minimum distance classifier=nearest-centroid classifier=nearest mean classifier

杨健老师的论文KPCA Plus LDA: A Complete Kernel Fisher Discriminant Framework for Feature Extraction and Recognition   5.1节采用该分类器，Why can LDA be performed in PCA transformed space也采用该分类器，等同于叶杰平老师论文Generalized Linear Discriminant Analysis: A Unified Framework and Efficient Model Selection    IV节的nearest-centroid classifier（也即汪增福老师讲的平均样本法），定义如下：（摘自网页 http://homepages.inf.ed.ac.uk/rbf/HIPR2/classify.htm）

Suppose that each training class is represented by a prototype (or mean) vector:

where is the number of training pattern vectors from class . In the example classification problem given above, and as shown in Figure 2.

Figure 2 Feature space: + sewing needles, o bolts, * class mean

Based on this, we can assign any given pattern to the class of its closest prototype by determining its proximity to each . If Euclidean distance is our measure of proximity, then the distance to the prototype is given by

It is not difficult to show that this is equivalent to computing

and assign to class if yields the largest value.
显然，minimum distance classifier的效率要比nearest neighbor classifier (NN)要低，因为对于任意一个测试样本，前者只需要计算到训练样本的几个类心的距离，而nearest neighbor classifier (NN)要计算与所有训练样本的距离。杨健老师论文KPCA Plus LDA   5.2节也有原话：A minimum distance classifier is employed for computational efficiency.

Other reference:
Mar 24, 2012 gmail 附件讲义7.3节有minimum distance classifier的英文描述