Fused Group Lasso Regularized Multi-Task Feature Learning and Its Application to the Cognitive Performance Prediction of Alzheimer’s Disease

Alzheimer’s disease (AD) is characterized by gradual neurodegeneration and loss of brain function, especially for memory during early stages. Regression analysis has been widely applied to AD research to relate clinical and biomarker data such as predicting cognitive outcomes from MRI measures. Recently, multi-task based feature learning (MTFL) methods with sparsity-inducing \( \ell _{2,1} \)-norm have been widely studied to select a discriminative feature subset from MRI features by incorporating inherent correlations among multiple clinical cognitive measures. However, existing MTFL assumes the correlation among all tasks is uniform, and the task relatedness is modeled by encouraging a common subset of features via sparsity-inducing regularizations that neglect the inherent structure of tasks and MRI features. To address this issue, we proposed a fused group lasso regularization to model the underlying structures, involving 1) a graph structure within tasks and 2) a group structure among the image features. To this end, we present a multi-task feature learning framework with a mixed norm of fused group lasso and \( \ell _{2,1} \)-norm to model these more flexible structures. For optimization, we employed the alternating direction method of multipliers (ADMM) to efficiently solve the proposed non-smooth formulation. We evaluated the performance of the proposed method using the Alzheimer’s Disease Neuroimaging Initiative (ADNI) datasets. The experimental results demonstrate that incorporating the two prior structures with fused group lasso norm into the multi-task feature learning can improve prediction performance over several competing methods, with estimated correlations of cognitive functions and identification of cognition-relevant imaging markers that are clinically and biologically meaningful.