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. Author manuscript; available in PMC: 2014 Jul 2.
Published in final edited form as: IEEE Trans Med Imaging. 2014 Mar 25;33(7):1447–1463. doi: 10.1109/TMI.2014.2313812

TABLE I.

Metric Optimization Algorithm

Inputs:ℳ1, ℳ2, Ninit, Nincr, Nmax. Outputs: optimized metric w on ℳ1.

  1. Initialization: For ℳ2, fix its embedding with N = Nmax.For ℳ1, set N = Ninit and w =1.

  2. 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.

  3. If N = Nmax, stop the algorithm. Otherwise, set N = min(Nmax, N + Nincr), and go to step 2.