The process for constructing the informed metric between the samples X p is repeated similarly to build new partition trees T 1 z and T 1 t for the samples X z and X t , respectively, along with their corresponding gEMD and diffusion maps. Thus, the first iteration of the questionnaire algorithm is completed. The informed metrics can then be used to iteratively generate T m p , T m z , and T m t , where m ∈ N represents the number of the iterations. The procedure converges; the convergence, existence, and uniqueness of the iterative EMD are proven in using an entropic regularization approach. Over multiple iterations, as the geometry of the data is reorganized, the weighted l 1 norm of the tensor-Haar coefficients decreases and converges. (This norm measures the local variability of the data tensor and is computed by .)