最近邻分类中邻序的选择
Choice of neighbor order in nearest-neighbor classification
摘要：
$k$ th-最近邻规则可以说是最简单和最直观的非参数分类过程。然而，这种方法的应用受到抑制的知识缺乏其属性，特别是关于它的方式，它是由$k$的值的影响，并通过经验选择$k$的技术的缺乏。在本文中，我们详细的方式，其中值的$k$确定的误分类错误。我们考虑两个模型，泊松和二项式，为训练样本。在第一种模型下，数据被记录在泊松流中，并根据先验概率“分配”给两个总体中的一个或另一个。特别地，两个训练样本中的数据的总数是泊松分布的随机变量。然而，在二项模型下，训练样本中的数据总数是固定的，尽管每个数据值再次以随机方式分配。虽然与泊松模型和二项式模型相关的风险和后悔值是不同的，但它们渐近等价于一阶模型，并且也等价于与基于核的分类器相关的风险，这些分类器是针对两个衍生品的情况定制的。这些性质激发了选择$k$值的新方法。
英文摘要：
The $k$th-nearest neighbor rule is arguably the simplest and most intuitively appealing nonparametric classification procedure. However, application of this method is inhibited by lack of knowledge about its properties, in particular, about the manner in which it is influenced by the value of $k$; and by the absence of techniques for empirical choice of $k$. In the present paper we detail the way in which the value of $k$ determines the misclassification error. We consider two models, Poisson and Binomial, for the training samples. Under the first model, data are recorded in a Poisson stream and are "assigned" to one or other of the two populations in accordance with the prior probabilities. In particular, the total number of data in both training samples is a Poisson-distributed random variable. Under the Binomial model, however, the total number of data in the training samples is fixed, although again each data value is assigned in a random way. Although the values of risk and regret associated with the Poisson and Binomial models are different, they are asymptotically equivalent to first order, and also to the risks associated with kernel-based classifiers that are tailored to the case of two derivatives. These properties motivate new methods for choosing the value of $k$.
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