Functional networks (FNs) hold significant promise in understanding brain function. Independent component analysis (ICA) has been applied in estimating FNs from functional magnetic resonance imaging (fMRI). However, determining an optimal model order for ICA remains challenging, leading to criticism about the reliability of FN estimation. Here, we propose a SMART (splitting-merging assisted reliable) ICA method that automatically extracts reliable FNs by clustering independent components (ICs) obtained from multi-model-order ICA using a simplified graph while providing linkages among FNs deduced from different-model orders. We extend SMART ICA to multi-subject fMRI analysis, validating its effectiveness using simulated and real fMRI data. Based on simulated data, the method accurately estimates both group-common and group-unique components and demonstrates robustness to parameters. Using two age-matched cohorts of resting fMRI data comprising 1,950 healthy subjects, the resulting reliable group-level FNs are greatly similar between the two cohorts, and interestingly the subject-specific FNs show progressive changes while age increases. Furthermore, both small-scale and large-scale brain FN templates are provided as benchmarks for future studies. Taken together, SMART ICA can automatically obtain reliable FNs in analyzing multi-subject fMRI data, while also providing linkages between different FNs.

功能网络（FN）在理解大脑功能方面具有重要前景。独立成分分析 (ICA) 已应用于根据功能磁共振成像 (fMRI) 估算 FN。然而，确定 ICA 的最佳模型阶数仍然具有挑战性，导致对 FN 估计可靠性的批评。在这里，我们提出了一种 SMART（可靠拆分合并辅助）ICA 方法，该方法通过使用简化图对从多模型阶 ICA 获得的独立分量（IC）进行聚类来自动提取可靠的 FN，同时提供从不同模型阶推导出的 FN 之间的链接。我们将 SMART ICA 扩展到多受试者 fMRI 分析，并使用模拟和真实 fMRI 数据验证其有效性。基于模拟数据，该方法准确地估计了群体共同成分和群体独特成分，并证明了参数的鲁棒性。使用由 1,950 名健康受试者组成的两个年龄匹配的静息 fMRI 数据队列，得出的可靠的组级 FN 在两个队列之间非常相似，有趣的是，随着年龄的增加，受试者特定的 FN 显示出渐进的变化。此外，还提供了小规模和大规模的大脑 FN 模板作为未来研究的基准。综上所述，SMART ICA 可以在分析多受试者 fMRI 数据时自动获得可靠的 FN，同时还提供不同 FN 之间的联系。