The study presented in this paper focuses on comparing Nonlinear Dimensionality Reduction (NLDR) tech- niques applied on an MRI dataset for Alzheimer's disease classification. Given the increasing prevalence of Alzheimer's disease and the necessity for early and accurate diagnosis, our research aims to enhance diagnostic methods using advanced data analysis techniques. Magnetic Resonance Imaging (MRI) is a critical tool for observing the structural changes in the brain associated with Alzheimer's. However, the high-dimensional nature of MRI data poses significant challenges for effective analysis. Linear Dimensionality Reduction (LDR) methods are often inadequate for capturing the complex, nonlinear relationships in the data. Therefore, our study explores the application of NLDR algorithms such as Isomap, Locally Linear Embedding (LLE), Diffusion Maps and t-Distributed Stochastic Neighbor Embedding (t-SNE) to address these challenges. The research involves a comparative analysis of these NLDR techniques in terms of their ability to pre- serve the structural integrity of the MRI data and their impact on the performance of classification models for Alzheimer's disease. We used the most common metrics for clustering performance and we trained a classification model to determine the impact on classification. The results indicate that the application of these methods are able to capture the intrinsic geometric relationships between data points and increase the classification metrics. The best results come from the t-SNE technique with the lowest number of dimensions needed and the biggest improvements in classification. This study aims to contribute to the advancement of Alzheimer's disease diagnosis through the application of sophisticated data reduction techniques, providing insights for future research in optimizing NLDR methods for clinical use.