  In scoring systems used to measure the endoscopic activity of ulcerative
colitis, such as Mayo endoscopic score or Ulcerative Colitis Endoscopic Index
Severity, levels increase with severity of the disease activity. Such relative
ranking among the scores makes it an ordinal regression problem. On the other
hand, most studies use categorical cross-entropy loss function to train deep
learning models, which is not optimal for the ordinal regression problem. In
this study, we propose a novel loss function, class distance weighted
cross-entropy (CDW-CE), that respects the order of the classes and takes the
distance of the classes into account in calculation of the cost. Experimental
evaluations show that models trained with CDW-CE outperform the models trained
with conventional categorical cross-entropy and other commonly used loss
functions which are designed for the ordinal regression problems. In addition,
the class activation maps of models trained with CDW-CE loss are more
class-discriminative and they are found to be more reasonable by the domain
experts.
