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.

Resampling Methods in Neural Networks: From Point to Interval Application to Coordinate Transformation

“…Here we use resampling methods in neural networks and apply them to coordinate transformation. The coordinate transformation is a classic problem that always arises in various fields of engineering sciences, such as to convert coordinates from one geodetic reference system into another one (Ziggah et al 2019a), to transform of 3-D point clouds from terrestrial laser scanning for deformation monitoring (Wujanz et al 2018), to design and optimize geodetic networks (Teunissen 1985) and so on.…”

Empirical study on the integration of total least squares and radial basis function neural network for coordinate transformation

“…Its efficacy as a coordinate transformation technique is well documented. Literature confirms that the ANN approaches could produce reasonable and promising results that are more satisfactory than the empirical affine, conformal and projective transformation methods (Tierra et al, 2009;Kumi-Boateng and Ziggah, 2017;Ziggah et al, 2016;Ziggah et al, 2019a;Ziggah et al, 2019b;Gullu and Narin, 2019). The strength of the ANN has been credited to its ability to effectively reduce the distortion and heterogeneity in spatial data related to the different geodetic datums.…”