Feasibility of using Group Method of Data Handling (GMDH) approach for horizontal coordinate transformation
Abstract
Machine learning algorithms have emerged as a new paradigm shift in geoscience computations and applications. The present study aims to assess the suitability of Group Method of Data Handling (GMDH) in coordinate transformation. The data used for the coordinate transformation constitute the Ghana national triangulation network which is based on the two-horizontal geodetic datums (Accra 1929 and Leigon 1977) utilised for geospatial applications in Ghana. The GMDH result was compared with other standard methods such as Backpropagation Neural Network (BPNN), Radial Basis Function Neural Network (RBFNN), 2D conformal, and 2D affine. It was observed that the proposed GMDH approach is very efficient in transforming coordinates from the Leigon 1977 datum to the official mapping datum of Ghana, i.e. Accra 1929 datum. It was also found that GMDH could produce comparable and satisfactory results just like the widely used BPNN and RBFNN. However, the classical transformation methods (2D affine and 2D conformal) performed poorly when compared with the machine learning models (GMDH, BPNN and RBFNN). The computational strength of the machine learning models’ is attributed to its self-adaptive capability to detect patterns in data set without considering the existence of functional relationships between the input and output variables. To this end, the proposed GMDH model could be used as a supplementary computational tool to the existing transformation procedures used in the Ghana geodetic reference network.
Keyword : coordinate transformation, machine learning, geodetic reference system, geodetic datum
How to Cite
Kumi-Boateng, B., & Ziggah, Y. Y. (2020). Feasibility of using Group Method of Data Handling (GMDH) approach for horizontal coordinate transformation. Geodesy and Cartography, 46(2), 55-66. https://doi.org/10.3846/gac.2020.10486
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
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Ivakhnenko, A. G. (1971). Polynomial theory of complex systems. IEEE Transactions on Systems, Man and Cybernetics, 4, 364–378. https://doi.org/10.1109/TSMC.1971.4308320
Jekabsons, G. (2010). GMDH-type polynomial neural networks for MATLAB. http://www.cs.rtu.lv/jekabsons/
Kavzoglu, T., & Saka, M. H. (2005). Modelling local GPS/Levelling geoid undulations using artificial neural networks. Journal of Geodesy, 78, 520–527. https://doi.org/10.1007/s00190-004-0420-3
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Al-Ruzouq, R., & Dimitrova, P. (2006, October 8–13). Photogrammetric techniques for cadastral map renewal. In Shaping the Change XXIII FIG Congress (pp. 1–15). Munich, Germany.
Angiuli, E., Del Frate, F., & Salvatori, L. (2006). Neural networks for oil spill detection using ERS and ENVISAT Imagery. In Proceedings of SEASAR, European Space Agency, (pp. 1–6). Italy.
Annan, R. F., Ziggah, Y. Y., Ayer, J., & Odutola, C. A. (2016). A hybridized centroid technique for 3D Molodensky-Badekas coordinate transformation in the Ghana geodetic reference network using total least squares approach. South African Journal of Geomatics, 5(3), 269–284. https://doi.org/10.4314/sajg.v5i3.1
Assaleh, K., Shanableh, T., & Kheil, Y. A. (2013). Group method of data handling for modeling magnetorheological dampers. Intelligent Control and Automation, 4(1), 70–79. https://doi.org/10.4236/ica.2013.41010
Ayer, J. (2008). Transformation models and procedures for framework integration of the Ghana national geodetic network. Ghana Surveyor, 1(2), 52–58.
Ayer, J., & Fosu, C. (2008). Map coordinates referencing and the use of GPS datasets in Ghana. Journal of Science and Technology, 28(1), 116–127. https://doi.org/10.4314/just.v28i1.33084
Ayer, J., & Tiennah, T. (2008). Datum transformations by iterative solution of the abridging inverse Molodensky formulae. Ghana Surveyor, 1(2), 59–66.
Ayoub, M. A., Negash, B. M., & Saaid, I. M. (2015). Modeling pressure drop in vertical wells using group method of data handling (GMDH) approach. In Proceedings of International Conference on Integrated Petroleum Engineering and Geosciences (pp. 69–78). Singapore. https://doi.org/10.1007/978-981-287-368-2_6
Barsi, P. (2001). Performing coordinate transformation by artificial neural network. Allgemeine Vermessungs Nachrichten, 4, 134–137.
