Radar sensors are an important part of driver assistance systems and intelligent vehicles due to their robustness against all kinds of adverse conditions, e.g., fog, snow, rain, or even direct sunlight. This robustness is achieved by a substantially larger wavelength compared to light-based sensors such as cameras or lidars. As a side effect, many surfaces act like mirrors at this wavelength, resulting in unwanted ghost detections. In this article, we present a novel approach to detect these ghost objects by applying data-driven machine learning algorithms. For this purpose, we use a large-scale automotive data set with annotated ghost objects. We show that we can use a state-of-the-art automotive radar classifier in order to detect ghost objects alongside real objects. Furthermore, we are able to reduce the amount of false positive detections caused by ghost images in some settings.