  Galaxy clusters appear as extended sources in XMM-Newton images, but not all
extended sources are clusters. So, their proper classification requires visual
inspection with optical images, which is a slow process with biases that are
almost impossible to model. We tackle this problem with a novel approach, using
convolutional neural networks (CNNs), a state-of-the-art image classification
tool, for automatic classification of galaxy cluster candidates. We train the
networks on combined XMM-Newton X-ray observations with their optical
counterparts from the all-sky Digitized Sky Survey. Our data set originates
from the X-CLASS survey sample of galaxy cluster candidates, selected by a
specially developed pipeline, the XAmin, tailored for extended source detection
and characterisation. Our data set contains 1 707 galaxy cluster candidates
classified by experts. Additionally, we create an official Zooniverse citizen
science project, The Hunt for Galaxy Clusters, to probe whether citizen
volunteers could help in a challenging task of galaxy cluster visual
confirmation. The project contained 1 600 galaxy cluster candidates in total of
which 404 overlap with the expert's sample. The networks were trained on expert
and Zooniverse data separately. The CNN test sample contains 85
spectroscopically confirmed clusters and 85 non-clusters that appear in both
data sets. Our custom network achieved the best performance in the binary
classification of clusters and non-clusters, acquiring accuracy of 90 %,
averaged after 10 runs. The results of using CNNs on combined X-ray and optical
data for galaxy cluster candidate classification are encouraging and there is a
lot of potential for future usage and improvements.
