Abstract
Currently, the use of deep learning for solving ordinal classification problems, where categories follow a natural order, has not received much attention. In this paper, we propose an unimodal regularisation based on the beta distribution applied to the cross-entropy loss. This regularisation encourages the distribution of the labels to be a soft unimodal distribution, more appropriate for ordinal problems. Given that the beta distribution has two parameters that must be adjusted, a method to automatically determine them is proposed. The regularised loss function is used to train a deep neural network model with an ordinal scheme in the output layer. The results obtained are statistically analysed and show that the combination of these methods increases the performance in ordinal problems. Moreover, the proposed beta distribution performs better than other distributions proposed in previous works, achieving also a reduced computational cost.
Highlights
In the last decade, ordinal classification/regression has received an increasing interest in the literature [1,2,3]
When we analyse the results of all the metrics combined, we find that the method that uses stick breaking with beta regularised loss (SB CE-β) achieves the best result for Quadratic Weighted Kappa (QWK) and Classification Rate (CCR), and the second best for Minimum Sensitivity (MS)
We have proposed the application of a unimodal regularisation based on beta distributions for the cross-entropy loss
Summary
Ordinal classification/regression has received an increasing interest in the literature [1,2,3]. The methods focused on solving this kind of problems aim to determine the discrete category or ranking of a pattern in an ordinal scale. In medical problems where we obtain a diagnosis from images, the category is usually in an ordinal scale (e.g. Diabetic Retinopathy (DR) detection [5] with five levels of the disease). Another possible example is the prediction of the age range of people from photographs of their faces [6]. In [8] the authors try to predict convective situations in the Madrid-Barajas airport in Spain, which is crucial for this kind of transportation facilities as it can cause severe impact in flight scheduling and safety. These situations can be present in several degrees, resulting in dif-
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