Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric Inference on Kernel Density Estimates   We show that geometric inference of a point cloud can be calculated by
examining its kernel density estimate with a Gaussian kernel. This allows one
to consider kernel density estimates, which are robust to spatial noise,
subsampling, and approximate computation in comparison to raw point sets. This
is achieved by examining the sublevel sets of the kernel distance, which
isomorphically map to superlevel sets of the kernel density estimate. We prove
new properties about the kernel distance, demonstrating stability results and
allowing it to inherit reconstruction results from recent advances in
distance-based topological reconstruction. Moreover, we provide an algorithm to
estimate its topology using weighted Vietoris-Rips complexes.

28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg