Alzheimer's Disease (AD) is the most frequent form of degenerative dementia and its early diagnosis is essential for effective treatment. Functional imaging modalities including Single Photon Emission Computed Tomography (SPECT) are often used with such an aim. However, conventional evaluation of SPECT images relies on manual reorientation and visual evaluation of tomographic slices which is time consuming, subjective and therefore prone to error. Our aim is to show an automatic Computer-Aided Diagnosis (CAD) system for improving the early detection of the AD. For this purpose, affine invariant descriptors of 3D SPECT image can be useful. The method consists of four steps: evaluation of invariant descriptors obtained using spherical harmonic analysis, statistical testing of their significance, application of regularized binary index models, and model verification via leave-one-out cross-validation scheme. The second approach is based on Support Vector Machine (SVM) classifier and visualization with use of self-organizing maps. Our approaches were tested on SPECT data from 11 adult patients with definite Alzheimer's disease and 10 adult patients with Amyotrophic Lateral Sclerosis (ALS) who were used as controls. A significant difference between SPECT spherical cuts of AD group and ALS group was both visually and numerically evaluated.