Classification of nonlinear highdimensional data is usually not amenable to standard pattern recognition techniques because of an underlying small sample size conditions. To address the problem, a novel Supervised Locality Preserving Projection (SLPP) learning algorithm combined with a fuzzy feature extraction strategy and spectra factorization is developed in this paper. First, according to the problem that SLPP has the overlearning problem and does not preserve the diversity information of data which is also useful for data recognition, a concise transformation of feature extraction criterion is raised by minimizing the local scatter, which efficiently preserves the local structure and simultaneously maximize the diversity scatter, however, an equivalent form of linear discriminant analysis is obtained. Secondly, a reformative fuzzy algorithm based on the fuzzy knearest neighbor (FKNN) is implemented to achieve the distribution information of each original sample represented with fuzzy membership degree and is incorporated into the redefinition of the scatter matrices of SLPP. Thirdly, a matrix decomposition is proposed on the basis of matrix analysis theory in this paper, under the SLPP criterion, the technology of spectra factorization is utilized in order to reduce the dimension of samples. Experimental results conducts on the ORL and NUST603 face database demonstrate the effectiveness of the proposed method.
