  Multigraph matching is a recent variant of the graph matching problem. In
this framework, the optimization procedure considers several graphs and
enforces the consistency of the matches along the graphs. This constraint can
be formalized as a cycle consistency across the pairwise permutation matrices,
which implies the definition of a universe of
vertex~\citep{pachauri2013solving}. The label of each vertex is encoded by a
sparse vector and the dimension of this space corresponds to the rank of the
bulk permutation matrix, the matrix built from the aggregation of all the
pairwise permutation matrices. The matching problem can then be formulated as a
non-convex quadratic optimization problem (QAP) under constraints imposed on
the rank and the permutations. In this paper, we introduce a novel kernelized
multigraph matching technique that handles vectors of attributes on both the
vertices and edges of the graphs, while maintaining a low memory usage. We
solve the QAP problem using a projected power optimization approach and propose
several projectors leading to improved stability of the results. We provide
several experiments showing that our method is competitive against other
unsupervised methods.
