Least squares support vector machine model for coordinate transformation
Abstract
In coordinate transformation, the main purpose is to provide a mathematical relationship between coordinates related to different geodetic reference frames. This gives the geospatial professionals the opportunity to link different datums together. Review of previous studies indicates that empirical and soft computing models have been proposed in recent times for coordinate transformation. The main aim of this study is to present the applicability and performance of Least Squares Support Vector Machine (LS-SVM) which is an extension of the Support Vector Machine (SVM) for coordinate transformation. For comparison purpose, the SVM and the widely used Backpropagation Neural Network (BPNN), Radial Basis Function Neural Network (RBFNN), 2D conformal and affine methods were also employed. To assess how well the transformation results fit the observed data, the root mean square of the residual horizontal distances and standard deviation were used. From the results obtained, the LS-SVM and RBFNN had comparable results and were better than the other methods. The overall statistical findings produced by LS-SVM met the accuracy requirement for cadastral surveying applications in Ghana. To this end, the proposed LS-SVM is known to possess promising predictive capabilities and could efficiently be used as a supplementary technique for coordinate transformation.
Keyword : Coordinate transformation, Support vector machine, Least squares support vector machine, 2D Conformal model, 2D affine model
How to Cite
Ziggah, Y. Y., Hu, Y., Issaka, Y., & Laari, P. B. (2019). Least squares support vector machine model for coordinate transformation. Geodesy and Cartography, 45(1), 16-27. https://doi.org/10.3846/gac.2019.6053
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Deo, R. C., & Şahin, M. (2016). An extreme learning machine model for the simulation of monthly mean streamflow water level in eastern Queensland. Environmental monitoring and assessment, 188(2), 1-24. https://doi.org/10.1007/s10661-016-5094-9
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Durmaz, M., & Karslioglu, M. O. (2011). Non-parametric regional VTEC modeling with Multivariate Adaptive Regression B-Splines. Advances in Space Research, 48(9), 1523-1530. https://doi.org/10.1016/j.asr.2011.06.031
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Fosu, C., Poku-Gyamfi, Y., & Hein, W. G. (2006). Global Navigation Satellite System (GNSS) – A utility for sustainable development in Africa. 5th FIG Regional Conference on Promoting Land Administration and Good Governance, Workshop – AFREF I, Accra, Ghana (pp. 1-12).
Gencoglu, M. T., & Uyar, M. (2009). Prediction of flashover voltage of insulators using least squares support vector machines. Expert Systems with Applications, 36, 10789-10798. https://doi.org/10.1016/j.eswa.2009.02.021
Ghilani, C. (2010). Adjustment computations: Spatial Data Analysis (5th ed.). New York, USA: John Wiley and Sons Inc.
Gullu M., Yilmaz M., Yilmaz, I., & Turgut, B. (2011). Datum transformation by artificial neural networks for geographic information systems applications. International Symposium on Environmental Protection and Planning: Geographic Information Systems (GIS) and Remote Sensing (RS) Applications (ISEPP). Izmir-Turkey (pp. 13-19).
Gullu, M. (2010). Coordinate transformation by radial basis function neural network. Scientific Research and Essays, 5, 3141-3146.
Güraksin, G. E., Hakli, H., & Harun, U. (2014). Support vector machines classification based on particle swarm optimization for bone age determination. Applied Soft Computing, 24, 597-602. https://doi.org/10.1016/j.asoc.2014.08.007
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Hornik, K., Stinchcombe, M., & White, H. (1989). Multilayer feed forward networks are universal approximators. Neural Networks, 2, 359-366. https://doi.org/10.1016/0893-6080(89)90020-8
Huang, F. M., Wu, P., & Ziggah, Y. Y. (2016). GPS monitoring landslide deformation signal processing using time-series model. International Journal of Signal Processing, Image Processing and Pattern Recognition, 9(3), 321-332. https://doi.org/10.14257/ijsip.2016.9.3.28
Kavzoglu, T., & Saka, M. H. (2005). Modelling local GPS/levelling geoid undulations using artificial neural networks. Journal of Geodesy, 78(9), 520-527. https://doi.org/10.1007/s00190-004-0420-3
Kecman, V. (2001). Learning and soft computing. A Bradford Book. Massachusetts, USA: The MIT Press.
