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.
顯然,minimum distance classifier的效率要比nearest neighbor classifier (NN)要低,因為對于任意一個測試樣本,前者只需要計算到訓練樣本的幾個類心的距離,而nearest neighbor classifier (NN)要計算與所有訓練樣本的距離。楊健老師論文KPCA Plus LDA 5.2節也有原話:A minimum distance classifier is employed for computational efficiency.
Other reference:
Mar 24, 2012 gmail 附件講義7.3節有minimum distance classifier的英文描述