Existence of nonlinear weak classifier

Many studies have shown that there is always a weak classifier under appropriate conditions.It is particularly striking that the geometric differences was introduced into the research of the existence of weak classifiers by S.Mannor and R.Meir and,finally,the existence of linear weak classifier was subsumed into some geometric properties on sample sets.Therefore,with the information of the sample sets,only,it could be determined whether the weak classifier exists.On the basis of investigation results of S.Mannor and R.Meir,the nonlinear weak classifier in input space was united together with the linear classifier in characteristic space,by using the kernel method so that a judgment condition of the existence of the nonlinear weak classifier was obtained.