基于低秩近似的连接体平滑算法
Connectome Smoothing via Low-rank Approximations
摘要：
在对大脑网络进行定量研究的统计连接组学中，基于样本估计一组图的均值是一个核心问题。通常，这个问题特别困难，因为样本或队列规模相对较小，有时甚至是单个受试者。虽然使用邻接矩阵的逐元素样本均值是一种常见的方法，但该方法不利用图的任何潜在结构属性。我们建议使用一个低秩的方法，结合工具的尺寸选择和对角增强平滑的估计和提高性能的小样本量的天真的方法。随机块模型的理论结果表明，该方法提供了重大的改进时，有许多顶点。同样，我们证明了低秩方法优于各种独立的边缘分布以及来自磁共振成像的人类连接体数据的标准样本均值，特别是当样本量很小时。此外，低秩方法产生“本征连接组”，它与人脑的脑叶结构和小鼠大脑的超结构相关。这些结果表明，低秩方法是研究人员研究一般图形群体，特别是统计连接组学的工具箱的重要组成部分。
英文摘要：
In statistical connectomics, the quantitative study of brain networks, estimating the mean of a population of graphs based on a sample is a core problem. Often, this problem is especially difficult because the sample or cohort size is relatively small, sometimes even a single subject. While using the element-wise sample mean of the adjacency matrices is a common approach, this method does not exploit any underlying structural properties of the graphs. We propose using a low-rank method which incorporates tools for dimension selection and diagonal augmentation to smooth the estimates and improve performance over the naive methodology for small sample sizes. Theoretical results for the stochastic blockmodel show that this method offers major improvements when there are many vertices. Similarly, we demonstrate that the low-rank methods outperform the standard sample mean for a variety of independent edge distributions as well as human connectome data derived from magnetic resonance imaging, especially when sample sizes are small. Moreover, the low-rank methods yield "eigen-connectomes", which correlate with the lobe-structure of the human brain and superstructures of the mouse brain. These results indicate that low-rank methods are an important part of the tool box for researchers studying populations of graphs in general, and statistical connectomics in particular.
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