关键在于几何结构而非模型：功能连接分类中的有效秩与子空间对齐
It's the Geometry, Not the Model: Effective Rank and Subspace Alignment in Functional Connectivity Classification
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中文总结 AI 辅助
本研究通过有效秩和子空间方向分析，揭示功能连接分类中几何结构对跨站点迁移的关键影响，并提出以子空间对齐作为协调化评估标准。
中文摘要 AI 辅助
静息态功能连接（FC）被广泛用于对大脑表型和疾病进行分类。大多数处理流程使用全连接组，并通过模型设计寻求性能提升。我们转而研究FC几何结构如何约束分类和跨站点迁移。跨被试的FC变异集中在一个小的有效子空间内，这表明名义维度上存在大量冗余。在不同队列中，即使这些子空间的有效秩相当，其方向也可能不同，这可能限制迁移性能。基于来自HCP、ABIDE和ADHD-200的2,330名被试，有效秩分析揭示了强烈的谱集中性。在有效秩尺度上投影到前导成分可恢复全FC分类性能的大部分。在ABIDE中，站点特定的有效子空间对齐较弱，尽管各站点有效秩相当，但其主角度重叠在协变量调整后可预测成对迁移。在保持均值和协方差谱的同时改变子空间方向的受控旋转会使迁移降至随机水平，而位移匹配的标签正交旋转则不会。这些结果表明，在受控扰动下，子空间方向是迁移退化中的关键因素。本研究提供了FC泛化的几何诊断，并建议通过其对齐有效子空间的能力以及分类准确率来评估跨站点协调化方法。
英文摘要
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.
