  The impact of convolution neural networks (CNNs) in the supervised settings
provided tremendous increment in performance. The representations learned from
CNN's operated on hyperspherical manifold led to insightful outcomes in face
recognition, face identification, and other supervised tasks. A broad range of
activation functions were developed with hypersphere intuition which performs
superior to softmax in euclidean space. The main motive of this research is to
provide insights. First, the stereographic projection is implied to transform
data from Euclidean space ($\mathbb{R}^{n}$) to hyperspherical manifold
($\mathbb{S}^{n}$) to analyze the performance of angular margin losses.
Secondly, proving theoretically and practically that decision boundaries
constructed on hypersphere using stereographic projection obliges the learning
of neural networks. Experiments have demonstrated that applying stereographic
projection on existing state-of-the-art angular margin objective functions
improved performance for standard image classification data sets
(CIFAR-10,100). Further, we ran our experiments on malaria-thin blood smear
images, resulting in effective outcomes. The code is publicly available
at:https://github.com/barulalithb/stereo-angular-margin.
