Graphic analysis of population structure on genome-wide rheumatoid arthritis data

Principal-component analysis (PCA) has been used for decades to summarize the human genetic variation across geographic regions and to infer population migration history. Reduction of spurious associations due to population structure is crucial for the success of disease association studies. Recently, PCA has also become a popular method for detecting population structure and correction of population stratification in disease association studies. Inspired by manifold learning, we propose a novel 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 structures instead of principal components (PCs). For the whole genome-wide association data for the North American Rheumatoid Arthritis Consortium (NARAC) provided by Genetic Workshop Analysis 16, Laplacian eigenfunctions revealed more meaningful structures of the underlying population than PCA. The proposed method has connection to PCA, and it naturally includes PCA as a special case. Our simple method is computationally fast and is suitable for disease studies at the genome-wide scale.