Dimension reduction techniques have been successfully applied to face recognition and text information retrieval. The process can he time-consuming when the data set is large. This paper presents a multilevel framework to reduce the size of the data set, prior to performing dimension reduction. The algorithm exploits nearest-neighbor graphs. It recursively coarsens the data by finding a maximal matching level by level. The coarsened data at the lowest level is then projected using a known linear dimensionality reduction method. The same linear mapping is performed on the original data set, and on any new test data. The methods are illustrated on two applications: Eigenfaces (face recognition) and Latent Semantic Indexing (text mining). Experimental results indicate that the multilevel techniques proposed here offer a very appealing cost to quality ratio.