Graph-Based Multilevel Dimensionality Reduction with Applications to Eigenfaces and Latent Semantic Indexing

Dimension reduction techniques have been successfully applied to face recognition and text information retrieval. The process can be 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.