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Linear discriminant analysis (LDA) is one of the commonly used statistical methods for feature extraction in face recognition tasks. However, LDA often suffers from the small sample size (3S) problem, which occurs when the total number of training data is smaller than the dimension of input feature space. To deal with 3S problem, this paper proposes a novel approach for LDA-based face recognition using random projection (RP) technique. The advantages of random projection mainly include three aspects such as data-independent, dimensionality reduction and approximate distance preservation. So, based on the Johnson-Lindenstrauss theory, a new RP model is proposed for dimensionality reduction and simultaneously for learning the structure of the manifold with high accuracy. If the within-class scatter matrix is nonsingular in the randomly mapped feature space, LDA can be performed directly. Otherwise, RP will be followed by our previous regularized discriminant analysis (RDA) approach for face recognition. Two public available databases, namely FERET and CMU PIE databases, are selected for evaluation. Comparing with PCA, DLDA and Fisherface approaches, our proposed method gives the best performance.