Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Latent structure blockmodels for Bayesian spectral graph clustering   Spectral embedding of network adjacency matrices often produces node
representations living approximately around low-dimensional submanifold
structures. In particular, hidden substructure is expected to arise when the
graph is generated from a latent position model. Furthermore, the presence of
communities within the network might generate community-specific submanifold
structures in the embedding, but this is not explicitly accounted for in most
statistical models for networks. In this article, a class of models called
latent structure block models (LSBM) is proposed to address such scenarios,
allowing for graph clustering when community-specific one dimensional manifold
structure is present. LSBMs focus on a specific class of latent space model,
the random dot product graph (RDPG), and assign a latent submanifold to the
latent positions of each community. A Bayesian model for the embeddings arising
from LSBMs is discussed, and shown to have a good performance on simulated and
real world network data. The model is able to correctly recover the underlying
communities living in a one-dimensional manifold, even when the parametric form
of the underlying curves is unknown, achieving remarkable results on a variety
of real data.

2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys