  Gravitational waves are emitted from deep within a core-collapse supernova,
which may enable us to determine the mechanism of the explosion from a
gravitational-wave detection. Previous studies suggested that it is possible to
determine if the explosion mechanism is neutrino-driven or magneto-rotationally
powered from the gravitational-wave signal. However, long duration
magneto-rotational waveforms, that cover the full explosion phase, were not
available during the time of previous studies, and explosions were just assumed
to be magneto-rotationally driven if the model was rapidly rotating. Therefore,
we perform an updated study using new 3D long-duration magneto-rotational
core-collapse supernova waveforms that cover the full explosion phase, injected
into noise for the Advanced LIGO, Einstein Telescope and NEMO
gravitational-wave detectors. We also include a category for failed explosions
in our signal classification results. We then determine the explosion mechanism
of the signals using three different methods: Bayesian model selection,
dictionary learning, and convolutional neural networks. The three different
methods are able to distinguish between neutrino-driven explosions and
magneto-rotational explosions, even if the neutrino-driven explosion model is
rapidly rotating. However they can only distinguish between the non-exploding
and neutrino-driven explosions for signals with a high signal to noise ratio.
