  Ground based gamma-ray observations with Imaging Atmospheric Cherenkov
Telescopes (IACTs) play a significant role in the discovery of very high energy
(E > 100 GeV) gamma-ray emitters. The analysis of IACT data demands a highly
efficient background rejection technique, as well as methods to accurately
determine the energy of the recorded gamma-ray and the position of its source
in the sky. We present results for background rejection and signal direction
reconstruction from first studies of a novel data analysis scheme for IACT
measurements. The new analysis is based on a set of Convolutional Neural
Networks (CNNs) applied to images from the four H.E.S.S. phase-I telescopes. As
the H.E.S.S. cameras pixels are arranged in a hexagonal array, we demonstrate
two ways to use such image data to train CNNs: by resampling the images to a
square grid and by applying modified convolution kernels that conserve the
hexagonal grid properties.
  The networks were trained on sets of Monte-Carlo simulated events and tested
on both simulations and measured data from the H.E.S.S. array. A comparison
between the CNN analysis to current state-of-the-art algorithms reveals a clear
improvement in background rejection performance. When applied to H.E.S.S.
observation data, the CNN direction reconstruction performs at a similar level
as traditional methods. These results serve as a proof-of-concept for the
application of CNNs to the analysis of events recorded by IACTs.
