  Graph clustering aims at discovering a natural grouping of the nodes such
that similar nodes are assigned to a common cluster. Many different algorithms
have been proposed in the literature: for simple graphs, for graphs with
attributes associated to nodes, and for graphs where edges represent different
types of relations among nodes. However, complex data in many domains can be
represented as both attributed and multi-relational networks.
  In this paper, we propose SpectralMix, a joint dimensionality reduction
technique for multi-relational graphs with categorical node attributes.
SpectralMix integrates all information available from the attributes, the
different types of relations, and the graph structure to enable a sound
interpretation of the clustering results. Moreover, it generalizes existing
techniques: it reduces to spectral embedding and clustering when only applied
to a single graph and to homogeneity analysis when applied to categorical data.
Experiments conducted on several real-world datasets enable us to detect
dependencies between graph structure and categorical attributes, moreover, they
exhibit the superiority of SpectralMix over existing methods.
