Directional discontinuities (DDs) are defined as abrupt changes of the magnetic field orientation. We use observations from ESA’s Cluster mission to compile a database of events: 4216 events are identified in January-April 2007, and 5194 in January-April 2008. Localized time-scale images depicting angular changes are created for each event, and a preliminary classification algorithm is designed to distinguish between: simple - isolated events, and complex - multiple overlapping events. In 2007, 1806 events are pre-classified as simple, and 2410 as complex; in 2008, 1997 events are simple, and 3197 are complex. A supervised machine learning approach is used to recognize and predict these events. Two models are trained: one for 2007, which is used to predict the results in 2008, and vice-versa for 2008. To validate our results, we investigate the discontinuity occurrence rate as a function of spacecraft location. When the spacecraft is in the solar wind, we find an occurrence rate of ~2 DDs per hour and a 50/50 % ratio of simple/complex events. When the spacecraft is in the Earth’s magnetosheath, we find that the total occurrence rate remains around 2 DDs/h, but the ratio of simple/complex events changes to ~25/75 %. This implies that about half of the simple events observed in the solar wind are classified as complex when observed in the magnetosheath. This demonstrates that our classification scheme can provide meaningful insights, and thus be relevant for future studies on interplanetary discontinuities.