Building upon the recent advances and successes in the application of deep learning to the medical field, we propose in this work a new approach to detect and classify early-stage Alzheimer patients using online handwriting (HW) loop patterns. To cope with the lack of training data prevalent in the tasks of classification of neuro-degenerative diseases from behavioral data, we investigate several data augmentation techniques. In this respect, compared to the traditional data augmentation techniques proposed for HW-based Parkinson detection, we investigate a variant of Generative Adversarial Networks (GANs), DoppelGANger, especially tailored for times series and hence suitable for synthesizing realistic online handwriting sequences. Based on a 1D-Convolutional Neural Network (1D-CNN) to perform Alzheimer classification, we show, on a real dataset related to HW and Alzheimer, that our DoppelGANger-based augmentation model allow the CNN to significantly outperform both the current state of the art and the other data augmentation techniques.