Computer-aided diagnosis (CAD) systems constitute a powerful tool for early diagnosis of Alzheimer's disease (AD), but limitations on interpretability and performance exist. In this work, a fully automatic CAD system based on supervised learning methods is proposed to be applied on segmented brain magnetic resonance imaging (MRI) from Alzheimer's disease neuroimaging initiative (ADNI) participants for automatic classification. The proposed CAD system possesses two relevant characteristics: optimal performance and visual support for decision making. The CAD is built in two stages: a first feature extraction based on independent component analysis (ICA) on class mean images and, secondly, a support vector machine (SVM) training and classification. The obtained features for classification offer a full graphical representation of the images, giving an understandable logic in the CAD output, that can increase confidence in the CAD support. The proposed method yields classification results up to 89% of accuracy (with 92% of sensitivity and 86% of specificity) for normal controls (NC) and AD patients, 79% of accuracy (with 82% of sensitivity and 76% of specificity) for NC and mild cognitive impairment (MCI), and 85% of accuracy (with 85% of sensitivity and 86% of specificity) for MCI and AD patients.