Generic face detection algorithms do not perform very well in the mobile domain due to significant presence of occluded and partially visible faces. One promising technique to handle the challenge of partial faces is to design face detectors based on facial segments. In this paper two such face detectors namely, SegFace and DeepSegFace, are proposed that detect the presence of a face given arbitrary combinations of certain face segments. Both methods use proposals from facial segments as input that are found using weak boosted classifiers. SegFace is a shallow and fast algorithm using traditional features, tailored for situations where real time constraints must be satisfied. On the other hand, DeepSegFace is a more powerful algorithm based on a deep convolutional neutral network (DCNN) architecture. DeepSegFace offers certain advantages over other DCNN-based face detectors as it requires relatively little amount of data to train by utilizing a novel data augmentation scheme and is very robust to occlusion by design. Extensive experiments show the superiority of the proposed methods, specially DeepSegFace, over other state-of-the-art face detectors in terms of precision-recall and ROC curve on two mobile face datasets.