  Structure inference is an important task for network data processing and
analysis in data science. In recent years, quite a few approaches have been
developed to learn the graph structure underlying a set of observations
captured in a data space. Although real-world data is often acquired in
settings where relationships are influenced by a priori known rules, such
domain knowledge is still not well exploited in structure inference problems.
In this paper, we identify the structure of signals defined in a data space
whose inner relationships are encoded by multi-layer graphs. We aim at properly
exploiting the information originating from each layer to infer the global
structure underlying the signals. We thus present a novel method for combining
the multiple graphs into a global graph using mask matrices, which are
estimated through an optimization problem that accommodates the multi-layer
graph information and a signal representation model. The proposed mask
combination method also estimates the contribution of each graph layer in the
structure of signals. The experiments conducted both on synthetic and
real-world data suggest that integrating the multi-layer graph representation
of the data in the structure inference framework enhances the learning
procedure considerably by adapting to the quality and the quantity of the input
data.
