Multilayer graphs are commonly used to model relationships of different types between data points. In this paper, we propose a method for multilayer graph data clustering, which combines the different graph layers in the Riemann manifold of Semi-Positive Definite (SPD) graph laplacian matrices. The resulting combination can be seen as a low-dimensional representation of the original data points. In addition, we consider that data can also carry signal values and not only graph information. We thus propose new clustering solution for such hybrid data by training a neural network such that the transformed data points are orthonormal, and their distance on the aggregated graph is minimized. Experiments on synthetic and real data show that our method leads to a significant improvement with respect to state-of-the-art clustering algorithms for graph data.
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