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In two-dimensional local graph embedding discriminant analysis(2DLGEDA), the intrinsic graph characterizes the intraclass compactness and connects each data point with its neighboring within the same class, while the penalty graph connects the marginal points and characterizes the interclass separability. But in the real world, face images are always affected by variations in illumination conditions and different facial expressions. So, the fuzzy two-dimensional local graph embedding analysis (F2DLGEA) algorithm is proposed, in which the fuzzy k-nearest neighbor (FKNN) is implemented to achieve the distribution local information of original samples. Experimental results on ORL face databases and PolyU palmprint show the effectiveness of the proposed method.