**Abstract:** Deep neural networks have led to state-of-the-art results in many medical imaging tasks including Alzheimer's disease (AD) detection based on structural magnetic resonance imaging (MRI) data. However, the network decisions are often perceived as being highly non-transparent making it difficult to apply these algorithms in clinical routine. In this study, we propose using layer-wise relevance propagation (LRP) to visualize convolutional neural network decisions for AD based on MRI data. Similarly to other visualization methods, LRP produces a heatmap in the input space indicating the importance of each voxel contributing to the final classification outcome. In contrast to susceptibility maps produced by guided backpropagation ("Which change in voxels would change the outcome most?"), the LRP method is able to directly highlight positive contributions to the network classification in the input space. Thus, the highlighted areas can be interpreted as the 'positive evidence' used by the network for deciding whether an individual has AD. We find that this LRP-evidence indeed fulfills those expectations that one would have towards AD evidence: (1) it is very specific for individuals ("Why does this person have AD?") with high inter-patient variability, (2) there is very little evidence for AD in healthy controls and (3) areas that exhibit a lot of evidence correlate well with what is known from literature. To quantify the latter, we compute size-corrected metrics of the summed evidence per brain area, e.g. the 'evidence density' or 'evidence gain'. Although these metrics produce very individual 'fingerprints' of relevance patterns for AD patients, a lot of importance is put on areas in the temporal lobe including hippocampus and amygdala. We conclude that LRP provides a powerful tool for assisting clinicians in finding evidence for AD (and potentially other diseases) in structural MRI data.
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