Bias of Nearest Neighbor Error Estimates
Bias of Nearest Neighbor Error Estimates
复制标题
最近邻误差估计的偏差
DOI：
10.1109/tpami.1987.4767875
复制
发表时间：
1987
影响因子：
23.6
通讯作者：
D. Hummels
中科院分区：
文献类型：
--
作者：
K. Fukunaga;D. Hummels
有限样本最近邻（NN）误差从其渐近值的偏差进行了检查。表达式得到的NN和2-NN误差的偏差与样本大小，维数，度量和分布。这些表达式将样本大小的影响与分布的影响隔离开来，给出了一个明确的关系，显示了偏倚如何随着样本大小的增加而变化。实验结果表明，该表达式准确地预测的偏见。它表明，当数据的维数是高的，它可能不可能简单地通过增加样本容量来估计渐近误差。一个新的程序，建议缓解这个问题。这个过程涉及到测量的平均NN误差在几个样本量和使用我们推导的偏差和样本量之间的关系外推的渐近NN误差的估计。结果被扩展到多类问题。一个最佳的度量，以尽量减少偏差的选择进行了讨论。
The bias of the finite-sample nearest neighbor (NN) error from its asymptotic value is examined. Expressions are obtained which relate the bias of the NN and 2-NN errors to sample size, dimensionality, metric, and distributions. These expressions isolate the effect of sample size from that of the distributions, giving an explicit relation showing how the bias changes as the sample size is increased. Experimental results are given which suggest that the expressions accurately predict the bias. It is shown that when the dimensionality of the data is high, it may not be possible to estimate the asymptotic error simply by increasing the sample size. A new procedure is suggested to alleviate this problem. This procedure involves measuring the mean NN errors at several sample sizes and using our derived relationship between the bias and the sample size to extrapolate an estimate of the asymptotic NN error. The results are extended to the multiclass problem. The choice of an optimal metric to minimize the bias is also discussed.