# Multidimensional Comparisons Between Constrained ICA/IVA Algorithms for Multi-Subject fMRI Data Analysis

## TL;DR

This paper compares three advanced algorithms for analyzing brain scans from many people, showing how each performs differently in finding brain networks and biomarkers.

## Contribution

The paper provides a comprehensive multidimensional comparison of three constrained ICA/IVA algorithms for multi-subject fMRI data analysis.

## Key findings

- tf-cIVA excels in reproducibility and temporal functional network connectivity.
- ar-cIVA is most sensitive to group differences in spatial FNC.
- ar-cEBM offers superior scalability and stable spatial maps despite not using joint processing.

## Abstract

Large-scale functional magnetic resonance imaging (fMRI) datasets provide exciting opportunities for understanding and improving brain health. Data-driven techniques such as independent component analysis (ICA) and independent vector analysis (IVA) have been attractive solutions for multi-subject fMRI analysis, as the extraction of functional connectivity networks is the key step in many studies. Constrained versions of ICA and IVA help significantly improve performance and interpretability, but their comparative advantages and the practical impact of their different formulations remain unclear. This work addresses this gap by conducting a comprehensive comparison of three state-of-the-art constrained algorithms: threshold-free constrained IVA (tf-cIVA), adaptive-reverse constrained IVA (ar-cIVA), and adaptive-reverse constrained ICA (ar-cEBM). These methods differ significantly in how they leverage the cross-subject information (joint processing of IVA versus the subject-wise approach of constrained ICA) and in their definitions of the closeness with the references (Lagrangian-based adaptive thresholding versus a threshold-free regularization term). We perform a multidimensional comparison among these methods using multiple metrics such as reproducibility, scalability, alignment with references, connectivity, and consistency on a multi-site fMRI dataset of 429 subjects. Our results reveal replicability across the three methods regarding their spatial correlation with the references and identification of biomarkers, as well as distinct trade-offs in other aspects: tf-cIVA excels in reproducibility and produces highly structured temporal functional network connectivity (FNC), making it a strong candidate for dynamic or connectivity-based analyses. Meanwhile, ar-cIVA demonstrates the greatest sensitivity to group differences in spatial FNC, suggesting its utility for identifying spatial biomarkers. Finally, ar-cEBM, via its subject-wise approach, offers superior computational scalability for large datasets. Surprisingly, despite not jointly modeling cross-subject information, ar-cEBM produces more stable spatial maps across subjects, suggesting its flexible density matching may be more critical for group consistency than the joint-processing framework itself. Therefore, besides providing a complete picture, the work provides practical guidance, indicating that the algorithm choice might depend on the specific research question.