The visual pursuit of moving targets is a natural behaviour that has been exploited in, for example, medical diagnosis, law enforcement, and human computer interaction. Most proposed algorithms to detect this behaviour are based on some kind of motion similarity metric that assumes small or no distortion between the trajectory described by the target being pursued and the sensor measurements. We propose a novel algorithm based on 1D Convolutional Neural Networks (1D-CNNs), and investigate the performance of the 1D-CNN against 4 state-ofthe-art similarity based algorithms (SAs), using a novel dataset containing data from 10 participants. Their performances are evaluated using two trajectory shapes (circle and square), two target speeds (120/s and 240/ s), and three window sizes (0.5, 1.0 and 1.5 s). All algorithms have been trained or optimized to maximize the Matthew's Correlation Coefficient (MCC). Our results show that the 1D-CNN outperforms the SAs in all cases, requiring smaller window sizes to robustly detect the pursuits.