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For the task of relevance analysis, the conventional Tukey's test may beapplied to the set of all pairwise comparisons. However, there were few studiesthat discuss both nonparametric k-sample comparisons and relevance analysis inhigh dimensions. Our aim is to capture the degree of relevance between combinedsamples and provide additional insights and advantages in high-dimensionalk-sample comparisons. Our solution is to extend a graph-based two-samplecomparison and investigate its availability for large and unequal sample sizes.We propose two distribution-free test statistics based on between-sample edgecounts and measure the degree of relevance by standardized counts. Theasymptotic permutation null distributions of the proposed statistics arederived, and the power gain is proved when the sample sizes are smaller thanthe square root of the dimension. We also discuss different edge costs in thegraph to compare the parameters of the distributions. Simulation comparisonsand real data analysis of tumors and images further convince the value of ourproposed method. Software implementing the relevance analysis is available inthe R package Relevance.

Two edge-count tests and relevance analysis in k high-dimensional samples