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Representing manifolds using fewer examples has the advantages of eliminating the influence of outliers and noisy points and simultaneously accelerating the evaluation of predictors learned from the manifolds. In this paper, we give the definition of manifold-preserving sparse graphs as a representation of sparsified manifolds and present a simple and efficient manifold-preserving graph reduction algorithm. To characterize the manifold-preserving properties, we derive a bound on the expecteddoi:10.1016/j.neucom.2012.08.070 fatcat:xty2tsh5nzbfhpjra7vbnvosey