A tool to validate the assumptions on ratios of nearest neighbors’ distances: the Consecutive Ratio Paths

The estimation of the intrinsic dimension is an essential step in many data analyses involving, for example, dimensionality reduction. Likelihood-based estimators, which rely on the distributions of the ratios of distances between nearest neighbors, have been recently proposed. However, these distributional results de- pend on several assumptions. One of the most important is the local homogeneity of the point process characterizing the data-generating mechanism. By exploiting a recent theoretical result, we develop the Consecutive Ratio Paths, a graphical tool to assess the validity of the local-homogeneity assumption in a dataset. This tool is also helpful to uncover the presence of multiple latent manifolds, a potential indicator of the existence of heterogeneous intrinsic dimensions.