Classification-Based on Crescent Elongation Data Using Multinomial Logistic Regression

Abstract The determination of the beginning of the Hijri month through the observation of the new moon is an important process that requires scientific support to account for decision-making. This study aims to develop a model for the classification of hilal visibility using Multinomial Logistic Regression (MLR) by utilizing observation data from the Meteorology, Climatology, and Geophysics Agency (BMKG) for the 2021–2025 period. Using data that includes astronomical and geometric parameters such as the Solar azimuth, the Moon's azimuth, the height of the Sun, the height of the Moon, the difference in azimuth, and the elongation. The label assigns the visibility of the new moon into three categories, namely Dark (elongation < 5°), Faint (5° ≤ elongation < 12°), and Light (elongation ≥ 12°). Obtain a total of 2210 lines of existing datasets, then divide the dataset into different training scenarios, namely 60/40, 70/30, and 80/20, with a standardization process before modeling. Optimized the model with the hyperparameter setting of the regularization constant C in the range of 0.001 to 100, using the saga solver and L2 penalty. The test results show that the model's performance improves as the C value increases. Obtained the best configuration at a 60/40 split with C = 100, resulting in an F1-Score of 99.10%, near-perfect accuracy and recall, and a ROC-AUC value close to 1. These findings show that MLR is effective in classifying elongation-based hilal visibility, as well as potentially being used as a basis for technical decision-making in determining the beginning of the Hijri month. However, this study still requires additional validation, such as stratified k-fold assays and cross-site or year testing, to ensure the model's generalization capabilities and avoid potential data leakage.