  To further our knowledge of the complex physical process of galaxy formation,
it is essential that we characterize the formation and evolution of large
databases of galaxies. The spectral synthesis STARLIGHT code of Cid Fernandes
et al. (2004) was designed for this purpose. Results of STARLIGHT are highly
dependent on the choice of input basis of simple stellar population (SSP)
spectra. Speed of the code, which uses random walks through the parameter
space, scales as the square of the number of basis spectra, making it
computationally necessary to choose a small number of SSPs that are coarsely
sampled in age and metallicity. In this paper, we develop methods based on
diffusion map (Lafon & Lee, 2006) that, for the first time, choose appropriate
bases of prototype SSP spectra from a large set of SSP spectra designed to
approximate the continuous grid of age and metallicity of SSPs of which
galaxies are truly composed. We show that our techniques achieve better
accuracy of physical parameter estimation for simulated galaxies. Specifically,
we show that our methods significantly decrease the age-metallicity degeneracy
that is common in galaxy population synthesis methods. We analyze a sample of
3046 galaxies in SDSS DR6 and compare the parameter estimates obtained from
different basis choices.
