Title: A Witness complex for density landscapes

Abstract: We define a filtered simplicial complex associated to the superlevel sets of a sum of weighted Gaussians kernels $f(x)$, with uniform scale parameter $h>0$. Regarding $f$ as a kernel density estimator of a data set $\mathcal{D}\subset \mathbb{R}^m$, we obtain a method for filtering persistent homology by density in low or high dimensions. On the other hand, we also see that our construction can be highly visually descriptive.