# Ensemble Clustering in GPS Velocities: A Case Study of Turkey
###### Abstract  
Block modeling is an effective way to understand Earth's crustal deformation. However, the choice of block boundaries and the number of blocks affect the model results. Therefore, the subjectivity of this analysis should be avoided. Clustering analysis can be used to define the blocks of GPS (Global Positioning System) velocity fields without a priori information. Unfortunately, clustering methods also have unique solutions and differ with various algorithms. Ensemble methods could be an answer to enhance the clustering results for GPS velocities. In this study, we use ensemble clustering to identify block boundaries before block modeling without a priori information about the data. The ensemble clustering method is used for the first time in the clustering of GPS velocities and the case of Turkey is discussed. The published horizontal GPS velocities were first clustered with five different clustering methods and the optimum classes were determined using ensemble clustering methods. It is proven that the Meta-Clustering Algorithm can be used in terms of ensemble clustering for this region.  
clustering analysis; GPS velocities; ensemble clustering; Meta-CLustering algorithm +
Footnote †: journal: Applied  
Clustering (HAC), Euler-vector, and Gaussian Mixture Model (GMM) have been used in geodetic studies as well to find proper solutions that are acceptable and GPS velocities have been clustered to determine boundaries before block modeling [7; 10; 11; 12; 13; 14; 15; 16; 17]. However, as it is known, clustering is considered to be an inherently unsupervised learning method and forms normally a bottleneck problem. In other words, there is no a priori information about the underlying data distributions or about any specific properties that we want to find, or about what we consider proper solutions to the data. Each of the different clustering algorithms may produce different results by implicitly or explicitly imposing a particular structure on a similar data set. On the other hand, based on the impossibility theorem [18], there is no single clustering algorithm that can produce consistent and optimal results for different problems and there is no consensus on a universal standard for choosing any clustering algorithm for a specific problem. At this point, there is a need for efficient methods that can benefit from combining the strengths of many individual clustering algorithms [19]. To overcome this problem and to improve the quality of the single clustering algorithm results, the concept of combining different clustering results known as cluster ensemble (consensus clustering) has been introduced [20]. It has been broadly employed in clustering research for the purpose of enhancing the quality and robustness of individual clustering techniques [9; 21; 22].  
Therefore, the objective of this study is to explore 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, we first gathered horizontal velocities inferred from the published cGPS (continuous GPS) measurements in Turkey for clustering GPS velocities. Then, once the determined the number of clusters \(k\) that best represents, we clustered GPS velocities using five different clustering techniques including Balanced Iterative Reducing and Clustering using Hierarchies (BIRCH), \(k\)-means, mini batch \(k\)-means, HAC, and spectral clustering. After that, unlike the other studies, we investigated the performance of three cluster ensemble techniques known as Hybrid Bipartite Graph Formulation (HBGF), Meta-CLustering Algorithm (MCLA), and Non-Negative Matrix Factorization-based (NMF) consensus clustering to find out whether they produce proper results for GPS velocities or not. With this paper, ensemble clustering algorithms are used for the first time in the clustering of GPS-derived horizontal velocities.