基于半空间邻近图的实例学习
Instance-based learning using the Half-Space Proximal Graph
摘要：
基于实例的学习的主要例子是$k$ -最近邻规则（kNN），因其简单性和适应新的不可见数据和丢弃旧数据的能力而受到称赞。经常提到的主要缺点是分类复杂性，即$O(n)$，以及参数$k$的估计，即要使用的最近邻的数量。在分类时使用指标弥补了前者的不足，而后者则没有定论。提出了一种基于{ \em Half-Space Proximal}（HSP）图的无参数实例学习算法。HSP的邻居同时具有接近性和多样性的中心节点。为了对给定的查询进行分类，我们计算它的HSP邻居，并对它们应用简单的多数规则。在我们的实验中，所得到的分类器优于$KNN$的任何$k$在电池的数据集。这种改进即使在将加权多数规则应用于kNN和HSP分类器时也是如此。令人惊讶的是，当使用概率指数来近似HSP图并因此加速分类任务时，我们的方法可以{ \em提高}其准确性，这与使用概率指数的kNN分类器形成鲜明对比。
英文摘要：
The primary example of instance-based learning is the $k$-nearest neighbor rule (kNN), praised for its simplicity and the capacity to adapt to new unseen data and toss away old data. The main disadvantages often mentioned are the classification complexity, which is $O(n)$, and the estimation of the parameter $k$, the number of nearest neighbors to be used. The use of indexes at classification time lifts the former disadvantage, while there is no conclusive method for the latter. This paper presents a parameter-free instance-based learning algorithm using the {\em Half-Space Proximal} (HSP) graph. The HSP neighbors simultaneously possess proximity and variety concerning the center node. To classify a given query, we compute its HSP neighbors and apply a simple majority rule over them. In our experiments, the resulting classifier bettered $KNN$ for any $k$ in a battery of datasets. This improvement sticks even when applying weighted majority rules to both kNN and HSP classifiers. Surprisingly, when using a probabilistic index to approximate the HSP graph and consequently speeding-up the classification task, our method could {\em improve} its accuracy in stark contrast with the kNN classifier, which worsens with a probabilistic index.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
