关于K最近邻判决规则错误率的新上界
New Upper Bounds on the Error Rate of the K-Nearest Neighbor Decision Rule
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摘要: 本文得出在二类情况下K最近邻判决规则错误率Rk的上界的闭合形式表达式 Rk≤(1+Ck)R* 式中Ck=1/(2.898K-1.898),R*是Bayes判决规则错误率.这个表达式不 但包含最近邻判决规则错误率R1的上界表达式R1≤2R*,而且所有的奇数K的数值 与级数形式的上确界非常接近.Abstract: In this paper, the following closed form expression for the upper bounds on the error rate Rk of the K-nearest neighbor decision rule for the two-class problem is obtained. Rk≤(1+Ck)R* where Ck=1/(2.898K-1.898), and R* is the error rate of the Bayes decision rule. This expression not only contains one on the error rate RI of the nearest neighbor decision rule R1≤2R*, but also numerically gives a good approximation to the series form supremum for all K odd.
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