9:15 AM - 9:30 AM
[SGD03-02] Velocity Field Clustering Using Objective Weights in a Distance Metric
Keywords:clustering, GNSS, velocity fields, block boundaries
The Earth's surface is globally divided into a dozen tectonic plates and, at a more local scale, into finer crustal blocks. Identifying these block boundaries is crucial for understanding the tectonics and seismic and volcanic activities in a target region. While block boundaries have often been determined based on geological information, crustal deformation velocity fields have also been used to determine block boundaries objectively. Both hierarchical and non-hierarchical clustering methods have been proposed for this purpose. Hierarchical clustering methods directly compare velocity vectors to discuss crustal blocks in local regions (Simpson et al. 2012; Takahashi et al. 2019). However, when the Euler pole is located near the target region, it is essential to consider rigid body motions. On the other hand, non-hierarchical clustering methods that consider the physical constraint of rigid body motion have been proposed. However, due to the nature of non-hierarchical clustering, identifying small crustal blocks remains unstable. Furthermore, limitations in computation time pose challenges to evaluating the stability of clustering results (Savage and Wells 2015; Takahashi and Hashimoto 2022).
Considering these issues, Takahashi et al. (2025) proposed a hierarchical clustering method using a metric based on the weighted sum of two dissimilarity measures: the dissimilarity of velocity vectors considering the effect of the spherical Earth (Parallel Translation; PT) and rigid body motion (Euler Vector; EV). This method was applied to the ITRF2008 (Altamimi et al., 2012) and Taiwan (Tsai et al., 2015), demonstrating its applicability from global to local scales and evaluating stabilities of the clustering results. However, their study subjectively set the weights of the two dissimilarity measures, EV and PT, to 1:1. Additionally, distant observation points were sometimes classified into the same cluster, highlighting a limitation of the method.
To address these issues, this study proposes a method using UMAP to objectively determine the weights of each term in the clustering distance metric for block boundary identification based on velocity field clustering. In addition to the distance metrics of EV and PT, we introduce the great-circle distance (GC) between observation points as a metric for hierarchical clustering.
In the proposed method, the magnitudes of the three terms (EV, PT, and GC) are first computed. Next, assuming the weights in each term, UMAP is applied to the weighted values. Hierarchical clustering is then performed on the two-dimensional features obtained through UMAP to generate dendrograms. Here, the dimensional reductioncompression effect of UMAP enhances the aggregation of clusters in a low-dimensional space, thereby clarifying latent cluster structures and improving clustering performance. This analysis is repeated for various weight combinations. The differences between the obtained dendrograms using different weights are evaluated using the Robinson-Foulds (RF) distance, and the optimal weight is determined based on the rate of change in RF distance.
We applied the proposed method to the ITRF2020 dataset (Altamimi et al., 2023), an improved global dataset with higher accuracy and a longer observation period than ITRF2008. Since residuals are reduced when considering the system-wide translational motion, the translation rate estimated by Altamimi et al. (2023) is subtracted from the dataset in advance.
To determine the weight of the newly introduced GC term, the weights of EV and PT were first fixed to 1:1, while the weight of GC was varied from 0 to 1.0×10-5 with an increment of 0.1×10-5. The results indicate that when the weight was set to EV:PT:GC = 1:1:0.4×10-5, the RF distance exhibited the most significant change. When this weight was applied to the ITRF2020 velocity field clustering, the obtained clustering results were largely consistent with the block boundaries presented in Altamimi et al. (2023). Furthermore, the introduction of the GC term resolved the issue of distant observation points being classified into the same cluster.
Future work involves optimizing the weights of all three terms (EV, PT, and GC) rather than only GC. Stability evaluations corresponding to different weight adjustments will also be conducted. Furthermore, the effect of excluding UMAP in the weight determination process will be tested to assess its influence on clustering performance. Through these investigations, we aim to validate the proposed method as a more objective approach for velocity field clustering, applicable from global to local scales.
Considering these issues, Takahashi et al. (2025) proposed a hierarchical clustering method using a metric based on the weighted sum of two dissimilarity measures: the dissimilarity of velocity vectors considering the effect of the spherical Earth (Parallel Translation; PT) and rigid body motion (Euler Vector; EV). This method was applied to the ITRF2008 (Altamimi et al., 2012) and Taiwan (Tsai et al., 2015), demonstrating its applicability from global to local scales and evaluating stabilities of the clustering results. However, their study subjectively set the weights of the two dissimilarity measures, EV and PT, to 1:1. Additionally, distant observation points were sometimes classified into the same cluster, highlighting a limitation of the method.
To address these issues, this study proposes a method using UMAP to objectively determine the weights of each term in the clustering distance metric for block boundary identification based on velocity field clustering. In addition to the distance metrics of EV and PT, we introduce the great-circle distance (GC) between observation points as a metric for hierarchical clustering.
In the proposed method, the magnitudes of the three terms (EV, PT, and GC) are first computed. Next, assuming the weights in each term, UMAP is applied to the weighted values. Hierarchical clustering is then performed on the two-dimensional features obtained through UMAP to generate dendrograms. Here, the dimensional reductioncompression effect of UMAP enhances the aggregation of clusters in a low-dimensional space, thereby clarifying latent cluster structures and improving clustering performance. This analysis is repeated for various weight combinations. The differences between the obtained dendrograms using different weights are evaluated using the Robinson-Foulds (RF) distance, and the optimal weight is determined based on the rate of change in RF distance.
We applied the proposed method to the ITRF2020 dataset (Altamimi et al., 2023), an improved global dataset with higher accuracy and a longer observation period than ITRF2008. Since residuals are reduced when considering the system-wide translational motion, the translation rate estimated by Altamimi et al. (2023) is subtracted from the dataset in advance.
To determine the weight of the newly introduced GC term, the weights of EV and PT were first fixed to 1:1, while the weight of GC was varied from 0 to 1.0×10-5 with an increment of 0.1×10-5. The results indicate that when the weight was set to EV:PT:GC = 1:1:0.4×10-5, the RF distance exhibited the most significant change. When this weight was applied to the ITRF2020 velocity field clustering, the obtained clustering results were largely consistent with the block boundaries presented in Altamimi et al. (2023). Furthermore, the introduction of the GC term resolved the issue of distant observation points being classified into the same cluster.
Future work involves optimizing the weights of all three terms (EV, PT, and GC) rather than only GC. Stability evaluations corresponding to different weight adjustments will also be conducted. Furthermore, the effect of excluding UMAP in the weight determination process will be tested to assess its influence on clustering performance. Through these investigations, we aim to validate the proposed method as a more objective approach for velocity field clustering, applicable from global to local scales.