Konakoğlu, B., Cakir, L., & Gökalp, E. (2016). 2D coordinates transformation using artificial neural networks. Geo Advances 2016: ISPRS Workshop on Multi-dimensional & Multi-scale Spatial Data Modeling, At Mimar Sinan Fine Arts University/Istanbul, Volume XLII-2/W1: 3rd International GeoAdvances Workshop, 2016.
Konakoğlu, B., & Gökalp, E. (2016). A Study on 2D similarity transformation using multilayer perceptron neural networks and a performance comparison with conventional and robust outlier detection methods. Acta Montanistica Slovaca, 21(4), 324-332.
Kotzev, V. (2013). Consultancy service for the selection of a new projection system for Ghana. Draft Final Reports, World Bank Second Land Administration Project (LAP-2), Ghana.
Kumi-Boateng, B., & Ziggah, Y. Y. (2017). Horizontal coordinate transformation using artificial neural network technology – A case study of Ghana geodetic reference network. Journal of Geomatics, 11(1), 1-11.
Li, X. Z., & Kong, J. M. (2014). Application of GA-SVM method with parameter optimization for landslide development prediction. Natural Hazards and Earth System Sciences, 14(3), 525-533. https://doi.org/10.5194/nhess-14-525-2014
Lin, L. S., & Wang, Y. J. (2006). A study on cadastral coordinate transformation using artificial neural network. Proceedings of the 27th Asian Conference on Remote Sensing (pp. 1-6). Ulaanbaatar, Mongolia.
Mihalache, R. M. (2012). Coordinate transformation for integrating map information in the new geocentric European system using artificial neural networks. GeoCAD, 1-8.
Mohammadi, K., Shamshirband, S., Motamedi, S., Petković, D., Hashim, R., & Gocic, M. (2015). Extreme learning machine based prediction of daily dew point temperature. Computers and Electronics in Agriculture, 117, 214-225. https://doi.org/10.1016/j.compag.2015.08.008
Monien, K., & Decker, R. (2005). Strengths and weaknesses of support vector machines within marketing data analysis. In Innovations in Classification, Data Science, and Information Systems (pp. 355-362). Berlin, Heidelberg: Springer. https://doi.org/10.1007/3-540-26981-9_41
Mugnier, J. C. (2000). OGP-Coordinate conversions and Transformations including formulae. COLUMN, Grids and Datums, The Republic of Ghana. Photogrammetric Engineering and Remote Sensing, 695-697.
Okwuashi, O., & Ndehedehe, C. (2015). Digital terrain model height estimate support vector machine regression. South African Journal of Science, 111(9/10), 1-5. https://doi.org/10.17159/sajs.2015/20140153
Okwuashi, O., & Ndehedehe, C. (2017). Tide modelling using support vector machine regression. Journal of Spatial Science, 62(1), 29-46.
Pal, M. (2009). Extreme‐learning‐machine‐based land cover classification. International Journal of Remote Sensing, 30(14), 3835-3841. https://doi.org/10.1080/01431160902788636
Park, J., & Sandberg, I. W. (1991). Universal approximation using radial basis function networks. Neural Computation, 3(2), 246-257. https://doi.org/10.1162/neco.1991.3.2.246
Poku-Gyamfi, Y. (2009). Establishment of GPS Reference Network in Ghana (PhD Dissertation). Universitat der Bundeswehr Munchen, Germany.
Smola, A., & Schölkopf, B. (2004). A tutorial on support vector regression. Statistics and Computing, 14, 199-222. https://doi.org/10.1023/B:STCO.0000035301.49549.88
Sorkhabi, O. M. (2015). Geoid determination based on log sigmoid function of artificial neural networks (A case study: Iran). Journal of Artificial Intelligence in Electrical Engineering, 3(12), 18-24.