Bishop, C. (2006). Pattern recognition and machine learning (1st ed.). Springer.
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. https://doi.org/10.1117/1.3518096
Chen, S., Cowan, C. F. N., & Grant, P. M. (1991). Orthogonal least squares learning algorithm for radial basis functions networks. IEEE Transaction on Neural Networks, 2(2), 302–309. https://doi.org/10.1109/72.80341
Deakin, R. E. (2007). Coordinate transformations for cadastral surveying (pp. 1–34). School of Mathematical and Geospatial Sciences, RMIT University.
Dönmez, Ş. Ö., & Tunc, A. (2016, July 12–19). Transformation methods for using combination of remotely sensed data and cadastral maps. In The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XLI-B4, 2016 XXIII ISPRS Congress (pp. 587–589). Prague, Czech Republic. https://doi.org/10.5194/isprs-archives-XLI-B4-587-2016
Dzidefo, A. (2011). Determination of transformation parameters between the World Geodetic System 1984 and the Ghana Geodetic Network (Master’s Thesis). Department of Civil & Geomatic Engineering, KNUST, Kumasi, Ghana.
El-Assal, A., El-Rabbany, A., & Mesbah, S. (2011). GPS outage recovery using wavelet and neural network models in support of multibeam hydrography. In Proceedings of OCEANS IEEE (pp. 1–7). IEEE. https://doi.org/10.1109/Oceans-Spain.2011.6003541
Elshambaky, H. T., Kaloop, M. R., & Hu, J. W. (2018). A novel three-direction datum transformation of geodetic coordinates for Egypt using artificial neural network approach. Arabian Journal of Geosciences, 11(6), 110. https://doi.org/10.1007/s12517-018-3441-6
Farlow, S. J. (1984). Self-organizing methods in modeling: GMDH type algorithms. CRC Press, Marcel-Dekker.
Fosu, C., Poku-Gyamfi, Y., & Hein, W. G. (2006). Global Navigation Satellite System (GNSS) – A Utility for Sustainable Development in Africa. In Proceedings of 5th FIG Regular Conference on Promoting Land Administration and Good Governance, Workshop – AFREF I (pp. 1–12). Accra, Ghana.
Fotiou, A., & Kaltsikis, C. J. (2016). Computationally efficient methods and solutions with least squares similarity transformation models. Retrieved January 2, 2018, from https://www.researchgate.net/profile/Aristeidis_Fotiou/publication/309732142_Computationally_efficient_methods_and_solutions_with_least_squares_similarity_transformation_models/links/58204df808ae12715afbb0c6.pdf
Ghilani, C. D. (2010). Adjustment computations: Spatial data analysis (5 ed.). John Wiley and Sons Inc.
Gullu, M. (2010). Coordinate transformation by radial basis function neural network. Scientific Research and Essays, 5, 3141–3146.
Gullu, M., Yilmaz, M., Yilmaz, I., & Turgut, B. (2011). Datum transformation by artificial neural networks for geographic information systems applications. In International Symposium on Environmental Protection and Planning: Geographic Information Systems (GIS) and Remote Sensing (RS) Applications (ISEPP) (pp. 13–19). Izmir, Turkey. https://doi.org/10.5053/isepp.2011.1-6
Haykin, S. (1999). Neural networks: A comprehensive foundation. 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, G. B., & Babri, H. A. (1998). Upper bounds on the number of hidden neurons in feedforward networks with arbitrary bounded nonlinear activation functions. IEEE Transaction on Neural Networks, 9(1), 224–229. https://doi.org/10.1109/72.655045
Huang, G. B., Chen, L., & Siew, C. K. (2006a). Universal approximation using incremental constructive feedforward networks with random hidden nodes. IEEE Transaction on Neural Networks, 17(4), 879–892. https://doi.org/10.1109/TNN.2006.875977
Huang, G. B., Zhu, Q. Y., & Siew, C. K. (2006b). Extreme learning machine: Theory and applications. Neurocomputing, 70(1), 489–501. https://doi.org/10.1016/j.neucom.2005.12.126
Ivakhnenko, A. G. (1966). Group method of data handling a rival of the method of stochastic approximation. Soviet Automatic Control, 13, 43–71.
