Comparative study of two sparse multinomial logistic regression models in decoding visual stimuli from brain activity of fMRI

Recently, sparse algorithms, such as Sparse Multinomial Logistic Regression (SMLR), have been successfully applied in decoding visual information from functional magnetic resonance imaging (fMRI) data, where the contrast of visual stimuli was predicted by a classifier. The contrast classifier combined brain activities of voxels with sparse weights. For sparse algorithms, the goal is to learn a classifier whose weights distributed as sparse as possible by introducing some prior belief about the weights. There are two ways to introduce a sparse prior constraints for weights: the Automatic Relevance Determination (ARD-SMLR) and Laplace prior (LAP-SMLR). In this paper, we presented comparison results between the ARD-SMLR and LAP-SMLR models in computational time, classification accuracy and voxel selection. Results showed that, for fMRI data, no significant difference was found in classification accuracy between these two methods when voxels in V1 were chosen as input features (totally 1017 voxels). As for computation time, LAP-SMLR was superior to ARD-SMLR; the survived voxels for ARD-SMLR was less than LAP-SMLR. Using simulation data, we confirmed the classification performance for the two SMLR models was sensitive to the sparsity of the initial features, when the ratio of relevant features to the initial features was larger than 0.01, ARD-SMLR outperformed LAP-SMLR; otherwise, LAP-SMLR outperformed LAP-SMLR. Simulation data showed ARD-SMLR was more efficient in selecting relevant features.