High dimensional document collections restrict the choice of data processing methods, especially machine learning methods, which need to calculate the inter-vector distances. The paper describes the development and evaluation of three different dimensionality reduction methods for document representation. Specifically, these methods are latent semantic indexing, random mapping and the two combined together. We are interested in how far these dimensionality reduction methods affect accurate measurement of document categorization. The results show that LSI performs better in terms of the F1-measure; however RM+LSI has a very close performance record with a much lower computational cost.