Considering the fact that points of interest on 3D shapes can be discriminated from a geometric perspective, it is reasonable 5 to map the geometric signature of a point p to a probability value encoding to what degree p is a point of interest, especially for a specific 6 class of 3D shapes. Based on the observation, we propose a three-phase algorithm for learning and predicting points of interest on 3D 7 shapes by using multiple feature descriptors. Our algorithm requires two separate deep neural networks (stacked auto-encoders) to 8 accomplish the task. During the first phase, we predict the membership of the given 3D shape according to a set of geometric 9 descriptors using a deep neural network. After that, we train the other deep neural network to predict a probability distribution defined 10 on the surface representing the possibility of a point being a point of interest. Finally, we use a manifold clustering technique to extract a 11 set of points of interest as the output. Experimental results show superior detection performance of the proposed method over the 12 previous state-of-the-art approaches.