Abstract
This study provides a comprehensive comparison of four different machine learning models including the group method of data handling (GMDH), M5 model tree (M5MT), multivariate adaptive regression spline (MARS), and Gaussian process regression (GPR) for predicting geoid undulation. For the first time, GMDH and M5MT were applied for this purpose. The obtained results were also compared with the classic inverse distance to a power (IDP) interpolation method. In order to assess the consistency of our results, two test sites with different topographic features were used for the evaluation of the models. In constructing the models, the geographic coordinate values and the geoid undulation value were used as inputs and output, respectively. Several statistical indices and rank analysis were used for evaluation of the models. According to the comparative results of all models in both test sites, the GMDH yielded the best performance among the developed models. The M5MT also exhibited acceptable results. Thus, it may be concluded that the proposed GMDH and M5MT have the potential to be alternative models that could assist geoscientists working with the geoid.
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References
Albayrak M, Özlüdemir MT, Aref MM, Halicioglu K (2020) Determination of Istanbul geoid using GNSS/levelling and valley cross levelling data. Geodesy Geodyn 11(3):163–173. https://doi.org/10.1016/j.geog.2020.01.003
Cakir L, Konakoglu B (2019) The impact of data normalization on 2D coordinate transformation using GRNN. Geod Vestnik 63(4):541–553. https://doi.org/10.15292/geodetski-vestnik.2019.04.541-553
Cakir L, Yilmaz N (2014) Polynomials, radial basis functions and multilayer perceptron neural network methods in local geoid determination with GPS/levelling. Measurement 57:148–153. https://doi.org/10.1016/j.measurement.2014.08.003
Dargahi-Zarandi A, Hemmati-Sarapardeh A, Hajirezaie S, Dabir B, Atashrouz S (2017) Modeling gas/vapor viscosity of hydrocarbon fluids using a hybrid GMDH-type neural network system. J Mol Liq 236:162–171. https://doi.org/10.1016/j.molliq.2017.03.066
Dawod GM, Abdel-Aziz TM (2020) Utilization of geographically weighted regression for geoid modelling in Egypt. J Appl Geod 14(1):1–12. https://doi.org/10.1515/jag-2019-0009
Doganalp S (2016) Geoid height computation in strip-area project by using least-squares collocation. Acta Geodyn Geomater 13(2):182. https://doi.org/10.13168/AGG.2015.0054
Doganalp S, Selvi HZ (2015) Local geoid determination in strip area projects by using polynomials, least-squares collocation and radial basis functions. Measurement 73:429–438. https://doi.org/10.1016/j.measurement.2015.05.030
Erol B, Erol S (2013) Learning-based computing techniques in geoid modeling for precise height transformation. Comput Geosci 52:95–107. https://doi.org/10.1016/j.cageo.2012.09.010
Erol S, Erol B (2021) A comparative assessment of different interpolation algorithms for prediction of GNSS/levelling geoid surface using scattered control data. Measurement 173:108623. https://doi.org/10.1016/j.measurement.2020.108623
Erol S, Özögel E, Kuçak RA, Erol B (2020) Utilizing airborne LiDAR and UAV photogrammetry techniques in local geoid model determination and validation. ISPRS ISPRS Int J Geoinf 9(9):528. https://doi.org/10.3390/ijgi9090528
Fan J, Zhang Q, Zhu J, Zhang M, Yang Z, Cao H (2020) Robust deep auto-encoding Gaussian process regression for unsupervised anomaly detection. Neurocomputing 376:180–190. https://doi.org/10.1016/j.neucom.2019.09.078
Friedman JH (1991) Multivariate adaptive regression splines. Ann Stat 19:1–141
