Magnetic resonance imaging is one of the flagship techniques for non-invasive medical diagnosis. Yet, high-resolution three-dimensional (3D) imaging poses a challenge on machine learning applications: how to determine the optimal trade-off between computational cost and imaging details retained? Here, we present two scalable approaches for image classification relying on topological data analysis and ensemble classification on parallelized 3D convolutional neural networks. We demonstrate the applicability of our models on a classification task of MR images of Alzheimer's disease patients and cognitively normal subjects. Our approaches achieve competitive results in terms of area under the precision recall curve (0.95+/-0.03).