Department of Radiology, The University of Chicago, Chicago, Illinois, United States of America.
PLoS One. 2009 Dec 1;4(12):e7928. doi: 10.1371/journal.pone.0007928.
Principal components analysis has been used for decades to summarize genetic variation across geographic regions and to infer population migration history. More recently, with the advent of genome-wide association studies of complex traits, it has become a commonly-used tool for detection and correction of confounding due to population structure. However, principal components are generally sensitive to outliers. Recently there has also been concern about its interpretation. Motivated from geometric learning, we describe a method based on spectral graph theory. Regarding each study subject as a node with suitably defined weights for its edges to close neighbors, one can form a weighted graph. We suggest using the spectrum of the associated graph Laplacian operator, namely, Laplacian eigenfunctions, to infer population structure. In simulations and real data on a ring species of birds, Laplacian eigenfunctions reveal more meaningful and less noisy structure of the underlying population, compared with principal components. The proposed approach is simple and computationally fast. It is expected to become a promising and basic method for population genetics and disease association studies.
主成分分析已被广泛应用于数十年，用于概括地理区域的遗传变异，并推断人口迁移历史。最近，随着复杂性状的全基因组关联研究的出现，它已成为一种常用的工具，用于检测和校正由于人口结构引起的混杂。然而，主成分通常对异常值很敏感。最近也有人对其解释表示担忧。受几何学习的启发，我们描述了一种基于谱图理论的方法。将每个研究对象视为一个节点，其边缘与相邻节点的权重适当定义，就可以形成一个加权图。我们建议使用关联图拉普拉斯算子的谱，即拉普拉斯特征函数，来推断人口结构。在鸟类环种的模拟和真实数据中，与主成分相比，拉普拉斯特征函数揭示了更有意义且噪声更小的底层人口结构。所提出的方法简单且计算速度快。预计它将成为群体遗传学和疾病关联研究的一种有前途的基本方法。
