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METHOD AND SOFTWARE FOR FAST CONSTRUCTION OF PRINCIPAL MANIFOLDS APPROXIMATIONS

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 refinement of the vertexes positions. This allows very effective implementations of the algorithm; the computational complexity grows linearly with the number of points with relatively small constant factor. Another advantage is that the same algorithmic kernel is applied to construct principal manifolds of different dimensions and topologies. We demonstrate how flexibility of the approach allows easily numerous adaptive strategies like principal graph constructing, etc. The algorithm is implemented as a C++ package. We describe the approach and provide several examples with speed performance characteristics.