Abstract: With rapid progress in high-throughput genotyping and neuroimaging, researches of complex brain disorders, such as Alzheimers Disease (AD), have gained significant attention in recent years. Many prediction models have been studied to relate neuroimaging measures to cognitive status over the progressions when these disease develops. Missing data is one of the biggest challenge in accurate cognitive score prediction of subjects in longitudinal neuroimaging studies. To tackle this problem, in this paper we propose a novel formulation to learn an enriched representation for imaging biomarkers that can simultaneously capture both the information conveyed by baseline neuroimaging records and that by progressive variations of varied counts of available follow-up records over time. While the numbers of the brain scans of the participants vary, the learned biomarker representation for every participant is a fixed-length vector, which enable us to use traditional learning models to study AD developments. Our new objective is formulated to maximize the ratio of the summations of a number of L1-norm distances for improved robustness, which, though, is difficult to efficiently solve in general. Thus we derive a new efficient iterative solution algorithm and rigorously prove its convergence. We have performed extensive experiments on the Alzheimers Disease Neuroimaging Initiative (ADNI) dataset. A performance gain has been achieved to predict four different cognitive scores, when we compare the original baseline representations against the learned representations with enrichments. These promising empirical results have demonstrated improved performances of our new method that validate its effectiveness.