Choice of neighbor order in nearest-neighbor classification
最近邻分类中的邻居阶数选择AI 解读 ↓
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最近邻分类中的邻居阶数选择
- 研究问题
- k近邻二分类的误分类误差如何随邻居数变化，训练样本量随机或固定时，这一关系能否支持数据驱动的选择？
- 方法与思路
- 作者分别研究总样本量随机的Poisson训练模型和总样本量固定的Binomial训练模型，比较其风险与遗憾的渐近性质。
- 材料陈述的贡献
- 摘要称两种模型的风险与遗憾具有一阶渐近等价性，并与适配二阶光滑情形的核分类器风险相联系，启发新的邻居数选择方法。
- 阅读关注点
- 应核对误分类风险展开、邻居数随样本量增长的范围、两类训练模型的区别，以及经验选择规则的具体保证。
- 阅读边界
- 材料为OpenAlex索引摘要，稿件版本未注明；一阶渐近等价不意味着有限样本风险相同，摘要未说明选择算法细节或刊本变化。
原文摘要
The kth-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.