Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterization and Inference of Graph Diffusion Processes from
  Observations of Stationary Signals   Many tools from the field of graph signal processing exploit knowledge of the
underlying graph's structure (e.g., as encoded in the Laplacian matrix) to
process signals on the graph. Therefore, in the case when no graph is
available, graph signal processing tools cannot be used anymore. Researchers
have proposed approaches to infer a graph topology from observations of signals
on its nodes. Since the problem is ill-posed, these approaches make
assumptions, such as smoothness of the signals on the graph, or sparsity
priors. In this paper, we propose a characterization of the space of valid
graphs, in the sense that they can explain stationary signals. To simplify the
exposition in this paper, we focus here on the case where signals were i.i.d.
at some point back in time and were observed after diffusion on a graph. We
show that the set of graphs verifying this assumption has a strong connection
with the eigenvectors of the covariance matrix, and forms a convex set. Along
with a theoretical study in which these eigenvectors are assumed to be known,
we consider the practical case when the observations are noisy, and
experimentally observe how fast the set of valid graphs converges to the set
obtained when the exact eigenvectors are known, as the number of observations
grows. To illustrate how this characterization can be used for graph recovery,
we present two methods for selecting a particular point in this set under
chosen criteria, namely graph simplicity and sparsity. Additionally, we
introduce a measure to evaluate how much a graph is adapted to signals under a
stationarity assumption. Finally, we evaluate how state-of-the-art methods
relate to this framework through experiments on a dataset of temperatures.

30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph