  We use a purely data-driven rectified factor analysis to identify early-type
galaxies with recent star formation in DR4 of the SDSS Spectroscopic Catalogue.
We compare the spectra and environment of these galaxies with `normal'
early-types, and a sample of independently selected E+A galaxies. We calculate
the projected local galaxy surface density (Sigma_5 and Sigma_10) for each
galaxy in our sample, and find that the dependence, on projected local density,
of the properties of E+As is not significantly different from that of
early-types with young stellar populations, dropping off rapidly towards denser
environments, and flattening off at densities < 0.1-0.3 Mpc^-2. The dearth of
E+A galaxies in dense environments confirms that E+As are most likely the
products of galaxy-galaxy merging or interactions, rather than star-forming
galaxies whose star formation has been quenched by processes unique to dense
environments. We see a tentative peak in the number of E+A galaxies at Sigma_10
\~ 0.1-0.3 Mpc^-2, which may represent the local galaxy density at which the
rate of galaxy-galaxy merging or interaction rate peaks. Analysis of the
spectra of our early-types with young stellar populations suggests that they
have a stellar component dominated by F stars, ~ 1-4 Gyr old, together with a
mature, metal-rich population characteristic of `typical' early-types. The
young stars represent > 10% of the stellar mass in these galaxies. This,
together with the similarity of the environments in which this `E+F' population
and the E+A galaxy sample are found, suggests that E+F galaxies used to be E+A
galaxies, but have evolved by a further ~ one to a few Gyr. Our factor analysis
is sensitive enough to identify this hidden population. (Abridged)
