Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Graphon based Clustering and Testing of Networks: Algorithms and Theory   Network-valued data are encountered in a wide range of applications and pose
challenges in learning due to their complex structure and absence of vertex
correspondence. Typical examples of such problems include classification or
grouping of protein structures and social networks. Various methods, ranging
from graph kernels to graph neural networks, have been proposed that achieve
some success in graph classification problems. However, most methods have
limited theoretical justification, and their applicability beyond
classification remains unexplored. In this work, we propose methods for
clustering multiple graphs, without vertex correspondence, that are inspired by
the recent literature on estimating graphons -- symmetric functions
corresponding to infinite vertex limit of graphs. We propose a novel graph
distance based on sorting-and-smoothing graphon estimators. Using the proposed
graph distance, we present two clustering algorithms and show that they achieve
state-of-the-art results. We prove the statistical consistency of both
algorithms under Lipschitz assumptions on the graph degrees. We further study
the applicability of the proposed distance for graph two-sample testing
problems.

9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an