分类中软间隔损失函数的V_γ维

On the V_γ dimension of soft margin loss functions in classification

推广能力是刻画学习机器性能优劣的重要指标,它的界在算法设计中有着重要的作用.人们往往用VC维或者Vγ维来给出推广能力的界.计算了分类中一类特殊的范围较广的软间隔损失函数的Vγ维,并给出使用此种损失函数的核分类器的推广能力的界.

Generalization performance is an important index that describes the perfectness of a learning machine,whose bound plays a vital role in algorithm designing.Usually give the bounds by VC dimension or V_γ dimension.But in most cases in classification when the choosed loss function is a real-valued one in an infinite RKHS,the VC dimension turns out to be infinite,thus it is not useful to us.This paper calculates the upper bound of the V_γ dimension of a wide and special kind of soft margin loss functions in classification,then gives the upper bound of generalization performance of this kind of kernel classifiers.