Polar regions and Greenland in particular are highly sensitive to global warming. Impacts on Greenland's glaciers may be observed through the increasing number of calving events. However, a direct assessment of the calving activity is limited due to the remoteness of polar regions and the cloudy weather which makes impossible a recurrent observation through satellite imagery. To tackle this issue, we exploit the seismological network deployed in Greenland which actively records seismic signals associated with calving events, hereinafter referred to as glacial earthquakes. These seismic signals present a broad frequency range and a wide diversity of waveform which make them difficult to discriminate from tectonic events as well as anthropogenic and natural noises. In this study, we start from two catalogues of known events, one for glacial earthquake events which occurred between 1993 and 2013 and one for earthquakes which occurred in the same time period, and we implement a detection algorithm based on the STA/LTA method to extract signals' events from continuous data. Then, we train and test a machine learning processing chain based on the Random Forest algorithm which allows us to automatically associate the events respectively with calving and tectonic activity, with a certain probability. Finally, we investigate 844 selected days spanning time of continuous data from the Greenland regional seismic network which results in a new, more exhaustive, catalogue of glacial earthquakes expanded of 1633 newly detected glacial events. Moreover, we extensively discuss the choice of the features used to describe glacial earthquakes, in particular the 39 new features created in this study which have drastically improved our results with 7 of the 10 best features being in the added set. The perspective of further expansion of the glacial earthquake catalogue applying the processing chain discussed in this paper on different time spans highlights how combining seismology and machine learning can increase our understanding of the spatio-temporal evolution of calving activity in remote regions.