A new data-adaptive network design methodology based on the k-means clustering and modified ISODATA algorithm for regional gravity field modeling via spherical radial basis functions

Uluğ, Raşit
Karslıoğlu, Mahmut Onur
© 2022, Springer-Verlag GmbH Germany, part of Springer Nature.In this study, a new data-adaptive network design methodology called k-SRBF is presented for the spherical radial basis functions (SRBFs) in regional gravity field modeling. In this methodology, the cluster centers (centroids) obtained by the k-means clustering algorithm are post-processed to construct a network of SRBFs by replacing the centroids with the SRBFs. The post-processing procedure is inspired by the heuristic method, Iterative Self-Organizing Data Analysis Technique (ISODATA), which splits clusters within the user-defined criteria to avoid over- and under-parameterization. These criteria are the minimum spherical distance between the centroids and the minimum number of samples for each cluster. The bandwidth (depth) of each SRBF is determined using the generalized cross-validation (GCV) technique in which only the observations within the radius of impact area (RIA) are used. The numerical tests are carried out with real and simulated data sets to investigate the effect of the user-defined criteria on the network design. Different bandwidth limits are also examined, and the appropriate lower and upper bandwidth limits are chosen based on the empirical signal covariance function and user-defined criteria. Also, additional tests are performed to verify the performance of the proposed methodology in combining different types of observations, such as terrestrial and airborne data available in Colorado. The results reveal that k-SRBF is an effective methodology to establish a data-adaptive network for SRBFs. Moreover, the proposed methodology improves the condition number of normal equation matrix so that the least-squares procedure can be applied without regularization considering the user-defined criteria and bandwidth limits.
Journal of Geodesy


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Citation Formats
R. Uluğ and M. O. Karslıoğlu, “A new data-adaptive network design methodology based on the k-means clustering and modified ISODATA algorithm for regional gravity field modeling via spherical radial basis functions,” Journal of Geodesy, vol. 96, no. 11, pp. 0–0, 2022, Accessed: 00, 2023. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85142501988&origin=inward.