Nowadays, Alzheimer’s disease is one of the most extended dementias. In first stages, the affected person starts by loosing memory and fluency in language. In order to avoid a quick development of this dementia, it is crucial an early diagnosis. This project aims to increase the rate of detection of persons suffering from Alzheimer’s disease through the computation of the Laplace-Beltrami operator spectrum of the hippocampal structure. Our assumption, supported by recent literature, is that its shape differs from a person suffering from Alzheimer’s disease to a control patient. Spectral shape retrieval techniques are exploited to address this problem. Briefly, we mesh the segmented magnetic resonance images of the hippocampus. Then, three different shape descriptors are computed for every point in the mesh. The first two descriptors are related to the heat diffusion in the mesh (the heat kernel signature and the scale-invariant heat kernel signature) and the last one is based on the probability of finding a quantum particle at a particular point of the mesh (the wave kernel signature). Each of these descriptors are then used separately in the bag of features framework to find which yields a better performance in identifying Alzheimer’s disease. Both methods are tested against the DEMCAM and the ADNI datasets. The descriptor yielding the best results is the scale-invariant heat kernel signature. It correctly classifies 95% and 80% of subjects of each database repectively. In addition, we study which region and descriptor best captures the deformation in the hippocampus. We propose a novel spectral segmentation of the hippocampal structure using recent results on the decreasing rearrangement of integrable functions. This provides a sub-structure segmentation of the hippocampus, allowing local analysis. Results demostrate that it is possible to discriminate both classes by considering just one of the regions. Finally, according to experimental results, we show that there is no need of preprocessing the hippocampus to improve the signal-to-noise ratio as the signatures described are robust to topological perturbations.