Fixed simplex coordinates for angular margin loss in CapsNet

A more stationary and discriminative embedding is necessary for robust classification of images. We focus our attention on the newel CapsNet model and we propose the angular margin loss function in composition with margin loss. We define a fixed classifier implemented with fixed weights vectors obtained by the vertex coordinates of a simplex polytope. The advantage of using simplex polytope is that we obtain the maximal symmetry for stationary features angularly centred. Each weight vector is to be considered as the centroid of a class in the dataset. The embedding of an image is obtained through the capsule network encoding phase, that is identified as digitcaps matrix. Based on the centroids from the simplex coordinates and the embedding from the model, we compute the angular distance between the image embedding and the centroid of the correspondent class of the image. We take this angular distance as angular margin loss. We keep the computation proposed for margin loss in the original architecture of CapsNet. We train the model to minimise the angular between the embedding and the centroid of the class and maximise the magnitude of the embedding for the predicted class. The experiments on different datasets demonstrate that the angular margin loss improves the capability of capsule networks with complex datasets.