Comparative performance analysis of binary variants of FOX optimization algorithm with half-quadratic ensemble ranking method for thyroid cancer detection

Abstract Thyroid cancer is a life-threatening condition that arises from the cells of the thyroid gland located in the neck’s frontal region just below the adam’s apple. While it is not as prevalent as other types of cancer, it ranks prominently among the commonly observed cancers affecting the endocrine system. Machine learning has emerged as a valuable medical diagnostics tool specifically for detecting thyroid abnormalities. Feature selection is of vital importance in the field of machine learning as it serves to decrease the data dimensionality and concentrate on the most pertinent features. This process improves model performance, reduces training time, and enhances interpretability. This study examined binary variants of FOX-optimization algorithms for feature selection. The study employed eight transfer functions (S and V shape) to convert the FOX-optimization algorithms into their binary versions. The vision transformer-based pre-trained models (DeiT and Swin Transformer) are used for feature extraction. The extracted features are transformed using locally linear embedding, and binary FOX-optimization algorithms are applied for feature selection in conjunction with the Naïve Bayes classifier. The study utilized two datasets (ultrasound and histopathological) related to thyroid cancer images. The benchmarking is performed using the half-quadratic theory-based ensemble ranking technique. Two TOPSIS-based methods (H-TOPSIS and A-TOPSIS) are employed for initial model ranking, followed by an ensemble technique for final ranking. The problem is treated as multi-objective optimization task with accuracy, F2-score, AUC-ROC and feature space size as optimization goals. The binary FOX-optimization algorithm based on the $$V_1$$ V 1 transfer function achieved superior performance compared to other variants using both datasets as well as feature extraction techniques. The proposed framework comprised a Swin transformer to extract features, a Fox optimization algorithm with a V1 transfer function for feature selection, and a Naïve Bayes classifier and obtained the best performance for both datasets. The best model achieved an accuracy of 94.75%, an AUC-ROC value of 0.9848, an F2-Score of 0.9365, an inference time of 0.0353 seconds, and selected 5 features for the ultrasound dataset. For the histopathological dataset, the diagnosis model achieved an overall accuracy of 89.71%, an AUC-ROC score of 0.9329, an F2-Score of 0.8760, an inference time of 0.05141 seconds, and selected 12 features. The proposed model achieved results comparable to existing research with small features space.