Proof that vertex vectors sequential projection method is not general

Development of a chemometric method can be very hard task indeed. In a recent paper [Chemom. Intell. Lab. Syst. 82 (2006) 154–164], Wang et al. proved that, using p-normalization (p ≥ 1) for two-way data, the vertex vectors (which will be the pure variables if they exist) maximize a certain quadratic form over all points on a simplex (p = 1) or a polyhedral hyper-“spherical” surface (p > 1). Based on this theorem, they developed a procedure for determining pure variables. In this paper, we point out that the procedure proposed by Wang et al. could fail for cases p > 1, thus their result can not be considered as the generalization of method of Jiang et al. [Chemom. Intell. Lab. Syst. 65 (2003) 51–65].