Dimensionality estimation for two data sets with nonuniform local $di$⁠: a “tiara” (top row), where dimension varies smoothly from 2 to 1, and a “spinning top” (bottom row, middle cross-section shown), where dimension reduces from 3 to 1 as one moves from the bulky part toward the tip. Using the optimal $k$ for MLE could not produce good results for the entire data set (here, $k$$=$ 32 for both data sets). The NCD method, in contrast, was able to correctly adapt to the local geometry by taking advantage of the data graph produced by the IAN kernel.