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Abstract: Using deep learning techniques, anomalies in the paranasal sinus system can be detected automatically in MRI images and can be further analyzed and classified based on their volume, shape and other parameters like local contrast. However due to limited training data, traditional supervised learning methods often fail to generalize. Existing deep learning methods in paranasal anomaly classification have been used to diagnose at most one anomaly. In our work, we consider three anomalies. Specifically, we employ a 3D CNN to separate maxillary sinus volumes without anomaly from maxillary sinus volumes with anomaly. To learn robust representations from a small labelled dataset, we propose a novel learning paradigm that combines contrastive loss and cross-entropy loss. Particularly, we use a supervised contrastive loss that encourages embeddings of maxillary sinus volumes with and without anomaly to form two distinct clusters while the cross-entropy loss encourages the 3D CNN to maintain its discriminative ability. We report that optimising with both losses is advantageous over optimising with only one loss. We also find that our training strategy leads to label efficiency. With our method, a 3D CNN classifier achieves an AUROC of 0.85 {\textpm} 0.03 while a 3D CNN classifier optimised with cross-entropy loss achieves an AUROC of 0.66 {\textpm} 0.1. Our source code is available at https://github.com/dawnofthedebayan/SupConCE{\_}MICCAI{\_}22.