We present an analysis of the optical spectra of narrow emission-line galaxies, based on mean field independent component analysis (MFICA), a blind source separation technique. Samples of galaxies were drawn from the Sloan Digital Sky Survey (SDSS) and used to generate compact sets of 'continuum' and 'emission-line' component spectra. These components can be linearly combined to reconstruct the observed spectra of a wider sample of galaxies. Only 10 components - five continuum and five emission line - are required to produce accurate reconstructions of essentially all narrow emission-line galaxies to a very high degree of accuracy; the median absolute deviations of the reconstructed emission-line fluxes, given the signal-to-noise ratio (S/N) of the observed spectra, are 1.2-1.8σ for the strong lines. After applying the MFICA components to a large sample of SDSS galaxies, we identify the regions of parameter space that correspond to pure star formation and pure active galactic nucleus (AGN) emission-line spectra, and produce high S/N reconstructions of these spectra. The physical properties of the pure star formation and pure AGN spectra are investigated by means of a series of photoionization models, exploiting the faint emission lines that can be measured in the reconstructions. We are able to recreate the emission-line strengths of the most extreme AGN case by assuming that the central engine illuminates a large number of individual clouds with radial distance and density distributions, f(r) ∝ r γ and g(n) ∝ n β, respectively. The best fit is obtained with γ = −0.75 and β = −1.4. From the reconstructed star formation spectra, we are able to estimate the starburst ages. These preliminary investigations serve to demonstrate the success of the MFICA-based technique in identifying distinct emission sources, and its potential as a tool for the detailed analysis of the physical properties of galaxies in large-scale surveys.