{Introduction: } Dementia is a neurological disorder associated with aging that can cause a loss of cognitive functions, impacting daily life. Alzheimer's disease (AD) is the most common cause of dementia, accounting for 50--70\% of cases, while frontotemporal dementia (FTD) affects social skills and personality. Electroencephalography (EEG) provides an effective tool to study the effects of AD on the brain. {Methods: } In this study, we propose to use shallow neural networks applied to two sets of features: spectral-temporal and functional connectivity using four methods. We compare three supervised machine learning techniques to the CNN models to classify EEG signals of AD / FTD and control cases. We also evaluate different measures of functional connectivity from common EEG frequency bands considering multiple thresholds. {Results and Discussion: } Results showed that the shallow CNN-based models achieved the highest accuracy of 94.54\% with AEC in test dataset when considering all connections, outperforming conventional methods and providing potentially an additional early dementia diagnosis tool. \url{https://doi.org/10.3389%2Ffneur.2023.1270405}