Exploring the SDSS Photometric Galaxies with Clustering Redshifts
  We apply clustering-based redshift inference to all extended sources from the
Sloan Digital Sky Survey photometric catalogue, down to magnitude r = 22. We
map the relationships between colours and redshift, without assumption of the
sources' spectral energy distributions (SED). We identify and locate
star-forming, quiescent galaxies, and AGN, as well as colour changes due to
spectral features, such as the 4000 \AA{} break, redshifting through specific
filters. Our mapping is globally in good agreement with colour-redshift tracks
computed with SED templates, but reveals informative differences, such as the
need for a lower fraction of M-type stars in certain templates. We compare our
clustering-redshift estimates to photometric redshifts and find these two
independent estimators to be in good agreement at each limiting magnitude
considered. Finally, we present the global clustering-redshift distribution of
all Sloan extended sources, showing objects up to z ~ 0.8. While the overall
shape agrees with that inferred from photometric redshifts, the clustering
redshift technique results in a smoother distribution, with no indication of
structure in redshift space suggested by the photometric redshift estimates
(likely artifacts imprinted by their spectroscopic training set). We also infer
a higher fraction of high redshift objects. The mapping between the four
observed colours and redshift can be used to estimate the redshift probability
distribution function of individual galaxies. This work is an initial step
towards producing a general mapping between redshift and all available
observables in the photometric space, including brightness, size,
concentration, and ellipticity.
