The examination of Alzheimer’s disease (AD) using adaptive machine learning algorithms has unveiled promising findings. However, achieving substantial credibility in medical contexts necessitates a combination of notable accuracy, minimal processing time, and universality across diverse populations. Therefore, we have formulated a hybrid methodology in this study to classify AD by employing a brain MRI image dataset. We incorporated an averaging filter during preprocessing in the initial stage to reduce extraneous details. Subsequently, a combined strategy was utilized, involving principal component analysis (PCA) in conjunction with stepwise linear discriminant analysis (SWLDA), followed by an artificial neural network (ANN). SWLDA employs a combination of forward and backward recursion methods to choose a restricted set of features. The forward recursion identifies the most interconnected features based on partial Z-test values. Conversely, the backward recursion method eliminates the least correlated features from the same feature space. After the extraction and selection of features, an optimized artificial neural network (ANN) was utilized to differentiate the various classes of AD. To demonstrate the significance of this hybrid approach, we utilized publicly available brain MRI datasets using a 10-fold cross-validation strategy. The proposed method excelled over existing state-of-the-art systems, attaining weighted average recognition rates of 99.35% and 96.66%, respectively, across all the datasets.