Machine learning techniques have become more attractive and widely used for medical image processing purposes. In particular, the diagnosis of neurodegenerative diseases has recently shown a potential field of application for these methods. The performance comparison of a unique algorithm in various study contexts can be biased, which usually leads to incorrect results. In this context, this study consists in comparing the performance of different machine learning techniques, identifying their main trends and their application for the diagnosis of Alzheimer's disease (AD). We presented a computer-aided diagnosis system for the early diagnosis of AD by analyzing brain data from the OASIS dataset. The principal component analysis (PCA) and the uniform manifold approximation and projection (UMAP) technique have been evaluated on the magnetic resonance imaging and positron emission tomography images as feature selection techniques. After that, the features are fed into nine machine learning models namely Support vector machine (SVM), Artificial neural networks, Decision trees, Random Forests, Discriminant analysis, Regression analysis, Naive Bayes, k-Nearest neighbors, and Ensemble learning. The performance of the proposed classifiers is investigated by the confusion matrix. In addition, area under the curve, Matthews correlation coefficient, accuracy, and F1-scoremetrics are calculated regarding this matrix. Our results indicate that the SVM-PCA/UMAP schemes provide a significant advantage over the other classifiers. Moreover, they are more efficient than the baseline model based on the voxels-as-features reference feature extraction approach.