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Diffusion on complex networks is a convenient framework to describe a great
variety of transport systems. Failure phenomena in a link of the network may
simulate the presence of a break or a congestion effect in the system. A real
time detection of failures can mitigate their effect and allow to optimize the
control procedures on the transport network. The main objective of this work is
to provide a dimensionality reduction technique for a transport network where a
diffusive dynamics takes place, to detect presence of a failure by a limited
number of observations. Our approach is based on the susceptibility response of
the network state under random perturbations of the link weights. The
correlations among the nodes fluctuations is exploited in order to provide the
clustering procedure. The network dimensionality is therefore reduced
introducing `representative nodes' for each cluster and generating a reduced
network model, whose dynamical state is detected by the observations. We
realize a failure identification procedure for the whole network, studying the
dynamics of the coarse-grained network. The localization efficiency of the
proposed clustering algorithm, averaging over all possible single-edge
failures, is compared with traditional structure-based clustering using
different graph configurations. We show that the proposed clustering algorithm
is more sensitive than traditional clustering techniques to detect link failure
with higher stationary fluxes.