There is currently a lack of an efficient, objective and systemic approach towards the classification of Alzheimer's disease (AD), due to its complex etiology and pathogenesis. As AD is inherently dynamic, it is also not clear how the relationships among AD indicators vary over time. To address these issues, we propose a hybrid computational approach for AD classification and evaluate it on the heterogeneous longitudinal AIBL dataset. Specifically, using clinical dementia rating as an index of AD severity, the most important indicators (mini-mental state examination, logical memory recall, grey matter and cerebrospinal volumes from MRI and active voxels from PiB-PET brain scans, ApoE, and age) can be automatically identified from parallel data mining algorithms. In this work, Bayesian network modelling across different time points is used to identify and visualize time-varying relationships among the significant features, and importantly, in an efficient way using only coarse-grained data. Crucially, our approach suggests key data features and their appropriate combinations that are relevant for AD severity classification with high accuracy. Overall, our study provides insights into AD developments and demonstrates the potential of our approach in supporting efficient AD diagnosis.