A novel data-adaptive network design methodology based on the k-means clustering and modified ISODATA algorithm for regional gravity field modeling via SRBF

Date

2024-1-5

Author

Uluğ, Raşit

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

76
views

103
downloads

Cite This

This thesis presents a new data-adaptive network design methodology called k-SRBF for the spherical radial basis functions (SRBFs) in regional gravity field modeling. This methodology employs a post-processing procedure for the centroids obtained by the k-means clustering algorithm. The post-processing procedure, which is the modified version of the Iterative Self-Organizing Data Analysis Technique (ISODATA) splits, merges and deletes the clusters within an initial candidate network, considering the user-defined criteria. An improved version that addresses the limitations of the initial version is also presented, which reduces complexity and computation time. The bandwidth of each SRBF is determined using the generalized cross-validation (GCV) technique in which only the observations within the radius of the impact area are used. Different bandwidth limits are examined and the appropriate lower and upper bandwidth limits are chosen based on the empirical signal covariance function and user-defined criteria. 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. Additional tests are performed to verify the performance of the proposed methodology in combining different types of observations. The results reveal that k-SRBF is an effective methodology to establish a data-adaptive network for SRBFs. Furthermore, the 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. A weighted approach of the improved k-SRBF methodology is also created. Finally, an efficient Python-based software is developed in which k-SRBF is employed.

Subject Keywords

Regional gravity field modeling, Spherical radial basis functions, Data-adaptive network design, k-means clustering algorithm, ISODATA

URI

https://hdl.handle.net/11511/108242

Collections

Graduate School of Natural and Applied Sciences, Thesis