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This paper develops a supervised discriminant technique, called graph embedding discriminant analysis (GEDA), for dimensionality reduction of high-dimensional data in small sample size problems. GEDA can be seen as a linear approximation of a multimanifold-based learning framework in which nonlocal property is taken into account besides the marginal property and local property. GEDA seeks to find a set of perfect projections that not only can impact the samples of intraclass and maximize the margin of interclass, but also can maximize the nonlocal scatter at the same time. This characteristic makes GEDA more intuitive and more powerful than linear discriminant analysis (LDA) and marginal fisher analysis (MFA). The proposed method is applied to face recognition and is examined on the Yale, ORL and AR face image databases. The experimental results show that GEDA consistently outperforms LDA and MFA when the training sample size per class is small. [ABSTRACT FROM AUTHOR]