Abstract
The popularity of Artificial Neural Network (ANN) methodology has been growing in a wide variety of areas in geodesy and geospatial sciences. Its ability to perform coordinate transformation between different datums has been well documented in literature. In the application of the ANN methods for the coordinate transformation, only the train-test (hold-out cross-validation) approach has usually been used to evaluate their performance. Here, the data set is divided into two disjoint subsets thus, training (model building) and testing (model validation) respectively. However, one major drawback in the hold-out cross-validation procedure is inappropriate data partitioning. Improper split of the data could lead to a high variance and bias in the results generated. Besides, in a sparse dataset situation, the hold-out cross-validation is not suitable. For these reasons, the K-fold cross-validation approach has been recommended. Consequently, this study, for the first time, explored the potential of using K-fold cross-validation method in the performance assessment of radial basis function neural network and Bursa-Wolf model under data-insufficient situation in Ghana geodetic reference network. The statistical analysis of the results revealed that incorrect data partition could lead to a false reportage on the predictive performance of the transformation model. The findings revealed that the RBFNN and Bursa-Wolf model produced a transformation accuracy of 0.229 m and 0.469 m, respectively. It was also realised that a maximum horizontal error of 0.881 m and 2.131 m was given by the RBFNN and Bursa-Wolf. The obtained results per the cadastral surveying and plan production requirement set by the Ghana Survey and Mapping Division are applicable. This study will contribute to the usage of K-fold cross-validation approach in developing countries having the same sparse dataset situation like Ghana as well as in the geodetic sciences where ANN users seldom apply the statistical resampling technique.
Highlights
Positional information about natural and man-made features is shown on maps as coordinates
This means that the radial basis function neural network (RBFNN) transformed outputs do not differ greatly from the measured training data and was able to learn the training data in a more effective manner due to its adaptive computational capabilities compared with the parametric method of the Bursa-Wolf model
The obtained RBFNN results were compared with the Bursa-Wolf model
Summary
Positional information about natural and man-made features is shown on maps as coordinates. The use of K-fold cross-validation (KCV) technique has been recommended (Burman, 1989; Reitermanová, 2010; Kohavi, 1995) It is for these reasons that this study applied for the first time, the KCV technique to evaluate the coordinate transformation performance of the widely used ANN (radial basis function neural network) as well as the similarity model (Bursa-Wolf). The ANN approach has only been tested for transforming coordinates between two local geodetic data, namely Accra and Leigon data in Ghana This can be found in Ziggah et al (2016). The present study applied the ANN approach which usage in Ghana for global to local datum transformation has been hampered due to limited data availability.
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