A Proofs

A.2 Proof of proposition 1 Let Pœ{B,D,E}, k be a valid kernel (assumptions of theorem 1) with K Inversion of conditional with Bayes rule gives: 'W œS As a complement, we now explicit the simple forms taken by the posterior limit graph in each case. A.3 Proof of theorem 2 We consider the following hierarchical model, for Nonetheless it can be simplified as we now show. We focus on finding the optimal eigenvectors first. Only the left term in (18) depends on R. The optimization problem for eigenvectors writes: min tr! Note that the identity permutation i.e. for i œ [n], (i) =i is optimal in this case as the ( We will choose this U in what follows as the sign of the axes do not influence the characterization of the final result in Z as a PCA embedding. Note that this solution is not unique if there are repeated eigenvalues.