The early detection of Alzheimer's disease (AD) is an important challenge. In this paper, we propose a novel method for early detection of AD using only electroencephalographic (EEG) recordings for patients with Mild Cognitive Impairment (MCI) without any clinical symptoms of the disease who later developed AD. In our method, first a blind source separation algorithm is applied to extract the most significant spatiotemporal uncorrelated components; afterward these components are wavelet transformed; subsequently the wavelets or more generally time frequency representation (TFR) is approximated with sparse bump modeling approach. Finally, reliable and discriminant features are selected and reduced with orthogonal forward regression and the random probe methods. The proposed features were finally fed to a simple neural network classifier. The presented method leads to a substantially improved performance (93% correctly classified - improved sensitivity and specificity) over classification results previously published on the same set of data. We hope that the new computational and machine learning tools provide some new insights in a wide range of clinical settings, both diagnostic and predictive.