The suggested technique combines optimised feature selection models with topological data analysis to improve the prediction of thyroid illness through the use of machine learning algorithms. Thorough examination of thyroid characteristics leads to the creation of distinct matrices, while preprocessing methods tackle problems like noisy variables and missing data. Feature selection approaches prioritise significant data attributes, so that dataset quality is improved and the number of dimensions is reduced. The integration of Topological Data Analysis (TDA) with the Butterfly Optimisation Algorithm simplifies the process of selecting features, resulting in a 30% decrease in the feature space while maintaining a 91% accuracy in attribute selection. The RNNClass, which is a kind of Recurrent Neural Network (RNN), achieves a classification accuracy of 89% in identifying thyroid disorders via unsupervised learning. The evaluation criteria, namely accuracy, recall, and F1-score, demonstrate substantial enhancements compared to the current techniques. The suggested method, TDA-BOA + RNNClass, achieves an accuracy of 94% overall, with a 7% decrease in false negative rates compared to traditional approaches. This demonstrates its potential to improve the prediction and classification of thyroid diseases.