An Unbiased Penalty for Sparse Classification with Application to Neuroimaging Data

We present a novel formulation for discriminative anatomy detection in high dimensional neuroimaging data. While most studies solve this problem using mass univariate approaches, recent works show better accuracy and variable selection using a sparse classification model. Such methods typically use an l1 penalty for imposing sparseness and a graph net (GN) or a total variation (TV) penalty for ensuring spatial continuity and interpretability of the results. However it is known that the l1 and TV penalties have inherent bias that leads to less stable region detection and less accurate prediction. To overcome these limitations, we propose a novel variable selection method in the context of classification, based on the Smoothly Clipped Absolute Deviation (SCAD) penalty. We experimentally show superiority of three models based on the SCAD and SCADTV penalties when compared to the classical l1 and TV penalties in both simulated and real MRI data from a multiple sclerosis study.