Inputs:ℳ1, ℳ2, Ninit, Nincr, Nmax. Outputs: optimized metric w on ℳ1.
Initialization: For ℳ2, fix its embedding with N = Nmax.For ℳ1, set N = Ninit and w =1.
Iterative optimization of the metric
2.1 Compute the eigen-system of ℳ1 with the current weight w and find the optimal embedding.
2.2 Find the maps between ℳ1 and ℳ2, i.e., the matrix A and B.
2.3 Compute the gradient and update w.
2.4 If convergence is reached, go to step 3; otherwise continue the iteration.
If N = Nmax, stop the algorithm. Otherwise, set N = min(Nmax, N + Nincr), and go to step 2.
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