Temporally-constrained group sparse learning for longitudinal data analysis.

Sparse learning has recently received increasing attentions in neuroimaging research such as brain disease diagnosis and progression. Most existing studies focus on cross-sectional analysis, i.e., learning a sparse model based on single time-point of data. However, in some brain imaging applications, multiple time-points of data are often available, thus longitudinal analysis can be performed to better uncover the underlying disease progression patterns. In this paper, we propose a novel temporally-constrained group sparse learning method aiming for longitudinal analysis with multiple time-points of data. Specifically, for each time-point, we train a sparse linear regression model by using the imaging data and the corresponding responses, and further use the group regularization to group the weights corresponding to the same brain region across different time-points together. Moreover, to reflect the smooth changes between adjacent time-points of data, we also include two smoothness regularization terms into the objective function, i.e., one fused smoothness term which requires the differences between two successive weight vectors from adjacent time-points should be small, and another output smoothness term which requires the differences between outputs of two successive models from adjacent time-points should also be small. We develop an efficient algorithm to solve the new objective function with both group-sparsity and smoothness regularizations. We validate our method through estimation of clinical cognitive scores using imaging data at multiple time-points which are available in the Alzheimer's disease neuroimaging initiative (ADNI) database.