  We propose a deep metric learning model to create embedded sub-spaces with a
well defined structure. A new loss function that imposes Gaussian structures on
the output space is introduced to create these sub-spaces thus shaping the
distribution of the data. Having a mixture of Gaussians solution space is
advantageous given its simplified and well established structure. It allows
fast discovering of classes within classes and the identification of mean
representatives at the centroids of individual classes. We also propose a new
semi-supervised method to create sub-classes. We illustrate our methods on the
facial expression recognition problem and validate results on the FER+,
AffectNet, Extended Cohn-Kanade (CK+), BU-3DFE, and JAFFE datasets. We
experimentally demonstrate that the learned embedding can be successfully used
for various applications including expression retrieval and emotion
recognition.
