Bidirectional Weighted Cross-Entropy for Imbalanced Pressure Injury Classification

Accurate classification of pressure injuries from clinical images remains challenging because clinical datasets are often small and class-imbalanced. We propose bidirectional weighted cross-entropy (BWCE), a conditional prediction-dependent cost-sensitive loss that assigns higher costs to minority-to-majority misclassification. BWCE combines a true-label weight for underrepresented classes with a predicted class weight for majority predicted classes and applies the joint factor only to misclassified samples. We evaluated BWCE on 853 pressure-injury images using 3 × 10 repeated stratified cross-validation. BWCE-log was compared with CE, WCE, focal loss, class-balanced cross-entropy (CB-CE), LDAM, and BWCE ablation/mapping variants under aligned splits, initialization, architecture, and training settings. In the primary comparison using standard metrics, BWCE-log showed competitive recall, F1-score, and AUC and improved recall relative to CE. Minority-focused analyses showed that BWCE-log reduced minority-to-majority errors relative to CE and focal loss, whereas CB-CE and LDAM showed stronger performance on selected minority-focused endpoints. Ablation analyses suggested that prediction-dependent information contributed to the BWCE performance profile, although most variant differences were not statistically significant after correction. These findings support BWCE as a direction-aware cost-sensitive alternative for modeling clinically undesirable error directions at the loss-design level, rather than as a uniformly superior replacement for existing imbalance-aware objectives.