  The widely-used cross-entropy (CE) loss-based deep networks achieved
significant progress w.r.t. the classification accuracy. However, the CE loss
can essentially ignore the risk of misclassification which is usually measured
by the distance between the prediction and label in a semantic hierarchical
tree. In this paper, we propose to incorporate the risk-aware inter-class
correlation in a discrete optimal transport (DOT) training framework by
configuring its ground distance matrix. The ground distance matrix can be
pre-defined following a priori of hierarchical semantic risk. Specifically, we
define the tree induced error (TIE) on a hierarchical semantic tree and extend
it to its increasing function from the optimization perspective. The semantic
similarity in each level of a tree is integrated with the information gain. We
achieve promising results on several large scale image classification tasks
with a semantic tree structure in a plug and play manner.
