer Science, McGill University, Montreal, P.Q., Canada.
When (X1, ¿1),..., (Xn, ¿n) are independent identically distributed random vectors from IRd X {0, 1} distributed as (X, ¿), and when ¿ is estimated by its nearest neighbor estimate ¿(1), then Cover and Hart have shown that P{¿(1) ¿ ¿}n ¿ ¿ ¿ 2E {¿ (X) (1 - ¿(X))} ¿ 2R*(1 - R*) where R* is the Bayes probability of error and ¿(x) = P{¿ = 1 | X = x}. They have conditions on the distribution of (X, ¿). We give two proofs, one due to Stone and a short original one, of the same result for all distributions of (X, ¿). If ties are carefully taken care of, we also show that P{¿(1) ¿ ¿|X1, ¿1, ..., Xn, ¿n} converges in probability to a constant for all distributions of (X, ¿), thereby strengthening results of Wagner and Fritz.
Citation:
Luc Devroye, "On the Inequality of Cover and Hart in Nearest Neighbor Discrimination," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 3, no. 1, pp. 75-78, Jan. 1981, doi:10.1109/TPAMI.1981.4767052
Usage of this product signifies your acceptance of the Terms of Use.