  Signal processing over single-layer graphs has become a mainstream tool owing
to its power in revealing obscure underlying structures within data signals.
However, many real-life datasets and systems, {including those in Internet of
Things (IoT)}, are characterized by more complex interactions among distinct
entities, which may represent multi-level interactions that are harder to be
captured with a single-layer graph, and can be better characterized by
multilayers graph connections. Such multilayer or multi-level data structure
can be more naturally modeled by high-dimensional multilayer graphs (MLG)}. To
generalize traditional graph signal processing (GSP) over multilayer graphs for
analyzing multi-level signal features and their interactions, this work
proposes a tensor-based framework of multilayer graph signal processing
(M-GSP). Specifically, we introduce core concepts of M-GSP and study properties
of MLG spectrum space, followed by fundamentals of MLG-based filter design. To
illustrate novel aspects of M-GSP, we further explore its link with traditional
signal processing and GSP. We provide example applications to demonstrate the
efficacy and benefits of applying multilayer graphs and M-GSP in practical
scenarios.