Heddam S, Kisi O (2018) Modelling daily dissolved oxygen concentration using least square support vector machine, multivariate adaptive regression splines and M5 model tree. J Hydrol 559:499–509. https://doi.org/10.1016/j.jhydrol.2018.02.061
Inyurt S, Sekertekin A (2019) Modeling and predicting seasonal ionospheric variations in Turkey using artificial neural network (ANN). Astrophys Space Sci 364(4):62. https://doi.org/10.1007/s10509-019-3545-9
Ivakhnenko A, Ivakhnenko G (1995) The review of problems solvable by algorithms of the group method of data handling (GMDH). Pattern Recog and Image Anal 5(4):527–535
Ivakhnenko AG, Müller JA (1997) Recent developments of self-organising modeling in prediction and analysis of stock market. Microelectron Reliab 37:1053–1072
Jekabsons G (2016) Adaptive regression splines toolbox for Matlab/Octave ver. 1.13.0. Institute of Applied Computer Systems Riga Technical University, Latvia. http://www.cs.rtu.lv/jekabsons/Files/ARESLab.pdf
Kaloop MR, Rabah M, Hu JW, Zaki A (2018) Using advanced soft computing techniques for regional shoreline geoid model estimation and evaluation. Mar Georesour Geotechnol 36(6):688–697. https://doi.org/10.1080/1064119X.2017.1370622
Kaloop MR, Zaki A, Al-Ajami H, Rabah M (2019) Optimizing local geoid undulation model using GPS/levelling measurements and heuristic regression approaches. Surv Rev 52(375):544–554. https://doi.org/10.1080/00396265.2019.1665615
Karaaslan Ö, Kayıkçı ET, Aşık Y (2016) Comparison of local geoid height surfaces, in the province of Trabzon. Arab J of Geosci 9(431):1–12. https://doi.org/10.1007/s12517-016-2470-2
Kavzoglu T, Saka MH (2005) Modelling local GPS/levelling geoid undulations using artificial neural networks. J Geod 78(9):520–527. https://doi.org/10.1007/s00190-004-0420-3
Keshtegar B, Mert C, Kisi O (2018) Comparison of four heuristic regression techniques in solar radiation modeling: Kriging method vs RSM, MARS and M5 model tree. Renew Sustain Energy Rev 81:330–341. https://doi.org/10.1016/j.rser.2017.07.054
Kisi O, Parmar KS, Soni K, Demir V (2017) Modeling of air pollutants using least square support vector regression, multivariate adaptive regression spline, and M5 model tree models. Air Qual Atmos Health 10(7):873–883. https://doi.org/10.1007/s11869-017-0477-9
Kumi-Boateng B, Ziggah YY (2020) Feasibility of using Group Method of Data Handling (GMDH) approach for horizontal coordinate transformation. Geod Cartogr 46(2):55–66. https://doi.org/10.3846/gac.2020.10486
Lázaro-Gredilla M, Quinonero-Candela J, Rasmussen CE, Figueiras-Vidal AR (2010) Sparse spectrum Gaussian process regression. J Mach Learn Res 11:1865–1881
Liao DC, Wang QJ, Zhou YH, Liao XH, Huang CL (2012) Long-term prediction of the earth orientation parameters by the artificial neural network technique. J Geodyn 62:87–92. https://doi.org/10.1016/j.jog.2011.12.004
Ligas M, Szombara S (2018) Geostatistical prediction of a local geometric geoid-kriging and cokriging with the use of EGM2008 geopotential model. Stud Geophys Geod 62(2):187–205. https://doi.org/10.1007/s11200-017-0713-7
Madala HR, Ivakhnenko AG (1994) Inductive learning algorithms for complex systems modeling. CRC Press, Boca Raton
Mallika IL, Ratnam DV, Ostuka Y, Sivavaraprasad G, Raman S (2018) Implementation of hybrid ionospheric TEC forecasting algorithm using PCA-NN method. IEEE J Sel Top Appl Earth Obs Remote Sens 12(1):371–381. https://doi.org/10.1109/JSTARS.2018.2877445
Quinlan JR (1992) Learning with continuous classes. In: Proceedings of the 5th Australian joint conference on artificial intelligence pp 343–348. https://doi.org/10.1142/9789814536271
