Application of kernel ridge regression to network levelling via Mathematica

• Autorzy: Völgyesi L. , Paláncz B. , Fekete K. , Popper G.
• Konferencja: Geodetic and Geodynamic Programmes of the CEI (9; Symposium; 25-30.04.2005; Vienna, Austria)
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

adjustment; levelling; support vector regression; kernel ridge regression; software Mathematica 5.1

PL

dostosowanie; niwelacja; regresja wektorowa; regresja grzbietowa; oprogramowanie Mathematica 5.1

• Wydawca: Wydział Geodezji i Kartografii Politechniki Warszawskiej
• Czasopismo: Reports on Geodesy
• Rocznik: 2005
• Tom: z. 2/73
• Strony: 263--276
• Opis fizyczny: Bibliogr. 7 poz., rys., wykr.

Twórcy

autor

Völgyesi L.

• Department of Geodesy and Surveying, Research Group for HAS-BUTE Physical Geodesy and Geodynamics, Budapest University of Technology and Economics, H-1521 Budapest, Müegyetem rkp 3

autor

Paláncz B.

• Department of Photogrammetry and Geoinformatics, Budapest University of Technology and Economics, H-1521 Budapest, Müegyetem rkp 3

autor

Fekete K.

• Department of Photogrammetry and Geoinformatics, Budapest University of Technology and Economics, H-1521 Budapest, Müegyetem rkp 3

autor

Popper G.

• Department of Structural Mechanics, Research Group for HAS-BUTE Computational Structural Mechanics, Budapest University of Technology and Economics, H-1521 Budapest, Müegyetem rkp 3

Bibliografia

• Carosio A. (1996): Fehlertheorie... ETH Zürich, Dep. Geodätische Wissenschaften.
• Cristianini N., Shawe-Taylor J. (2003): An Introduction to Support Vector Machines and other kernel-based learning methods, Cambridge University Press.
• Jianjun Z. (1996): Robustness and robust estimate, Journal of Geodesy, pp. 586-590.
• Mitchell T. (1997): Machine Learning, McGraw-Hill.
• Schölkopf B., Smola A. J., Müller K. (1999): Kernel principal... In Schölkopf B., et all. Ed. Adv. in Kernel Methods-Support Vector Learning, pp. 327-352, MIT Press.
• Wicki F. (1991): Zuverlässigkeitstheorie, Beurteilungskriterien... ETH Zurich, Institute für Geodäsie und Photogrammetrie, Bericht Nr. 176.
• Wicki F. (1999): Robuste Schätzverfahren... ETH Zürich, Institute für Geodäsie und Photogrammetrie, Dissertation ETH Nr. 12894.