We propose a novel graph clustering method guided by additional information on the underlying structure of the clusters (or communities). The problem is formulated as the matching of a graph to a template with smaller dimension, hence matching $n$ vertices of the observed graph (to be clustered) to the $k$ vertices of a template graph, using its edges as support information, and relaxed on the set of orthonormal matrices in order to find a $k$ dimensional embedding. With relevant priors that encode the density of the clusters and their relationships, our method outperforms classical methods, especially for challenging cases.

Spatial relations between objects in an image have proved useful for structural object recognition. Structural constraints can act as regularization in neural network training, improving generalization capability with small datasets. Several relations can be modeled as a morphological dilation of a reference object with a structuring element representing the semantics of the relation, from which the degree of satisfaction of the relation between another object and the reference object can be derived. However, dilation is not differentiable, requiring an approximation to be used in the context of gradient-descent training of a network. We propose to approximate dilations using convolutions based on a kernel equal to the structuring element. We show that the proposed approximation, even if slightly less accurate than previous approximations, is definitely faster to compute and therefore more suitable for computationally intensive neural network applications.