Finding SDSS BALQSOs Using Non-Negative Matrix Factorisation
  Modern spectroscopic databases provide a wealth of information about the physical processes and environments associated with astrophysical populations. Techniques such as blind source separation (BSS), in which sets of spectra are decomposed into a number of components, offer the prospect of identifying the signatures of the underlying physical emission processes. Principle Component Analysis (PCA) has been applied with some success but is severely limited by the inherent orthogonality restriction that the components must satisfy.   Non-negative matrix factorisation (NMF) is a relatively new BSS technique that incorporates a non-negativity constraint on its components. In this respect, the resulting components may more closely reflect the physical emission signatures than is the case using PCA. We discuss some of the considerations that must be made when applying NMF and, through its application to the quasar spectra in the Sloan Digital Sky Survey (SDSS) DR6, we show that NMF is a fast method for generating compact and accurate reconstructions of the spectra.   The ability to reconstruct spectra accurately has numerous astrophysical applications. Combined with improved SDSS redshifts, we apply NMF to the problem of defining robust continua for quasars that exhibit strong broad absorption line (BAL) systems. The resulting catalogue of SDSS DR6 BAL quasars will be the largest available. Importantly, the NMF approach allows quantitative error estimates to be derived for the Balnicity Indices as a function of key astrophysical and observational parameters, such as the quasar redshifts and the signal-to-noise ratio of the spectra. 
James T. Allen, Paul C. Hewett, Vasily Belokurov, Vivienne Wild