Uniformity Testing Using Minimal Spanning Tree

Testing for uniformity of multivariate data is the initial step in exploratory pattern analysis. We propose a new uniformity testing method, which first computes the maximum (standardized) edge length in the MST of the given data. Large lengths indicate the existence of well-separated clusters or outliers in the data. For the data passing this edge inconsistency test, we generate two sub-samples of the data by a weighted re-sampling method, where the weights are computed based on the normalized edge lengths of MST of the entire data. The uniformity of the data is estimated by running the two-sample MST-test on these two sub-samples. Experiments with simulated and real data show the potential of the proposed test in identifying uniform or weakly clustered data. This test can also be used to rank various data sets based on their degree of uniformity.