Deep Simplex Classifier for Maximizing the Margin in Both Euclidean and Angular Spaces

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ÇEVİKALP H., Saribas H.

23nd Scandinavian Conference on Image Analysis, SCIA 2023, Lapland, Finland, 18 - 21 April 2023, vol.13886 LNCS, pp.91-107 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 13886 LNCS
  • Doi Number: 10.1007/978-3-031-31438-4_7
  • City: Lapland
  • Country: Finland
  • Page Numbers: pp.91-107
  • Keywords: classification, computer vision, deep learning, open set recognition, simplex classifier
  • Eskisehir Osmangazi University Affiliated: Yes


The classification loss functions used in deep neural network classifiers can be grouped 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 margin in the angular spaces. This paper 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 pairwise distances between class centers are always equivalent. This restriction corresponds to choosing centers from the vertices of a regular simplex. There is not any hyperparameter that must be set by the user in the proposed loss function, therefore the use of the proposed method is extremely easy for classical classification problems. Moreover, since the class samples are compactly clustered around their corresponding means, the proposed classifier is also very suitable for open set recognition problems where test samples can come from the unknown classes that are not seen in the training phase. Experimental studies show that the proposed method achieves the state-of-the-art accuracies on open set recognition despite its simplicity.