Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Doubly-Stochastic Normalization of the Gaussian Kernel is Robust to
  Heteroskedastic Noise   A fundamental step in many data-analysis techniques is the construction of an
affinity matrix describing similarities between data points. When the data
points reside in Euclidean space, a widespread approach is to from an affinity
matrix by the Gaussian kernel with pairwise distances, and to follow with a
certain normalization (e.g. the row-stochastic normalization or its symmetric
variant). We demonstrate that the doubly-stochastic normalization of the
Gaussian kernel with zero main diagonal (i.e., no self loops) is robust to
heteroskedastic noise. That is, the doubly-stochastic normalization is
advantageous in that it automatically accounts for observations with different
noise variances. Specifically, we prove that in a suitable high-dimensional
setting where heteroskedastic noise does not concentrate too much in any
particular direction in space, the resulting (doubly-stochastic) noisy affinity
matrix converges to its clean counterpart with rate $m^{-1/2}$, where $m$ is
the ambient dimension. We demonstrate this result numerically, and show that in
contrast, the popular row-stochastic and symmetric normalizations behave
unfavorably under heteroskedastic noise. Furthermore, we provide examples of
simulated and experimental single-cell RNA sequence data with intrinsic
heteroskedasticity, where the advantage of the doubly-stochastic normalization
for exploratory analysis is evident.

29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th