Visual High Dimensional Hypothesis Testing

In exploratory data analysis of known classes of high dimensional data, a central question is how distinct are the classes? The Direction Projection Permutation (DiProPerm) hypothesis test provides an answer to this that is directly connected to a visual analysis of the data. In this paper, we propose an improved DiProPerm test that solves 3 major challenges of the original version. First, we implement only balanced permutations to increase the test power for data with strong signals. Second, our mathematical analysis leads to an adjustment to correct the null behavior of both balanced and the conventional all permutations. Third, new confidence intervals (reflecting permutation variation) for test significance are also proposed for comparison of results across different contexts. This improvement of DiProPerm inference is illustrated in the context of comparing cancer types in examples from The Cancer Genome Atlas.