基于聚类分析的区域间相关性估计
Clustering-Based Inter-Regional Correlation Estimation
摘要：
在噪声存在的情况下，提出了一种新的分组测量相关性的非参数估计。这项工作的主要动机是从功能磁共振成像数据，其中大脑区域对应于空间单位组的功能脑网络的建设，和区域对之间的相关性定义的网络。挑战在于噪声和区域内相关性导致使用经典方法的区域间相关性估计不一致的事实。虽然一些现有的方法处理这些问题中的任何一个，但没有非参数方法同时处理这两个问题。为了解决这个问题，我们提出了两个程序之间的权衡：相关的区域平均值，这是不鲁棒的区域内相关性;和平均成对区域间的相关性，这是不鲁棒的噪声。为此，我们将数据投影到一个空间上，在这个空间中，欧氏距离被用作样本相关性的代理。然后，我们建议利用层次聚类聚集在每个区域内高度相关的变量之前，区域间的相关性估计。我们提供了一致性的结果，经验表明，我们的方法在质量方面超过了其他几种流行的方法。我们还提供了真实世界数据集的插图，进一步证明了其有效性。
英文摘要：
A novel non-parametric estimator of the correlation between grouped measurements of a quantity is proposed in the presence of noise. This work is primarily motivated by functional brain network construction from fMRI data, where brain regions correspond to groups of spatial units, and correlation between region pairs defines the network. The challenge resides in the fact that both noise and intra-regional correlation lead to inconsistent inter-regional correlation estimation using classical approaches. While some existing methods handle either one of these issues, no non-parametric approaches tackle both simultaneously. To address this problem, we propose a trade-off between two procedures: correlating regional averages, which is not robust to intra-regional correlation; and averaging pairwise inter-regional correlations, which is not robust to noise. To that end, we project the data onto a space where Euclidean distance is used as a proxy for sample correlation. We then propose to leverage hierarchical clustering to gather together highly correlated variables within each region prior to inter-regional correlation estimation. We provide consistency results, and empirically show our approach surpasses several other popular methods in terms of quality. We also provide illustrations on real-world datasets that further demonstrate its effectiveness.
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