Table 2 Different distance matrices used in the customized loss function

From: Automated classification of midpalatal suture maturation stages from CBCTs using an end-to-end deep learning framework

Matrix

Distance matrix

Application

Linear Distance Matrix

\(\begin{bmatrix} 0 & 1 & 2 & 3 & 4 \\ 1 & 0 & 1 & 2 & 3 \\ 2 & 1 & 0 & 1 & 2 \\ 3 & 2 & 1 & 0 & 1 \\ 4 & 3 & 2 & 1 & 0 \\ \end{bmatrix}\)

Enforces a linear penalty structure, assigning greater penalties as class distances increase, encouraging the model to avoid distant misclassifications.

Refined Proximity Penalty Matrix

\(\begin{bmatrix} 0 & 2 & 1 & 0.5 & 0.2 \\ 2 & 0 & 2 & 1 & 0.5 \\ 1 & 2 & 0 & 2 & 1 \\ 0.5 & 1 & 2 & 0 & 2 \\ 0.2 & 0.5 & 1 & 2 & 0 \\ \end{bmatrix}\)

Applies higher penalties for closer class misclassifications and lower penalties for more distant ones, refining the model’s ability to distinguish closely related classes.

  1. These matrices assign penalties for misclassifications based on the discrepancy between the predicted stage and the correct one, improving model learning
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