Null Foley–Sammon transform

In this paper, an important conclusion for linear discriminant analysis is proved: in the case of the small sample size, (number-of-classes-1) null projection directions (NPDs) do exist, on which, the within-class distance equals zero and the between-class distance is positive. The Null Foley–Sammon Transform (NFST), which is constituted by NPDs, is also proposed. Its effectiveness is evidenced by experiments on face recognition.