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This paper introduces a new algorithm called locality discriminating projection (LDP) for subspace learning, which provides a new scheme for discriminant analysis by considering both the manifold structure and the prior class information. In the LDP algorithm, the overlap among the class-specific manifolds is approximated by an invader graph, and a locality discriminant criterion is proposed to find the projections that best preserve the within-class local structures while decrease the between-class overlap. The feasibility of the LDP algorithm has been successfully tested in text data and visual recognition experiments. Experiment results show it is an effective technique for data modeling and classification comparing to linear discriminant analysis, locality preserving projection, and marginal Fisher analysis.