Pattern recognition in the ALFALFA.70 and Sloan Digital Sky Surveys: A
  catalog of $\sim$ 500,000 HI gas fraction estimates based on artificial
  neural networks
  The application of artificial neural networks (ANNs) for the estimation of HI
gas mass fraction (\fgas) is investigated, based on a sample of 13,674 galaxies
in the Sloan Digital Sky Survey (SDSS) with HI detections or upper limits from
the Arecibo Legacy Fast Arecibo L-band Feed Array (ALFALFA). We show that, for
an example set of fixed input parameters ($g-r$ colour and $i$-band surface
brightness), a multidimensional quadratic model yields \fgas\ scaling relations
with a smaller scatter (0.22 dex) than traditional linear fits (0.32 dex),
demonstrating that non-linear methods can lead to an improved performance over
traditional approaches. A more extensive ANN analysis is performed using 15
galaxy parameters that capture variation in stellar mass, internal structure,
environment and star formation. Of the 15 parameters investigated, we find that
$g-r$ colour, followed by stellar mass surface density, bulge fraction and
specific star formation rate have the best connection with \fgas. By combining
two control parameters, that indicate how well a given galaxy in SDSS is
represented by the ALFALFA training set (\pr) and the scatter in the training
procedure (\sigf), we develop a strategy for quantifying which SDSS galaxies
our ANN can be adequately applied to, and the associated errors in the \fgas\
estimation. In contrast to previous works, our \fgas\ estimation has no
systematic trend with galactic parameters such as M$_{\star}$, $g-r$ and SFR.
We present a catalog of \fgas\ estimates for more than half a million galaxies
in the SDSS, of which $\sim$ 150,000 galaxies have a secure selection parameter
with average scatter in the \fgas\ estimation of 0.22 dex.
