Application of support vector machine in geodesy for the classification of vertical displacements
Abstract
The article presents basic rules for constructing and training neural networks, called the Support Vector Machine technique. SVM networks can mainly be used for solving tasks of classification of linearly and nonlinearly separable data and regression as well as identifying signals and recognising increases.
In this paper SVM networks have been used for classifying linearly separable data in order to formulate a model of displacements of points representing a monitored object. The problem of learning networks requires the use of quadratic programming in search of an optimum point of a Lagrange function with respect to optimised parameters. Estimated parameters determine the location of the hyperplane which maximises the separation margin of both classes.
Keywords
linear SVM network, classification, displacements,References
[1] C.M. Bishop. Pattern Recognition and Machine Learning. Springer, 2006.[2] C. Burges. A tutorial on support vector machines for pattern recognition. Knowledge Discovery and Data Mining. Ed. Sama Fayyad, Kluwer, 1–43, 2000.
[3] J. Gil. Examples of applications of neural networks in geodesy [in Polish]. Publishing House of the University of Zielona Góra, Zielona Góra, 2006.
[4] S.M. Gunn. Support Vector Machines for Classification or Regression. Technical Report, 1998.
[5] S. Haykin. Neural networks, a comprehensive foundation. Macmillan College Publishing Company, New York, 1994.
[6] M. Mrówczyńska. A linear SVM network for determination of vertical displacement [in Polish: Sieć liniowa SVM do wyznaczenia przemieszczeń pionowych]. Przegląd Geodezyjny [Eng.: Geodesic Review], 3/2014, Warszawa, 2014.
[7] S. Osowski. Neural networks for information processing [in Polish]. Publishing House of Warsaw University of Technology, Warszawa, 2006.
[8] B. Schölkopf, A. Smola. Learning with Kernels: Support Vector Machines, Regularization, Optimization and Beyond. Massachusetts Institute of Technology Press, Cambridge, 2001.
[9] I. Steinwart, A. Christmann. Support Vector Machines. Springer, 2008.
[10] V. Vapnik. Statistical learning theory. Wiley, New York, 1998.
[11] L. Zanni, T. Serafini, G. Zanghirati. Parallel Software for Training Large Scale Support Vector Machines on Multiprocessor Systems. Journal of Machine Learning Research, 7: 1467–1492, 2006.