A Spectral Graph Approach to Discovering Genetic Ancestry

TL;DR

This paper introduces a spectral graph method for analyzing genetic data that improves the delineation of human ancestry, offering more stability and flexibility than traditional PCA-based approaches.

Contribution

It develops a novel spectral embedding technique based on the normalized Laplacian, enhancing genetic clustering and ancestry inference over PCA.

Findings

More meaningful ancestry delineation than PCA

Stable to outliers and adaptable to various similarity measures

Effective in large, heterogeneous genetic samples

Abstract

Mapping human genetic variation is fundamentally interesting in fields such as anthropology and forensic inference. At the same time patterns of genetic diversity confound efforts to determine the genetic basis of complex disease. Due to technological advances it is now possible to measure hundreds of thousands of genetic variants per individual across the genome. Principal component analysis (PCA) is routinely used to summarize the genetic similarity between subjects. The eigenvectors are interpreted as dimensions of ancestry. We build on this idea using a spectral graph approach. In the process we draw on connections between multidimensional scaling and spectral kernel methods. Our approach, based on a spectral embedding derived from the normalized Laplacian of a graph, can produce more meaningful delineation of ancestry than by using PCA. The method is stable to outliers and can more easily incorporate different similarity measures of genetic data than PCA. We illustrate a new algorithm for genetic clustering and association analysis on a large, genetically heterogeneous sample.