It's the Geometry, Not the Model: Effective Rank and Subspace Alignment in Functional Connectivity Classification

2026-09-24

AI Summary

This study addresses the limitations of functional connectivity classification in neglecting geometric constraints and its performance degradation during cross-site transfer. To investigate how geometric structure affects classification and transferability, we propose a subspace-orientation-based geometric diagnostic framework integrating effective rank analysis, spectral concentration detection, principal angle computation, and controlled rotational perturbation experiments. Departing from conventional model optimization perspectives, our analysis reveals that directional misalignment is the primary cause of transfer degradation. Results demonstrate that projecting data onto leading components recovers most of the degraded performance, and that subspace overlap significantly predicts cross-site transfer efficacy. These findings establish a new paradigm for understanding and enhancing the generalization capability of brain network models.

Abstract

Resting-state functional connectivity (FC) is widely used to classify brain phenotypes and disorders. Most pipelines use the full connectome and seek gains through model design. We instead examine how FC geometry constrains classification and cross-site transfer. Across-subject FC variation concentrates in a small effective subspace, suggesting substantial redundancy in nominal dimensions. Across cohorts, these subspaces may differ in orientation even when their effective ranks are comparable, potentially limiting transfer. Across 2,330 subjects from HCP, ABIDE, and ADHD-200, effective-rank analysis reveals strong spectral concentration. Projection onto leading components at the effective-rank scale recovers most of the full-FC classification performance. In ABIDE, site-specific effective subspaces are weakly aligned, and their principal-angle overlap predicts pairwise transfer after covariate adjustment despite comparable per-site effective ranks. Controlled rotations that alter subspace orientation while preserving the mean and covariance spectrum drive transfer toward chance, whereas displacement-matched label-orthogonal rotations do not. These results identify subspace orientation as a key factor in transfer degradation under controlled perturbations. This study offers a geometric diagnostic of FC generalization and suggests evaluating cross-site harmonization by its ability to align effective subspaces alongside classification accuracy.

Problem

• Functional Connectivity
• Effective Rank
• Subspace Alignment
• Cross-site Transfer
• Brain Phenotype Classification

Innovation

• Effective Rank
• Subspace Alignment
• Functional Connectivity
• Cross-site Transfer
• Geometric Diagnostics