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@misc{cogprints3919, month = {May}, title = {Elastic principal manifolds and their practical applications }, author = {A.N. Gorban and A.Yu. Zinovyev}, year = {2004}, keywords = {principal surface, machine learning, SOM, vizualization}, url = {http://cogprints.org/3919/}, abstract = {Principal manifolds defined as lines or surfaces passing through "the middle" of the data distribution serve as useful objects for many practical applications. We propose a new algorithm for fast construction of grid approximations of principal manifolds with given topology. One advantage of the method is a new form of the functional to be minimized, which becomes quadratic at the step of the vertexes positions refinement. This makes the algorithm very effective, especially for parallel implementations. } }