The problem of identification of ultra-high-energy cosmic ray (UHECR) sources is greatly complicated by the fact that even the highest energy cosmic rays may be deflected by tens of degrees in the galactic magnetic fields. We show that arrival directions of UHECRs from several nearest active galaxies form specific patterns in the sky, which can be effectively recognized by convolutional neural networks. We use one of the recently developed convnet implementations for images defined on the sphere to train the classifier that is able to detect patterns that can be present in the experimental data. We calculate the minimal detectable from-source event fractions for several realistic source candidates and discuss the method limitations.