Identifying Imaging Markers for Predicting Cognitive Assessments Using Wasserstein Distances Based Matrix Regression

Alzheimer's disease (AD) is a severe type of neurodegeneration which worsens human memory, thinking and cognition along a temporal continuum. How to identify the informative phenotypic neuroimaging markers and accurately predict cognitive assessment are crucial for early detection and diagnosis Alzheimer's disease. Regression models are widely used to predict the relationship between imaging biomarkers and cognitive assessment, and identify discriminative neuroimaging markers. Most existing methods use different matrix norms as the similarity measures of the empirical loss or regularization to improve the prediction performance, but ignore the inherent geometry of the cognitive data. To tackle this issue, in this paper we propose a novel robust matrix regression model with imposing Wasserstein distances on both loss function and regularization. It successfully integrate Wasserstein distance into the regression model, which can excavate the latent geometry of cognitive data. We introduce an efficient algorithm to solve the proposed new model with convergence analysis. Empirical results on cognitive data of the ADNI cohort demonstrate the great effectiveness of the proposed method for clinical cognitive predication.