Multi-class AUC maximization for imbalanced ordinal multi-stage tropical cyclone intensity change forecast

Intense tropical cyclones (TCs) cause significant damage to human societies. Forecasting the multiple stages of TC intensity changes is considerably crucial yet challenging. This difficulty arises due to imbalanced data distribution and the need for ordinal multi-class classification. While existing classification methods, such as linear discriminant analysis, have been utilized to predict rare rapidly intensifying (RI) stages based on features related TC intensity changes, they are limited to binary classification distinguishing between RI and non-RI stages. In this paper, we introduce a novel methodology to tackle the challenges of imbalanced ordinal multi-class classification. We extend the Area Under the Curve maximization technique with inter-instance/class cross-hinge losses and inter-class distance-based slack variables. The proposed loss function, implemented within a deep learning framework, demonstrates its effectiveness using real sequence data of multi-stage TC intensity changes, including satellite infrared images and environmental variables observed in the western North Pacific.