For supervised classification of functional data, several classifiers have been proposed in the literature, including the well-known classic $k$-nearest neighbors (kNN) classifier. The classic kNN classifier selects $k$ nearest neighbors around a new observation and determines its class-membership according to a majority vote. A difficulty arises when there are two classes having the same largest number of votes. To overcome this difficulty, we propose a new kNN classifier which selects $k$ nearest neighbors around a new observation from each class. The class-membership of the new observation is determined by the minimum average distance or semi-distance between the $k$ nearest neighbors and the new observation. Good performance of the new kNN classifier is demonstrated by three simulation studies and two real data examples.

中文翻译：

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一种新的用于功能数据的$k$-最近邻分类器

对于功能数据的监督分类，文献中提出了几种分类器，包括著名的经典$k$-最近邻（kNN）分类器。经典的 kNN 分类器围绕新观察选择 $k$ 最近邻，并根据多数投票确定其类成员。当有两个类别具有相同的最大票数时，就会出现困难。为了克服这个困难，我们提出了一个新的 kNN 分类器，它从每个类中围绕一个新的观察选择 $k$ 最近的邻居。新观测值的类成员由 $k$ 最近邻与新观测值之间的最小平均距离或半距离确定。三个模拟研究和两个真实数据示例证明了新的 kNN 分类器的良好性能。