Suykens, J. A. K, Vandewalle, J. (1999). Least square support vector machine classifiers. Neural Processing Letters, 9, 293-300. https://doi.org/10.1023/A:1018628609742
Suykens, J. A. K., Van Gestel, T., De Brabanter, J., De Moor, B., & Vandewalle, J. (2002). Least squares support vector machines. World Scientific, Singapore. https://doi.org/10.1142/5089
Tierra, A., Dalazoana, R., & De Freitas, S. (2008). Using an artificial neural network to improve the transformation of coordinates between classical geodetic reference frames. Computers & Geosciences, 34, 181-189. https://doi.org/10.1016/j.cageo.2007.03.011
Tierra, A., & Romero, R. (2014). Planes coordinates transformation between PSAD56 to SIRGAS using a Multilayer Artificial Neural Network. Geodesy and Cartography, 63, 199-209. https://doi.org/10.2478/geocart-2014-0014
Tierra, A. R., De Freitas, S. R. C., & Guevara, P. M. (2009). Using an artificial neural network to transformation of coordinates from PSAD56 to SIRGAS95. In H. Drewes (Ed.), Geodetic reference frames. International Association of Geodesy Symposia, 134, 173-178. Germany: Springer-Verlag Berlin Heidelberg. https://doi.org/10.1007/978-3-642-00860-3_27
Tiwari, M., Adamowski, J., & Adamowski, K. (2016). Water demand forecasting using extreme learning machines. Journal of Water and Land Development, 28(1), 37-52. https://doi.org/10.1515/jwld-2016-0004
Turgut, B. (2010). A Back-propagation artificial neural network approach for three-dimensional coordinate transformation. Scientific Research and Essays, 5, 3330-3335.
Turgut, B. (2016). Application of back propagation artificial neural networks for gravity field modelling. Acta Montanistica Slovaca, 21(3), 200-207.
Vapnik, V. N. (1998). Statistical learning theory. New York, USA: John Wiley & Sons.
Varga, M., Grgić, M., & Bašić, T. (2015). Empirical comparison of the geodetic coordinate transformation models: a case study of Croatia. Survey Review, 1-13.
Xiang-Yang, W., Jing-Wei, C., & Hong-Ying, Y. (2011). A New integrated SVM classifiers for relevance feedback content-based image retrieval using EM parameter estimation. Applied Soft Computing, 11(2), 2787-2804. https://doi.org/10.1016/j.asoc.2010.11.009
Yakubu, I., & Kumi-Boateng, B. (2015). Ramification of datum and ellipsoidal parameters on postprocessed differential global positioning system (DGPS) data – A case study. Ghana Mining Journal, 15, 1-9.
Yang, Y. X. (2009). Chinese geodetic coordinate system 2000. Chinese Scientific Bulletin, 54, 2714-2721. https://doi.org/10.1007/s11434-009-0342-9
Yilmaz, I., & Gullu, M. (2012). Georeferencing of historical maps using back propagation artificial neural network. Experimental Techniques, 36, 15-19. https://doi.org/10.1111/j.1747-1567.2010.00694.x
Zaletnyik, P. (2004). Coordinate transformation with neural networks and with Polynomials in Hungary. International Symposium on Modern Technologies, Education and Professional Practice in Geodesy and Related Fields (pp. 471-479). Sofia, Bulgaria.
Ziggah, Y. Y., Youjian, H., Laari, P. B., & Hui, Z. (2017). Novel approach to improve geocentric translation model performance using artificial neural network technology. Boletim de Ciências Geodesica, 23(1), 213-233. https://doi.org/10.1590/s1982-21702017000100014
Ziggah, Y. Y., Youjian, H., Tierra, A., Konaté, A. A., & Hui, Z. (2016). Performance evaluation of artificial neural networks for planimetric coordinate transformation – a case study, Ghana. Arabian Journal of Geosciences, 9(17), 1-16. https://doi.org/10.1007/s12517-016-2729-7
Ayer, J., & Fosu, C. (2008). Map coordinates referencing and the use of GPS datasets in Ghana. Journal of Science and Technology, 28, 116-127.
