With the continuous development of medical imaging data， longitudinal data analysis is gradually becoming an important research direction to understand and trace the process of the Alzheimer’s disease （AD）. At present， many longitudinal data analysis methods have been proposed， among which multi-task learning is widely used， which can integrate imaging data of multiple time points to improve the generalization ability of the model. Most existing methods can identify shared features at different time points， but these features will contain a certain amount of noise. At the same time， potential associations of disease progression at different time points remain under explored. In this paper， we propose a parameter decomposition and relation-induced multi-task learning （PDRIMTL） method to identify features from longitudinal data. The method can not only identify shared features after noise removal and improve the robustness of shared features， but also can model the intrinsic associations between different time points. The results show that the model can effectively improve the accuracy of AD identification on structural magnetic resonance imaging （sMRI） data at different time points.