平均距离分类器的一个推广
On a Generalization of the Average Distance Classifier
摘要：
在高维、低样本量（HDLSS）设置中，如果位置之间的差异被尺度差异掩盖，则基于欧几里德距离的简单平均距离分类器表现不佳。为了纠正这个问题，Chan和Hall（2009）提出了对平均距离分类器的修改。然而，现有的分类器不能区分时，人口在其他方面比位置和规模。在这篇文章中，我们提出了一些简单的平均距离分类器的转换来解决这个问题。即使底层种群具有相同的位置和规模，所得到的分类器也表现得很好。高维行为的建议分类理论研究。各种模拟以及真实数据集的数值实验表明，所提出的方法的实用性。
英文摘要：
In high dimension, low sample size (HDLSS)settings, the simple average distance classifier based on the Euclidean distance performs poorly if differences between the locations get masked by the scale differences. To rectify this issue, modifications to the average distance classifier was proposed by Chan and Hall (2009). However, the existing classifiers cannot discriminate when the populations differ in other aspects than locations and scales. In this article, we propose some simple transformations of the average distance classifier to tackle this issue. The resulting classifiers perform quite well even when the underlying populations have the same location and scale. The high-dimensional behaviour of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated as well as real data sets exhibit the usefulness of the proposed methodology.
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