Improved L2 Regularized Semi‐Supervised Extreme Learning Machine for Enhanced Rare Earth Component Content Prediction

ABSTRACT The traditional data‐driven methods for predicting the component content of rare earth elements (REEs) suffer from several drawbacks, notably a considerable delay in data labeling, elevated costs, and a massive quantity of unused unlabeled data. To enhance the prediction of REE component content, this paper suggests an improved L2 regularization semi‐supervised extreme learning machine based on DBSCAN and RBM, coined RBM‐DL2SELM. First, to mitigate the potential issues of an unresolvable Moore–Penrose generalized inverse or model overfitting, which are common in traditional graph‐based SELMs, the L2 regularization term is integrated into the SELM framework, forming the L2SELM model. This enhancement boosts the model's generalization ability. Second, the L2SELM model's structure is further refined by incorporating the density‐based spatial clustering of applications with noise (DBSCAN) algorithm. This step addresses concerns related to data imbalance in production processes, missing data entries, and potential data errors. Moreover, to overcome the instability issues stemming from the random initialization of weights and biases in the L2SELM, the restricted Boltzmann machine (RBM) is introduced for adaptive optimization to elevate both the prediction accuracy and reliability of the model. Finally, simulation verification using field data from Pr/Nd extraction demonstrates that the proposed method offers substantial advantages in terms of accuracy, stability, and data utilization. These attributes render it more suitable for practical applications in real‐world scenarios, where vast amounts of unlabeled data are typically available at rare earth extraction sites.