Starting from a recall of the theoretical framework, this paper presents the conditions and the strategy of implementation of CCA, a recent algorithm for non-linear mapping. Initially developed in a basic form, for non-linear and high-dimensional data sets, the algorithm is here adapted to the general, and more realistic, case of noisy data. This algorithm, which finds the manifold (in particular, the intrinsic dimentsion) of the data, has proved to be very efficient in the representation of highly folded data structures. We describe here how it can be tuned to find the average manifold and how robust the convergence is. A companion paper (this issue) presents various applications using this property.
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