Rabah M, Kaloop M (2013) The use of minimum curvature surface technique in geoid computation processing of Egypt. Arab J Geosci 6(4):1263–1272. https://doi.org/10.1007/s12517-011-0418-0
Rasmussen CE, Nickisch H (2010) Gaussian processes for machine learning (GPML) toolbox. J Mach Learn Res 11:3011–3015
Razin MRG, Voosoghi B (2016) Wavelet neural networks using particle swarm optimization training in modeling regional ionospheric total electron content. J Atmos Sol Terr Phys 149:21–30. https://doi.org/10.1016/j.jastp.2016.09.005
Stopar B, Ambrožič T, Kuhar M, Turk G (2006) GPS-derived geoid using artificial neural network and least squares collocation. Surv Rev 38(300):513–524. https://doi.org/10.1179/sre.2006.38.300.513
Tusat E, Mikailsoy F (2018) An investigation of the criteria used to select the polynomial models employed in local GNSS/leveling geoid determination studies. Arab J Geosci 11(24):801. https://doi.org/10.1007/s12517-018-4176-0
Tütüncü K, Şahman MA, Tuşat E (2021) A hybrid binary grey wolf optimizer for selection and reduction of reference points with extreme learning machine approach on local GNSS/leveling geoid determination. Appl Soft Comput 108(107444):1–13. https://doi.org/10.1016/j.asoc.2021.107444
Veronez MR, De Souza GC, Matsuoka TM, Reinhardt A, Da Silva RM (2011) Regional mapping of the geoid using GNSS (GPS) measurements and an artificial neural network. Remote Sens 3(4):668–683. https://doi.org/10.3390/rs3040668
Wang Y, Witten IH (1997) Induction of model trees for predicting continuous lasses. In: Proceedings of the poster papers of the European conference on machine learning. University of Economics, Faculty of Informatics and Statistics, Prague
Wang G, Liu L, Tu Y, Xu X, Yuan Y, Song M, Li W (2018) Application of the radial basis function neural network to the short term prediction of the Earth’s polar motion. Stud Geophys Geod 62(2):243–254. https://doi.org/10.1007/s11200-017-0805-4
Williams CKI, Rasmussen CE (2006) Gaussian processes for machine learning. MIT Press, Cambridge
Yanalak M, Baykal O (2001) Transformation of ellipsoid heights to local leveling heights. J Surv Eng 127(3):90–103. https://doi.org/10.1061/(ASCE)0733-9453(2001)127:3(90)
Yang Z, Chen Y (1999) Determination of local geoid with geometric method: case study. J Surv Eng 125(3):136–146. https://doi.org/10.1061/(ASCE)0733-9453(1999)125. :3(136)
Ziggah YY, Youjian H, Yu X, Basommi LP (2016) Capability of artificial neural network for forward conversion of geodetic coordinates (ϕ, λ, h) to cartesian coordinates (X, Y, Z). Math Geosci 48:687–721. https://doi.org/10.1007/s11004-016-9638-x
Ziggah YY, Youjian H, Tierra AR, Laari PB (2019) Coordinate transformation between global and local data based on artificial neural network with K-fold cross-validation in Ghana. Earth Sci Res J 23(1):67–77. https://doi.org/10.15446/esrj.v23n1.63860
Acknowledgements
The authors are deeply grateful to the Erzincan XXIV Regional Directorate of the Land Registry and Cadastre Directorate of Turkey for providing the data. The authors also thank the editor and three anonymous reviewers for their helpful comments that have improved the quality of the manuscript.
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Conceptualization: BK; Methodology and analysis: BK and AA; Visualization: BK and AA; Writing—original draft preparation: BK; Writing—review and editing: AA.
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Konakoglu, B., Akar, A. Prediction of geoid undulation using approaches based on GMDH, M5 model tree, MARS, GPR, and IDP. Acta Geod Geophys 57, 293–315 (2022). https://doi.org/10.1007/s40328-022-00378-4
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DOI: https://doi.org/10.1007/s40328-022-00378-4