New graph-based multi-sample tests for high-dimensional and non-Euclidean data

Abstract: Testing the equality in distributions of multiple samples is a common task in many fields. However, this problem for high-dimensional or non-Euclidean data has not been well explored. In this paper, we propose new nonparametric tests based on a similarity graph constructed on the pooled observations from multiple samples, and make use of both within-sample edges and between-sample edges, a straightforward but yet not explored idea. The new tests exhibit substantial power improvements over existing tests for a wide range of alternatives. We also study the asymptotic distributions of the test statistics, offering easy off-the-shelf tools for large datasets. The new tests are illustrated through an analysis of the age image dataset.