Analysis of a Custom Support Vector Machine for Photometric Redshift
  Estimation and the Inclusion of Galaxy Shape Information
  Aims: We present a custom support vector machine classification package for
photometric redshift estimation, including comparisons with other methods. We
also explore the efficacy of including galaxy shape information in redshift
estimation. Support vector machines, a type of machine learning, utilize
optimization theory and supervised learning algorithms to construct predictive
models based on the information content of data in a way that can treat
different input features symmetrically.
  Methods: The custom support vector machine package we have developed is
designated SPIDERz and made available to the community. As test data for
evaluating performance and comparison with other methods, we apply SPIDERz to
four distinct data sets: 1) the publicly available portion of the PHAT-1
catalog based on the GOODS-N field with spectroscopic redshifts in the range $z
< 3.6$, 2) 14365 galaxies from the COSMOS bright survey with photometric band
magnitudes, morphology, and spectroscopic redshifts inside $z < 1.4$, 3) 3048
galaxies from the overlap of COSMOS photometry and morphology with 3D-HST
spectroscopy extending to $z < 3.9$, and 4) 2612 galaxies with five-band
photometric magnitudes and morphology from the All-wavelength Extended Groth
Strip International Survey and $z < 1.57$.
  Results: We find that SPIDER-z achieves results competitive with other
empirical packages on the PHAT-1 data, and performs quite well in estimating
redshifts with the COSMOS and AEGIS data, including in the cases of a large
redshift range ($0 < z < 3.9$). We also determine from analyses with both the
COSMOS and AEGIS data that the inclusion of morphological information does not
have a statistically significant benefit for photometric redshift estimation
with the techniques employed here.
