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1 Reports on Geodesy

1 2005

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Application of kernel ridge regression to network levelling via Mathematica

Völgyesi L., Paláncz B., Fekete K., Popper G.

Reports on Geodesy

2005

z. 2/73

263-276

A new method based on support vector regression (SVR) bas been developed for network levelling. Employing zero insensitive margin and first order polynomial kemel, the general form of SVR bas been reduced to a kernel ridge regressor, which is a linear function approximator. Then this function approximation problem can be transformed into an adjustment problem, simply using proper recasting of the variabIes. Only one part of the measured values (training equations) is considered in the adjustment, the other part of them (test equations) is used to compute the risk of the data generalization. Then the quality of the estimation can be measured by computing the performance index of the levelling, a value which is a trade off between adjustment quality (residual of the test equations) and the adjustment risk (the ratio of the residual of the test equations and that of the training equations). This performance index can be optimized with the regularization term of the ridge regressor. The algorithm was implemented in Mathematica 5.1 and demonstrated by numerical example.