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Next-generation radio surveys will yield an unprecedented amount of data, warranting analysis by use of machine learning techniques. Convolutional neural networks are the deep learning technique that has proven to be the most successful in classifying image data. Capsule networks are a more recently developed technique that use capsules comprised of groups of neurons, that describe properties of an image including the relative spatial locations of features. The current work explores the performance of different capsule network architectures against simpler convolutional neural network architectures, in reproducing the classifications into the classes of unresolved, FRI and FRII morphologies. We utilise images from a LOFAR survey which is the deepest, wide-area radio survey to date, revealing more complex radio-source structures compared to previous surveys, presenting further challenges for machine learning algorithms. The 4- and 8-layer convolutional networks attain an average precision of 93.3% and 94.3% respectively, compared to 89.7% obtained with the capsule network, when training on original and augmented images. Implementing transfer learning achieves a precision of 94.4%, that is within the confidence interval of the 8-layer convolutional network. The convolutional networks always outperform any variation of the capsule network, as they prove to be more robust to the presence of noise in images. The use of pooling appears to allow more freedom for the intra-class variability of radio galaxy morphologies, as well as reducing the impact of noise.