  The labels in medical diagnosis task are usually discrete and successively
distributed. For example, the Diabetic Retinopathy Diagnosis (DR) involves five
health risk levels: no DR (0), mild DR (1), moderate DR (2), severe DR (3) and
proliferative DR (4). This labeling system is common for medical disease.
Previous methods usually construct a multi-binary-classification task or
propose some re-parameter schemes in the output unit. In this paper, we target
on this task from the perspective of loss function. More specifically, the
Wasserstein distance is utilized as an alternative, explicitly incorporating
the inter-class correlations by pre-defining its ground metric. Then, the
ground metric which serves as a linear, convex or concave increasing function
w.r.t. the Euclidean distance in a line is explored from an optimization
perspective. Meanwhile, this paper also proposes of constructing the smoothed
target labels that model the inlier and outlier noises by using a
unimodal-uniform mixture distribution. Different from the one-hot setting, the
smoothed label endues the computation of Wasserstein distance with more
challenging features. With either one-hot or smoothed target label, this paper
systematically concludes the practical closed-form solution. We evaluate our
method on several medical diagnosis tasks (e.g., Diabetic Retinopathy and
Ultrasound Breast dataset) and achieve state-of-the-art performance.
