Alzheimer’s disease (AD) is a progressively prevalent neurodegenerative disorder. Researchers harness neuroimaging techniques, notably magnetic resonance imaging (MRI), to develop machine learning (ML) frameworks for AD classification due to MRI’s ability to capture brain alterations linked to the disease. Nevertheless, the high dimensionality of features derived from MRI scans presents classification challenges. To address this, a range of ML techniques, including feature selection methods like filter, wrapper, and embedded approaches, are employed. Filter selection, while computationally efficient, may overlook crucial feature interactions. In contrast, wrapper selection, although computationally demanding, has the potential to capture these interactions. Embedded feature selection methods offer a solution by seamlessly integrating feature selection into the model training process, striking a balance between efficiency and accuracy in the selection process. In this investigation, we explore embedded feature selection for Alzheimer’s classification using the RidgeClassifier (RC), which effectively reduced features to 9%. Our comparative analysis encompassed multiple classifiers, including LR, SVM, RC, SSGD, GNB, LDA, KNN, DT, MNB, RF, GB, and Xgbt. Notably, RC demonstrated exceptional performance, achieving 97.77% accuracy, 97.10% precision, 98.24% specificity, 97.10% recall, 97.10% f1 score, and 97.67% AUC. Subsequent hyperparameter tuning using the Tree-structured Parzen Estimator (TPE) further elevated RC’s performance to 98.88% accuracy, 98.55% precision, 99.12% specificity, 98.55% recall, 98.55% f1 score, and 98.83% AUC. These outcomes underscore RC’s proficiency in extracting an optimal set of relevant brain regions, resulting in enhanced classification accuracy. Furthermore, our proposed framework outperformed established state-of-the-art studies in the field.