According to the WHO, approximately 50 million people worldwide have dementia and there are nearly 10 million new cases every year. Alzheimer’s disease is the most common form of dementia and may contribute to 60–70% of cases. It has been proved that early diagnosis is key to promoting early and optimal management. However, the early stage of dementia is often overlooked and patients are typically diagnosed when the disease progresses to a more advanced stage. The objective of this contribution is to predict Alzheimer’s early stages, not only dementia itself. To carry out this objective, different types of SVM and CNN machine learning classifiers will be used, as well as two different feature selection algorithms: PCA and mRMR. The different experiments and their performance are compared when classifying patients from MRI images. The newness of the experiments conducted in this research includes the wide range of stages that we aim to predict, the processing of all the available information simultaneously and the Segmentation routine implemented in SPM12 for preprocessing. We will make use of multiple slices and consider different parts of the brain to give a more accurate response. Overall, excellent results have been obtained, reaching a maximum F1 score of 0.9979 from the SVM and PCA classifier.