To study the effect of supermassive black holes (SMBHs) on their host galaxies it is important to study the hosts when the SMBH is near its peak activity. A method to investigate the host galaxies of high luminosity quasars is to obtain optical spect
ra at positions offset from the nucleus where the relative contribution of the quasar and host are comparable. However, at these extended radii the galaxy surface brightness is often low (20-22 mag per arcsec$^{2}$) and the resulting spectrum might have such low S/N that it hinders analysis with standard stellar population modeling techniques. To address this problem we have developed a method that can recover galaxy star formation histories (SFHs) from rest frame optical spectra with S/N $sim$ 5~AA$^{-1}$. This method uses the statistical technique diffusion k-means to tailor the stellar population modeling basis set. Our diffusion k-means minimal basis set, composed of 4 broad age bins, is successful in recovering a range of galaxy SFHs. Additionally, using an analytic prescription for seeing conditions, we are able to simultaneously model scattered quasar light and the SFH of quasar host galaxies (QHGs). We use synthetic data to compare results of our novel method with previous techniques. We also present the modeling results on a previously published QHG and show that galaxy properties recovered from a diffusion k-means basis set are less sensitive to noise added to this quasar host galaxy spectrum. Our new method has a clear advantage in recovering information from QHGs and could also be applied to the analysis of other low S/N galaxy spectra such as those typically obtained for high redshift objects or integral field spectroscopic surveys.
