Caveolae are plasma membrane invaginations whose formation requires caveolin-1 (Cav1), the adaptor protein polymerase I, and the transcript release factor (PTRF or CAVIN1). Caveolae have an important role in cell functioning, signaling, and disease. In the absence of CAVIN1/PTRF, Cav1 forms non-caveolar membrane domains called scaffolds. In this work, we train machine learning models to automatically distinguish between caveolae and scaffolds from single molecule localization microscopy (SMLM) data. We apply machine learning algorithms to discriminate biological structures from SMLM data. Our work is the first that is leveraging machine learning approaches (including deep learning models) to automatically identifying biological structures from SMLM data. In particular, we develop and compare three binary classification methods to identify whether or not a given 3D cluster of Cav1 proteins is a caveolae. The first uses a random forest classifier applied to 28 hand-crafted/designed features, the second uses a convolutional neural net (CNN) applied to a projection of the point clouds onto three planes, and the third uses a PointNet model, a recent development that can directly take point clouds as its input. We validate our methods on a dataset of super-resolution microscopy images of PC3 prostate cancer cells labeled for Cav1. Specifically, we have images from two cell populations: 10 PC3 and 10 CAVIN1/PTRF-transfected PC3 cells (PC3-PTRF cells) that form caveolae. We obtained a balanced set of 1714 different cellular structures. Our results show that both the random forest on hand-designed features and the deep learning approach achieve high accuracy in distinguishing the intrinsic features of the caveolae and non-caveolae biological structures. More specifically, both random forest and deep CNN classifiers achieve classification accuracy reaching 94% on our test set, while the PointNet model only reached 83% accuracy. We also discuss the pros and cons of the different approaches.