Detecting Alzheimer's disease (AD) early is crucial for effective management, with machine learning techniques increasingly utilised for their efficacy in predicting AD using cognitive tests. Ensemble machine learning models are particularly valuable for enhancing system robustness by combining multiple models. This article introduces a novel ensemble machine learning approach for early AD detection. Firstly, a novel feature selection technique, Neighbourhood Component Analysis and Correlation-based Filtration (NCA-F), is proposed to identify key cognitive features from a dataset. Subsequently, various machine learning classifiers are trained using NCA-F. The top classifiers are chosen for voting based on their performance. Voting employs an adaptive weight matrix process, where the output label of a model is multiplied by its F1score to determine its weight. Results demonstrate that adaptive voting achieves an accuracy of 93.92%, surpassing the 90.53% accuracy achieved by traditional artificial neural networks. Furthermore, the proposed technique enhances accuracy by 12.12% using the same features.