SLR: A Modified Logistic Regression Model with Sinkhorn Divergence for Alzheimer's Disease Classification.

Abstract

Logistic regression is a widely used model in machine learning, particularly as a baseline for binary classification tasks due to its simplicity, effectiveness, and interpretability. It is especially powerful when dealing with categorical features. Despite its advantages, standard logistic regression fails to capture the distributional and geometric structure of data, especially when features are derived from structured spaces like brain imaging. For instance, in Voxel-Based Morphometry (VBM), measurements from distinct brain regions follow a clear spatial organization, which standard logistic regression cannot fully leverage. In this paper, we propose Sinkhorn Logistic Regression (SLR), a variant of logistic regression that incorporates the Sinkhorn divergence as a loss function. This adaptation enables the model to leverage geometric information about the data distribution, enhancing its performance on structured datasets.