Deep learning has shown significant performance advantages in object recognition problems. In particular, convolutional neural networks (CNN's) have been a preferred approach when recognizing objects in imagery. In general, however, CNN's have been applied to closed set recognition problems - those problems where all the objects of interest are in both the training and test sets. This effort addresses target classification using synthetic aperture radar (SAR) as the imaging sensor. In addition, this effort investigates the open set classification problem where targets in the test set are not in the training set. In this open set problem, the objective is to correctly classify test target types represented in the training set while rejecting those not in the training set as unknown. This open set problem is addressed using a hybrid approach of CNN's combined with a novel support vector machine (SVM) approach called SV-means.