Classification of Alzheimer´s Disease from structural MRI using sparse logistic regression with optional spatial regularization

In this paper, we apply Sparse Logistic Regression Classifiers to the classification of 69 Alzheimer´s Disease and 60 normal control subjects based on voxel-wise grey matter volumes derived from structural MRI. Methods such as standard logistic regression cannot be used in such problems because of the large number of voxels in comparison to the number of training subjects. Sparse Logistic Regression (SLR) addresses this issue by incorporating a sparsity penalty into the log-likelihood, which effects an automatic feature selection within the classification framework. We apply two different formulations of sparse logistic regression and compare their classification accuracy with that of Penalized Logistic Regression (PLR) and Maximum uncertainty Linear Discriminant Analysis (MLDA). In the first approach, we use the original formulation of SLR in which correlated voxels are forced to have similar weights. In the second approach we use a spatially regularized formulation, SRSLR, to force the discriminating vector to be spatially smooth when viewed as an image. Evaluation of the methods using cross-validation shows similar classification accuracies for SLR and SRSLR, with both performing better than PLR and MLDA. In addition, SRSLR produced classifiers that were spatially smoother than those produced by SLR, which may better reflect the regional effects of Alzheimer´s Disease.