Document Classification using Nonnegative Matrix Factorization and Underapproximation

Michael W. Berry, Nicolas Gillis, François Glineur

Abstract: In this study, we use nonnegative matrix factorization (NMF) and nonnegative matrix underapproximation (NMU) approaches to generate feature vectors that can be used to cluster aviation safety reporting system (ASRS) documents obtained from the distributed national ASAP archive (DNAA). By preserving nonnegativity, both the NMF and NMU facilitate a sum-of-parts representation of the underlying term usage patterns in the ASRS document collection. Both the training and test sets of ASRS documents are parsed and then factored by both algorithms to produce a reduced-rank representations of the entire document space. The resulting feature and coefficient matrix factors are used to cluster ASRS documents so that the (known) associated anomalies of training documents are directly mapped to the feature vectors. Dominant features of test documents are then used to generate anomaly relevance scores for those documents.We demonstrate that the approximate solution obtained by NMU using Lagrangrian duality can lead to a better sum-of-parts representation and document classification accuracy.