Fair Multi-modal Canonical Correlation Analysis: A Neuroimaging Study of Alzheimer's Disease

This study addresses fairness concerns in Multi-modal Canonical Correlation Analysis (MCCA), a technique for analyzing relationships across multiple datasets. We introduce Fair MCCA (F-MCCA), which mitigates bias by optimizing for both correlation performance and demographic fairness. Our method quantifies disparities using Correlation Disparity Error (CDE) and employs a multi-objective optimization framework to derive projection matrices that achieve consistent correlation levels across sensitive groups. We validate F-MCCA on neuroimaging data from the Alzheimer's Disease Neuroimaging Initiative using sex as the sensitive attribute. Experiments demonstrate that F-MCCA substantially improves fairness metrics with minimal correlation performance sacrifice. In downstream classification tasks, F-MCCA reduces demographic parity difference and equalized odds difference while maintaining comparable accuracy to standard approaches. Results confirm that our method effectively balances analytical performance with fairness considerations, supporting more unbiased healthcare applications of multi-modal data analysis.