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With increasing life expectancy in developed countries, there is a corresponding increase in the frequency of diseases typically associated with old age, in particular dementia. In recent research, multivariate analysis of Positron Emission Tomography (PET) datasets has shown potential for classification between Alzheimer's disease (AD) patients and asymptomatic controls. In this work, the feasibility of multivariate analysis using Principal Component Analysis (PCA) and Fisher Discriminant Analysis (FDA) of Single Photon Emission Computed Tomography (SPECT) data is investigated. In order to obtain robust and reliable results, bootstrap resampling is applied and the robustness and classification accuracy of PCA/FDA are investigated. The robustness of the analysis is assessed by estimating the distribution of the angle between PCA/FDA discriminative vectors generated by bootstrap resampling, and the classification predictive accuracy is assessed using the 632 bootstrap estimator. The results indicate that PCA/FDA on SPECT data enables a robust differentiation between AD patients and asymptomatic controls based on three principal components, with a classification accuracy of 89%.