# Ensemble Clustering in GPS Velocities: A Case Study of Turkey
## 4 Conclusions  
In this study, the authors tried to answer the following questions \"Is there a better way to cluster GPS velocities? Which one is the proper solution (individual or ensemble clustering) about the cluster/block boundaries?\". In the direction of these research questions the results are given as follows:  
* Before clustering, the GAP algorithm was used to obtain a priori information about the distribution of GPS velocities and classify the data into five classes.
* Five different individual clustering methods, BIRCH, \(k\)-means, mini batch \(k\)-means, HAC, and spectral clustering, were used to classify the published horizontal GPS velocities into five clusters. In general, the individual clustering methods separated NAF and EAF immediately. Furthermore, some sites in the western part of Turkey were assigned for the Aegean block. However, the number of GPS sites and the area of this block are changing due to the used methods. Moreover, in complex regions such as eastern or southern parts of Turkey, GPS sites were assigned to distinct generally neighbor clusters.
* To enhance the differences in clustering methods, the performance of three different ensemble clustering methods, HBGF, MCLA, and NMF-based consensus clustering is utilized for the first time with a GPS velocity field.
* Among the three ensemble clustering methods, HBGF and NMF did not give satisfactory results.  
Figure 10: Comparison of individual clustering results with ensemble clustering for western Turkey with: (**a**) BIRCH; (**b**) HAC; (**c**) \(k\)-means; (**d**) mini batch \(k\)-means; (**e**) spectral clustering; (**f**) MCLA results. Black solid lines are the block model at [5]. Gray thin lines show active faults [23].  
* On the other hand, MCLA consensus results are successful and proven here to be used with GPS-derived velocities.
* As a result, the block boundaries created with the MCLA ensemble clustering algorithm are compatible with the literature.  
Conceptualization, S.O. and B.K.; methodology, B.K.; software, B.K.; investigation, S.O.; resources, S.O.; Writing--Original draft preparation, S.O. and B.K.; Writing--Review and editing, S.O. and B.K.; visualization, S.O. and B.K. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
Not applicable.  
The data can be found in the appendix of the paper at [[https://link.springer.com/article/10.1007/s00190-019-01235-z](https://link.springer.com/article/10.1007/s00190-019-01235-z)]([https://link.springer.com/article/10.1007/s00190-019-01235-z](https://link.springer.com/article/10.1007/s00190-019-01235-z)) (accessed on 15 February 2019). as site name, geographic coordinates, data span, horizontal velocities with standard deviations and their correlations.  
We used GMT 6 for the map figures [60].  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
BIRCH  
Balanced Iterative Reducing and Clustering using Hierarchies  
CONRS-TR  
Continuously Operating Reference Stations Turkey  
EAF  
East Anatolian Fault  
EMSRI  
Earth and Marine Sciences Research Institute  
GPS  
Global Positioning System  
GMM  
Gaussian Mixture Model  
HAC  
Hierarchical Agglomerative Clustering  
HBGF  
Hybrid Bipartite Graph Formulation  
MAGNET  
Marma Region Continuous Network  
MCLA  
Meta-Clustering Algorithm  
NAF  
North Anatolian Fault  
NMF  
Non-negative Matrix Factorization  
TNPGN  
Turkish National Permanent GNSS Network  
TUBITAK  
Scientific and Technical Research Council of Turkey