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%A A.N. Gorban %A A.Yu. Zinovyev %T Elastic principal manifolds and their practical applications %X 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. %D 2004 %K principal surface, machine learning, SOM, vizualization %L cogprints3919