Recent improvements in the frequency, type and availability of satellite images mean it is now feasible to routinely study volcanoes in remote and inaccessible regions, including those with no ground-based monitoring. In particular, Interferometric Synthetic Aperture Radar (InSAR) data can detect surface deformation, which has a strong statistical link to eruption. However, the dataset produced by the recently-launched Sentinel-1 satellite is too large to be manually analysed on a global basis. In this study, we systematically process >30,000 short-term interferograms at over 900 volcanoes and apply machine learning algorithms to automatically detect volcanic ground deformation. We use a convolutional neutral network (CNN) to classify interferometric fringes in wrapped interferograms with no atmospheric corrections. We employ a transfer learning strategy, and test a range of pretrained networks, finding that AlexNet is best suited to this task. The positive results are checked by an expert and fed back for model updating. Following training with a combination of both positive and negative examples, this method reduced the number of interferograms to ~100 which required further inspection, of which at least 39 are considered 'true positives'. We demonstrate that machine learning can efficiently detect large, rapid deformation signals in wrapped interferograms, but further development is required to detect slow or small deformation patterns which do not generate multiple fringes in short duration interferograms. This study is the first to use machine learning approaches for detecting volcanic deformation in large datasets, and demonstrates the potential of such techniques for developing alert systems based on satellite imagery.