The early detection Alzheimer's disease (AD) is an important challenge. In this paper, we propose a novel method for early detection of AD using electroencephalographic (EEG) recordings: first a blind source separation algorithm is applied to extract the most significant spatio-temporal components; these components are subsequently wavelet transformed; the resulting time-frequency representation is approximated by sparse "bump modeling"; finally, reliable and discriminant features are selected by orthogonal forward regression and the random probe method. These features are fed to a simple neural network classifier. The method was applied to EEG recorded in patients with Mild Cognitive Impairment (MCI) who later developed AD, and in age-matched controls. This method leads to a substantially improved performance (93% correctly classified, with improved sensitivity and specificity) over classification results previously published on the same set of data. The method is expected to be applicable to a wide variety of EEG classification problems.