Ayer, J. (2008). Transformation models and procedures for framework integration of Ghana geodetic network. The Ghana Surveyor, 1, 52-58.
Bishop, C. M. (1995). Neural networks for pattern recognition. UK: Oxford Press.
Chang, N. B., Han, M., Yao, W., Chen, L. C., & Xu, S. (2010). Change detection of land use and land cover in an urban region with SPOT-5 images and partial Lanczos extreme learning machine. Journal of Applied Remote Sensing, 4(1), 11-15.
Deo, R. C., & Şahin, M. (2016). An extreme learning machine model for the simulation of monthly mean streamflow water level in eastern Queensland. Environmental monitoring and assessment, 188(2), 1-24. https://doi.org/10.1007/s10661-016-5094-9
Deo, R. C., Tiwari, M. K., Adamowski, J. F., & Quilty, J. M. (2017). Forecasting effective drought index using a wavelet extreme learning machine (W-ELM) model. Stochastic Environmental Research and Risk Assessment, 31(5), 1211-1240. https://doi.org/10.1007/s00477-016-1265-z
Drucker, H., Burges, C. J. C., Kaufman, I., Smola, A., & Vapnik, V. (1997). Support vector regression machines. In M. Mozer, M. Jordan, & T. Petsche (Eds.), Advances in Neural Information Processing Systems, 9, 155-161. Cambridge, MA: MIT Press.
Durmaz, M., & Karslioglu, M. O. (2011). Non-parametric regional VTEC modeling with Multivariate Adaptive Regression B-Splines. Advances in Space Research, 48(9), 1523-1530. https://doi.org/10.1016/j.asr.2011.06.031
Farag, A., & Mohamed, R. M. (2004). Regression using support vector machines: Basic foundation. Technical Report, University of Louisville.
Fosu, C., Poku-Gyamfi, Y., & Hein, W. G. (2006). Global Navigation Satellite System (GNSS) – A utility for sustainable development in Africa. 5th FIG Regional Conference on Promoting Land Administration and Good Governance, Workshop – AFREF I, Accra, Ghana (pp. 1-12).
Gencoglu, M. T., & Uyar, M. (2009). Prediction of flashover voltage of insulators using least squares support vector machines. Expert Systems with Applications, 36, 10789-10798. https://doi.org/10.1016/j.eswa.2009.02.021
Ghilani, C. (2010). Adjustment computations: Spatial Data Analysis (5th ed.). New York, USA: John Wiley and Sons Inc.
Gullu M., Yilmaz M., Yilmaz, I., & Turgut, B. (2011). Datum transformation by artificial neural networks for geographic information systems applications. International Symposium on Environmental Protection and Planning: Geographic Information Systems (GIS) and Remote Sensing (RS) Applications (ISEPP). Izmir-Turkey (pp. 13-19).
Gullu, M. (2010). Coordinate transformation by radial basis function neural network. Scientific Research and Essays, 5, 3141-3146.
Güraksin, G. E., Hakli, H., & Harun, U. (2014). Support vector machines classification based on particle swarm optimization for bone age determination. Applied Soft Computing, 24, 597-602. https://doi.org/10.1016/j.asoc.2014.08.007
Haykin, S. (1990). Neural networks: a comprehensive foundation. New Jersey, USA: Prentice-Hall.
Hornik, K., Stinchcombe, M., & White, H. (1989). Multilayer feed forward networks are universal approximators. Neural Networks, 2, 359-366. https://doi.org/10.1016/0893-6080(89)90020-8
Huang, F. M., Wu, P., & Ziggah, Y. Y. (2016). GPS monitoring landslide deformation signal processing using time-series model. International Journal of Signal Processing, Image Processing and Pattern Recognition, 9(3), 321-332. https://doi.org/10.14257/ijsip.2016.9.3.28
Kavzoglu, T., & Saka, M. H. (2005). Modelling local GPS/levelling geoid undulations using artificial neural networks. Journal of Geodesy, 78(9), 520-527. https://doi.org/10.1007/s00190-004-0420-3
Kecman, V. (2001). Learning and soft computing. A Bradford Book. Massachusetts, USA: The MIT Press.
