Solving Logistic Regression with Group Cardinality Constraints for Time Series Analysis

We propose an algorithm to distinguish 3D+t images of healthy from diseased subjects by solving logistic regression based on cardinality constrained, group sparsity. This method reduces the risk of overfitting by providing an elegant solution to identifying anatomical regions most impacted by disease. It also ensures that consistent identification across the time series by grouping each image feature across time and counting the number of non-zero groupings. While popular in medical imaging, group cardinality constrained problems are generally solved by relaxing counting with summing over the groupings. We instead solve the original problem by generalizing a penalty decomposition algorithm, which alternates between minimizing a logistic regression function with a regularizer based on the Frobenius norm and enforcing sparsity. Applied to 86 cine MRIs of healthy cases and subjects with Tetralogy of Fallot (TOF), our method correctly identifies regions impacted by TOF and obtains a statistically significant higher classification accuracy than logistic regression without and relaxed grouped sparsity constraint.