Whole brain tractography data contain a large number of streamlines that require algorithms such as clustering to group the data into smaller sets for visualization and analysis. We present a deep-learning clustering algorithm based on the latent space of a variational autoencoder trained on the direct and flipped versions of the streamlines from 10 tractograms (17,294,232 streamlines in total). The model takes advantage of the low-dimensional representation of the data in latent space to apply an HDBSCAN clustering algorithm to perform automatic and fast clustering of the tractography datasets. The proposed method was evaluated in terms of segmentation quality using the Davies-Bouldin index (DB) and execution time against two other state-of-the-art methods, QuickBundles (QB) and FFClust. The results show that the proposed method has the best performance in terms of the DB index, closely followed by QB, and is the second fastest method, only slightly surpassed by FFClust. In addition, the proposed method allows for obtaining meaningful large clusters because it uses metrics based on the density of the groups instead of a distance threshold as the other methods.