This article introduces two methods that find compact deep feature models for approximating images in set based face recognition problems. The proposed method treats each image set as a nonlinear face manifold that is composed of linear components. To find linear components of the face manifold, we first split image sets into subsets containing face images which share similar appearances. Then, our first proposed method approximates each subset by using the center of the deep feature representations of images in those subsets. Centers modeling the subsets are learned by using distance metric learning. The second proposed method uses discriminative common vectors to represent image features in the subsets, and entire subset is approximated with an affine hull in this approach. Discriminative common vectors are subset centers that are projected onto a new feature space where the combined within-class variances coming from all subsets are removed. Our proposed methods can also be considered as distance metric learning methods using triplet loss function where the learned subcluster centers are the selected anchors. This procedure yields to applying distance metric learning to quantized data and brings many advantages over using classical distance metric learning methods. We tested proposed methods on various face recognition problems using image sets and some visual object classification problems. Experimental results show that the proposed methods achieve the state-of-the-art accuracies on the most of the tested image datasets.