Konakoğlu, B., Cakir, L., & Gökalp, E. (2016). 2D coordinates transformation using artificial neural networks. Geo Advances 2016: ISPRS Workshop on Multi-dimensional & Multi-scale Spatial Data Modeling, At Mimar Sinan Fine Arts University/Istanbul, Volume XLII-2/W1: 3rd International GeoAdvances Workshop, 2016.
Konakoğlu, B., & Gökalp, E. (2016). A Study on 2D similarity transformation using multilayer perceptron neural networks and a performance comparison with conventional and robust outlier detection methods. Acta Montanistica Slovaca, 21(4), 324-332.
Kotzev, V. (2013). Consultancy service for the selection of a new projection system for Ghana. Draft Final Reports, World Bank Second Land Administration Project (LAP-2), Ghana.
Kumi-Boateng, B., & Ziggah, Y. Y. (2017). Horizontal coordinate transformation using artificial neural network technology – A case study of Ghana geodetic reference network. Journal of Geomatics, 11(1), 1-11.
Li, X. Z., & Kong, J. M. (2014). Application of GA-SVM method with parameter optimization for landslide development prediction. Natural Hazards and Earth System Sciences, 14(3), 525-533. https://doi.org/10.5194/nhess-14-525-2014
Lin, L. S., & Wang, Y. J. (2006). A study on cadastral coordinate transformation using artificial neural network. Proceedings of the 27th Asian Conference on Remote Sensing (pp. 1-6). Ulaanbaatar, Mongolia.
Mihalache, R. M. (2012). Coordinate transformation for integrating map information in the new geocentric European system using artificial neural networks. GeoCAD, 1-8.
Mohammadi, K., Shamshirband, S., Motamedi, S., Petković, D., Hashim, R., & Gocic, M. (2015). Extreme learning machine based prediction of daily dew point temperature. Computers and Electronics in Agriculture, 117, 214-225. https://doi.org/10.1016/j.compag.2015.08.008
Monien, K., & Decker, R. (2005). Strengths and weaknesses of support vector machines within marketing data analysis. In Innovations in Classification, Data Science, and Information Systems (pp. 355-362). Berlin, Heidelberg: Springer. https://doi.org/10.1007/3-540-26981-9_41
Mugnier, J. C. (2000). OGP-Coordinate conversions and Transformations including formulae. COLUMN, Grids and Datums, The Republic of Ghana. Photogrammetric Engineering and Remote Sensing, 695-697.
Okwuashi, O., & Ndehedehe, C. (2015). Digital terrain model height estimate support vector machine regression. South African Journal of Science, 111(9/10), 1-5. https://doi.org/10.17159/sajs.2015/20140153
Okwuashi, O., & Ndehedehe, C. (2017). Tide modelling using support vector machine regression. Journal of Spatial Science, 62(1), 29-46.
Pal, M. (2009). Extreme‐learning‐machine‐based land cover classification. International Journal of Remote Sensing, 30(14), 3835-3841. https://doi.org/10.1080/01431160902788636
Park, J., & Sandberg, I. W. (1991). Universal approximation using radial basis function networks. Neural Computation, 3(2), 246-257. https://doi.org/10.1162/neco.1991.3.2.246
Poku-Gyamfi, Y. (2009). Establishment of GPS Reference Network in Ghana (PhD Dissertation). Universitat der Bundeswehr Munchen, Germany.
Smola, A., & Schölkopf, B. (2004). A tutorial on support vector regression. Statistics and Computing, 14, 199-222. https://doi.org/10.1023/B:STCO.0000035301.49549.88
Sorkhabi, O. M. (2015). Geoid determination based on log sigmoid function of artificial neural networks (A case study: Iran). Journal of Artificial Intelligence in Electrical Engineering, 3(12), 18-24.
