Neural network modeling of data with gaps: method of principal curves, Carleman's formula, and other
<|reference_start|>Neural network modeling of data with gaps: method of principal curves, Carleman's formula, and other: A method of modeling data with gaps by a sequence of curves has been developed. The new method is a generalization of iterative construction of singular expansion of matrices with gaps. Under discussion are three versions of the method featuring clear physical interpretation: linear - modeling the data by a sequence of linear manifolds of small dimension; quasilinear - constructing "principal curves: (or "principal surfaces"), univalently projected on the linear principal components; essentially non-linear - based on constructing "principal curves": (principal strings and beams) employing the variation principle; the iteration implementation of this method is close to Kohonen self-organizing maps. The derived dependencies are extrapolated by Carleman's formulas. The method is interpreted as a construction of neural network conveyor designed to solve the following problems: to fill gaps in data; to repair data - to correct initial data values in such a way as to make the constructed models work best; to construct a calculator to fill gaps in the data line fed to the input.<|reference_end|>
@article{gorban2003neural,
    title={Neural network modeling of data with gaps: method of principal curves,
  Carleman's formula, and other},
    author={A. N.Gorban, A. A. Rossiev, D. C. Wunsch II},
    journal={arXiv preprint arXiv:cond-mat/0305508},
    year={2003},
    archivePrefix={arXiv},
    eprint={cond-mat/0305508},
    primaryClass={cond-mat.dis-nn cs.NE physics.data-an}
}