  Network data appears in very diverse applications, like biological, social,
or sensor networks. Clustering of network nodes into categories or communities
has thus become a very common task in machine learning and data mining. Network
data comes with some information about the network edges. In some cases, this
network information can even be given with multiple views or multiple layers,
each one representing a different type of relationship between the network
nodes. Increasingly often, network nodes also carry a feature vector. We
propose in this paper to extend the node clustering problem, that commonly
considers only the network information, to a problem where both the network
information and the node features are considered together for learning a
clustering-friendly representation of the feature space. Specifically, we
design a generic two-step algorithm for multilayer network data clustering. The
first step aggregates the different layers of network information into a graph
representation given by the geometric mean of the network Laplacian matrices.
The second step uses a neural net to learn a feature embedding that is
consistent with the structure given by the network layers. We propose a novel
algorithm for efficiently training the neural net via stochastic gradient
descent, which encourages the neural net outputs to span the leading
eigenvectors of the aggregated Laplacian matrix, in order to capture the
pairwise interactions on the network, and provide a clustering-friendly
representation of the feature space. We demonstrate with an extensive set of
experiments on synthetic and real datasets that our method leads to a
significant improvement w.r.t. state-of-the-art multilayer graph clustering
algorithms, as it judiciously combines nodes features and network information
in the node embedding algorithms.