Suykens, J. A. K, Vandewalle, J. (1999). Least square support vector machine classifiers. Neural Processing Letters, 9, 293-300. https://doi.org/10.1023/A:1018628609742
Suykens, J. A. K., Van Gestel, T., De Brabanter, J., De Moor, B., & Vandewalle, J. (2002). Least squares support vector machines. World Scientific, Singapore. https://doi.org/10.1142/5089
Tierra, A., Dalazoana, R., & De Freitas, S. (2008). Using an artificial neural network to improve the transformation of coordinates between classical geodetic reference frames. Computers & Geosciences, 34, 181-189. https://doi.org/10.1016/j.cageo.2007.03.011
Tierra, A., & Romero, R. (2014). Planes coordinates transformation between PSAD56 to SIRGAS using a Multilayer Artificial Neural Network. Geodesy and Cartography, 63, 199-209. https://doi.org/10.2478/geocart-2014-0014
Tierra, A. R., De Freitas, S. R. C., & Guevara, P. M. (2009). Using an artificial neural network to transformation of coordinates from PSAD56 to SIRGAS95. In H. Drewes (Ed.), Geodetic reference frames. International Association of Geodesy Symposia, 134, 173-178. Germany: Springer-Verlag Berlin Heidelberg. https://doi.org/10.1007/978-3-642-00860-3_27
Tiwari, M., Adamowski, J., & Adamowski, K. (2016). Water demand forecasting using extreme learning machines. Journal of Water and Land Development, 28(1), 37-52. https://doi.org/10.1515/jwld-2016-0004
Turgut, B. (2010). A Back-propagation artificial neural network approach for three-dimensional coordinate transformation. Scientific Research and Essays, 5, 3330-3335.
Turgut, B. (2016). Application of back propagation artificial neural networks for gravity field modelling. Acta Montanistica Slovaca, 21(3), 200-207.
Vapnik, V. N. (1998). Statistical learning theory. New York, USA: John Wiley & Sons.
Varga, M., Grgić, M., & Bašić, T. (2015). Empirical comparison of the geodetic coordinate transformation models: a case study of Croatia. Survey Review, 1-13.
Xiang-Yang, W., Jing-Wei, C., & Hong-Ying, Y. (2011). A New integrated SVM classifiers for relevance feedback content-based image retrieval using EM parameter estimation. Applied Soft Computing, 11(2), 2787-2804. https://doi.org/10.1016/j.asoc.2010.11.009
Yakubu, I., & Kumi-Boateng, B. (2015). Ramification of datum and ellipsoidal parameters on postprocessed differential global positioning system (DGPS) data – A case study. Ghana Mining Journal, 15, 1-9.
Yang, Y. X. (2009). Chinese geodetic coordinate system 2000. Chinese Scientific Bulletin, 54, 2714-2721. https://doi.org/10.1007/s11434-009-0342-9
Yilmaz, I., & Gullu, M. (2012). Georeferencing of historical maps using back propagation artificial neural network. Experimental Techniques, 36, 15-19. https://doi.org/10.1111/j.1747-1567.2010.00694.x
Zaletnyik, P. (2004). Coordinate transformation with neural networks and with Polynomials in Hungary. International Symposium on Modern Technologies, Education and Professional Practice in Geodesy and Related Fields (pp. 471-479). Sofia, Bulgaria.
Ziggah, Y. Y., Youjian, H., Laari, P. B., & Hui, Z. (2017). Novel approach to improve geocentric translation model performance using artificial neural network technology. Boletim de Ciências Geodesica, 23(1), 213-233. https://doi.org/10.1590/s1982-21702017000100014
Ziggah, Y. Y., Youjian, H., Tierra, A., Konaté, A. A., & Hui, Z. (2016). Performance evaluation of artificial neural networks for planimetric coordinate transformation – a case study, Ghana. Arabian Journal of Geosciences, 9(17), 1-16. https://doi.org/10.1007/s12517-016-2729-7