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In this paper, distributed electroencephalographic (EEG) sources in the brain have been mapped with the objective of early diagnosis of Alzheimer's disease (AD). To this end, records from a montage of a high-density EEG from 17 early AD patients and 17 matched healthy control subjects were considered. Subjects were in eyes-closed, resting-state condition. Cortical EEG sources were modeled by the standardized low-resolution brain electromagnetic tomography (sLORETA) method. Relative logarithmic power spectral density values were obtained in the four conventional frequency bands (alpha, beta, delta, and theta) and 12 cortical regions. Results show that in the left brain hemisphere, the theta band of AD subjects shows an increase in the power, whereas the alpha band shows a decreased activity (P-value <;0.05). In the right brain hemisphere of AD subjects, a decreased activity is observed in all frequency bands. It was also noticed that the right temporal region shows a significant difference between the two groups in all frequency bands. Using a support vector machine, control and patient groups are discriminated with an accuracy of 84.4%, sensitivity 75.0%, and specificity of 93.7%.