Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An extension of the angular synchronization problem to the heterogeneous
  setting   Given an undirected measurement graph $G = ([n], E)$, the classical angular
synchronization problem consists of recovering unknown angles
$\theta_1,\dots,\theta_n$ from a collection of noisy pairwise measurements of
the form $(\theta_i - \theta_j) \mod 2\pi$, for each $\{i,j\} \in E$. This
problem arises in a variety of applications, including computer vision, time
synchronization of distributed networks, and ranking from preference
relationships. In this paper, we consider a generalization to the setting where
there exist $k$ unknown groups of angles $\theta_{l,1}, \dots,\theta_{l,n}$,
for $l=1,\dots,k$. For each $ \{i,j\} \in E$, we are given noisy pairwise
measurements of the form $\theta_{\ell,i} - \theta_{\ell,j}$ for an unknown
$\ell \in \{1,2,\ldots,k\}$. This can be thought of as a natural extension of
the angular synchronization problem to the heterogeneous setting of multiple
groups of angles, where the measurement graph has an unknown edge-disjoint
decomposition $G = G_1 \cup G_2 \ldots \cup G_k$, where the $G_i$'s denote the
subgraphs of edges corresponding to each group. We propose a probabilistic
generative model for this problem, along with a spectral algorithm for which we
provide a detailed theoretical analysis in terms of robustness against both
sampling sparsity and noise. The theoretical findings are complemented by a
comprehensive set of numerical experiments, showcasing the efficacy of our
algorithm under various parameter regimes. Finally, we consider an application
of bi-synchronization to the graph realization problem, and provide along the
way an iterative graph disentangling procedure that uncovers the subgraphs
$G_i$, $i=1,\ldots,k$ which is of independent interest, as it is shown to
improve the final recovery accuracy across all the experiments considered.

24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph