There is a longstanding ambiguity regarding the clinical diagnosis of dementia syndromes predominantly targeting executive functions versus behaviour and personality. This is due to an incomplete understanding of the macro-scale anatomy underlying these symptomatologies, a partial overlap in clinical features and the fact that both phenotypes can emerge from the same pathology and vice versa. We collected data from a patient cohort of which 52 had dysexecutive Alzheimer's disease, 30 had behavioural variant frontotemporal dementia (bvFTD), seven met clinical criteria for bvFTD but had Alzheimer's disease pathology (behavioural Alzheimer's disease) and 28 had amnestic Alzheimer's disease. We first assessed group-wise differences in clinical and cognitive features and patterns of fluorodeoxyglucose (FDG) PET hypometabolism. We then performed a spectral decomposition of covariance between FDG-PET images to yield latent patterns of relative hypometabolism unbiased by diagnostic classification, which are referred to as 'eigenbrains'. These eigenbrains were subsequently linked to clinical and cognitive data and meta-analytic topics from a large external database of neuroimaging studies reflecting a wide range of mental functions. Finally, we performed a data-driven exploratory linear discriminant analysis to perform eigenbrain-based multiclass diagnostic predictions. Dysexecutive Alzheimer's disease and bvFTD patients were the youngest at symptom onset, followed by behavioural Alzheimer's disease, then amnestic Alzheimer's disease. Dysexecutive Alzheimer's disease patients had worse cognitive performance on nearly all cognitive domains compared with other groups, except verbal fluency which was equally impaired in dysexecutive Alzheimer's disease and bvFTD. Hypometabolism was observed in heteromodal cortices in dysexecutive Alzheimer's disease, temporo-parietal areas in amnestic Alzheimer's disease and frontotemporal areas in bvFTD and behavioural Alzheimer's disease. The unbiased spectral decomposition analysis revealed that relative hypometabolism in heteromodal cortices was associated with worse dysexecutive symptomatology and a lower likelihood of presenting with behaviour/personality problems, whereas relative hypometabolism in frontotemporal areas was associated with a higher likelihood of presenting with behaviour/personality problems but did not correlate with most cognitive measures. The linear discriminant analysis yielded an accuracy of 82.1% in predicting diagnostic category and did not misclassify any dysexecutive Alzheimer's disease patient for behavioural Alzheimer's disease and vice versa. Our results strongly suggest a double dissociation in that distinct macro-scale underpinnings underlie predominant dysexecutive versus personality/behavioural symptomatology in dementia syndromes. This has important implications for the implementation of criteria to diagnose and distinguish these diseases and supports the use of data-driven techniques to inform the classification of neurodegenerative diseases.