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In this paper, we present Linear Discriminant Projections (LDP) for reducing dimensionality and improving discriminability of local image descriptors. We place LDP into the context of state-of-the-art discriminant projections and analyze its properties. LDP requires a large set of training data with point-to-point correspondence ground truth. We demonstrate that training data produced by a simulation of image transformations leads to nearly the same results as the real data with correspondence ground truth. This makes it possible to apply LDP as well as other discriminant projection approaches to the problems where the correspondence ground truth is not available, such as image categorization. We perform an extensive experimental evaluation on standard data sets in the context of image matching and categorization. We demonstrate that LDP enables significant dimensionality reduction of local descriptors and performance increases in different applications. The results improve upon the state-of-the-art recognition performance with simultaneous dimensionality reduction from 128 to 30.