We describe the application of non-negative matrix factorization to generate compact reconstructions of quasar spectra from the Sloan Digital Sky Survey (SDSS), with particular reference to broad absorption line quasars (BALQSOs). BAL properties are measured for SiIV{lambda}1400, CIV{lambda}1550, AlIII{lambda}1860 and MgII{lambda}2800, resulting in a catalogue of 3547 BALQSOs. Two corrections, based on extensive testing of synthetic BALQSO spectra, are applied in order to estimate the intrinsic fraction of CIV BALQSOs. First, the probability of an observed BALQSO spectrum being identified as such by our algorithm is calculated as a function of redshift, signal-to-noise ratio and BAL properties. Secondly, the different completenesses of the SDSS target selection algorithm for BALQSOs and non-BAL quasars are quantified.