Ivakhnenko, A. G. (1971). Polynomial theory of complex systems. IEEE Transactions on Systems, Man and Cybernetics, 4, 364–378. https://doi.org/10.1109/TSMC.1971.4308320
Jekabsons, G. (2010). GMDH-type polynomial neural networks for MATLAB. http://www.cs.rtu.lv/jekabsons/
Kavzoglu, T., & Saka, M. H. (2005). Modelling local GPS/Levelling geoid undulations using artificial neural networks. Journal of Geodesy, 78, 520–527. https://doi.org/10.1007/s00190-004-0420-3
Konakoğlu, B., Cakir, L., & Gökalp, E. (2016). 2D coordinates transformation using artificial neural networks. In Geo Advances 2016: ISPRS Workshop on Multi-dimensional & Multiscale Spatial Data Modeling. Volume XLII-2/W1: 3rd International GeoAdvances Workshop (pp. 183–186). Mimar Sinan Fine Arts University, Istanbul. https://doi.org/10.5194/isprs-archives-XLII-2-W1-183-2016
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.
Laari, P. B., Ziggah, Y. Y., & Annan, R. F. (2016). Determination of 3D transformation parameters for the Ghana geodetic reference network using ordinary least squares and total least squares techniques. International Journal of Geomatics and Geosciences, 7(3), 245–261.
Lao-Sheng, L., & Yi-Jin, W. (2006). A study on cadastral coordinate transformation using artificial neural network. In Proceedings of the 27th Asian Conference on Remote Sensing (pp. 1–6). Ulaanbaatar, Mongolia.
Li, X. Z., & Kong, J. M. (2014). Application of GA-SVM method with parameter optimization for landslide development prediction. Natural Hazard Earth System Science, 14(3), 525–533. https://doi.org/10.5194/nhess-14-525-2014
Malhotra, R., & Chug, A. (2014). Application of group method of data handling model for software maintainability prediction using object-oriented systems. International Journal of Systematic Assurance Engineering and Management, 5(2), 165–173. https://doi.org/10.1007/s13198-014-0227-4
Mugnier, J. C. (2000). OGP-coordinate conversions and transformations including formulae, COLUMN, Grids and Datums. The Republic of Ghana. In Photogrammetric Engineering and Remote Sensing (pp. 695–697). American Society for Photogrammetry and Remote Sensing (ASPRS).
Muller, V. A., & Hemond, F. H. (2013). Extended artificial neural networks: incorporation of a priori chemical knowledge enables use of ion selective electrodes for in-situ measurement of ions at environmentally relevant levels. Talanta, 117, 112–118. https://doi.org/10.1016/j.talanta.2013.08.045
Okwuashi, O., & Ndehedehe, C. (2017). Tide modelling using support vector machine regression. Journal of Spatial Science, 62(1), 29–46. https://doi.org/10.1080/14498596.2016.1215272
Orr, M. J. L. (1996). Introduction to radial basis function networks. Center for Cognitive Science, Edinburgh University, Scotland, UK.
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
Poku-Gyamfi, Y. (2009). Establishment of GPS reference network in Ghana (PhD Dissertation). Universitat der Bundeswehr Munchen, Germany.
Samui, P. (2012). Slope stability analysis using multivariate adaptive regression spline. Metaheuristics in Water, Geotechnical and Transportation Engineering, 14, 327–342. https://doi.org/10.1016/B978-0-12-398296-4.00014-3
Sarycheva, L. (2003). Using GMDH in ecological and socioeconomical monitoring problems. Systems Analysis Modelling Simulation, 43(10), 1409–1414. https://doi.org/10.1080/02329290290024925
Sisman, Y. (2014). Coordinate transformation of cadastral maps using different adjustment methods. Journal of Chinese Institute of Engineering, 37(7), 869–882. https://doi.org/10.1080/02533839.2014.888800
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 and 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, 99–209. 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. Geodetic Reference Frames, International Association of Geodesy Symposia, 134, 173–178. https://doi.org/10.1007/978-3-642-00860-3_27
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.
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