  We present a novel approach to photometric redshifts, one that merges the
advantages of both the template fitting and empirical fitting algorithms,
without any of their disadvantages. This technique derives a set of templates,
describing the spectral energy distributions of galaxies, from a catalog with
both multicolor photometry and spectroscopic redshifts. The algorithm is
essentially using the shapes of the templates as the fitting parameters. From
simulated multicolor data we show that for a small training set of galaxies we
can reconstruct robustly the underlying spectral energy distributions even in
the presence of substantial errors in the photometric observations. We apply
these techniques to the multicolor and spectroscopic observations of the Hubble
Deep Field building a set of template spectra that reproduced the observed
galaxy colors to better than 10%. Finally we demonstrate that these improved
spectral energy distributions lead to a photometric-redshift relation for the
Hubble Deep Field that is more accurate than standard template-based
approaches.
