The classification loss functions used in deep neural network classifiers can be split into two categories based on maximizing the margin in either Euclidean or angular spaces. Euclidean distances between sample vectors are used during classification for the methods maximizing the margin in Euclidean spaces whereas the Cosine similarity distance is used during the testing stage for the methods maximizing the margin in the angular spaces. This article introduces a novel classification loss that maximizes the margin in both the Euclidean and angular spaces at the same time. This way, the Euclidean and Cosine distances will produce similar and consistent results and complement each other, which will in turn improve the accuracies. The proposed loss function enforces the samples of classes to cluster around the centers that represent them. The centers approximating classes are chosen from the boundary of a hypersphere, and the pair-wise distances between class centers are always equivalent. This restriction corresponds to choosing centers from the vertices of a regular simplex inscribed in a hypersphere. The proposed loss function can be effortlessly applied to classical classification problems as there is a single hyperparameter that must be set by the user, and setting this parameter is straightforward. Additionally, the proposed method can effectively reject test samples from unfamiliar classes by measuring their distances from the known class centers, which are compactly clustered around their corresponding centers. Therefore, the proposed technique is especially suitable for open set recognition problems. Despite its simplicity, experimental studies have demonstrated that the proposed method outperforms other techniques in both open set recognition and classical classification problems. Interested individuals can access the source code for the proposed approach at https://github.com/Cevikalp/dsc.

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.

The classifiers that return compact acceptance regions are crucial for the success in anomaly detection and open set recognition settings since we have to determine and reject the anomalies and samples coming from the unknown classes. This paper introduces novel methods that approximate the class acceptance regions with compact hypersphere models for anomaly detection and open set recognition. As opposed to the other deep hypersphere classifiers, we treat the hypersphere centers as learnable parameters and update them based on the changing deep feature representations. In addition, we propose novel loss terms that are more robust to the noisy labels within the outlier exposure and background datasets. The proposed methods bear similarity to the deep distance metric learning classifiers using the triplet loss function with the exception that the anchors are set to the hypersphere centers which are updated dynamically. The experimental results show that the proposed methods achieve the state-of-the-art accuracies on the majority of the tested datasets in the context of anomaly detection and open set recognition.