We introduce a novel approach for instance segmentation of point clouds using a form of similarity learning. Specifically, our neural network, called PointSimNet, based on PointNet, learns to predict point features that are close to each other in feature space if the points belong to the same semantic category. A similarity matrix is used to find the optimal number of clusters using the eigengap heuristic. Spectral clustering is then performed on the similarity matrix to obtain the final set of instances. We also provide an optional step of constrained clustering where the user can guide the clustering to refine the segmentation results. We show that our instance segmentation method outperforms SGPN by an average precision of 20% points according to a measure without requiring any instance information in the training set. We also demonstrate that the user can improve the accuracy of results by adding a small number of constraints.