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Neural network modeling of data with gaps: method of principal curves, Carleman's formula, and other | | A. N.Gorban
; A. A. Rossiev
; D. C. Wunsch II
; | | Date: |
21 May 2003 | | Subject: | Disordered Systems and Neural Networks; Neural and Evolutionary Computing; Data Analysis, Statistics and Probability | cond-mat.dis-nn cs.NE physics.data-an | | Abstract: | 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. | | Source: | arXiv, cond-mat/0305508 | | Services: | Forum | Review | PDF | Favorites | |
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