Artificial neural network based calibrations for the prediction of
  galactic [NII] $\lambda$ 6584 and H$\alpha$ line luminosities
  The artificial neural network (ANN) is a well-established mathematical
technique for data prediction, based on the identification of correlations and
pattern recognition in input training sets. We present the application of ANNs
to predict the emission line luminosities of H$\alpha$ and [NII] $\lambda$6584
in galaxies. These important spectral diagnostics are used for metallicities,
active galactic nuclei (AGN) classification and star formation rates, yet are
shifted into the infra-red for galaxies above $z \sim 0.5$, or may not be
covered in spectra with limited wavelength coverage. The ANN is trained with a
large sample of emission line galaxies selected from the Sloan Digital Sky
Survey using various combinations of emission lines and stellar mass. The ANN
is tested for galaxies dominated by both star formation and AGN; in both cases
the H$\alpha$ and [NII] $\lambda$6584 line luminosities can be predicted with a
scatter $\sigma <$ 0.1 dex. We also show that the performance of the ANN does
not depend significantly on the covering fraction, mass or metallicity of the
data. Polynomial functions are derived that allow easy application of the ANN
predictions to determine H$\alpha$ and [NII] $\lambda$6584 line luminosities.
An ANN calibration for the Balmer decrement (H$\alpha$/H$\beta$) based on line
equivalent widths and colours is also presented. The effectiveness of the ANN
calibration is demonstrated with an independent dataset (the Galaxy Mass and
Assembly Survey). We demonstrate the application of our line luminosities to
the determination of gas-phase metallicities and AGN classification. The ANN
technique yields a significant improvement in the measurement of metallicities
that require [NII] and H$\alpha$ when compared with the function based
conversions of Kewley & Ellison. The AGN classification is successful for 86
per cent of SDSS galaxies.
