From clustering to ensemble clustering in GNSS velocities: A Meta CLustering-based approach

Year 2023, Volume: 13 Issue: 3, 661 - 674, 15.07.2023

Seda Özarpacı , Batuhan Kılıç , Mehmet Köküm , Uğur Doğan

https://doi.org/10.17714/gumusfenbil.1255423

Abstract

Although there are different approaches and models to understand and interpret the structures in crustal deformations, one of them is the block modeling method. Using block modeling, one can determine plate movements, parameters such as slip rates, locking depths or Euler poles on faults. However, the accuracy of the block modeling results is related to how well the block boundaries are determined. One of the most important steps of block modeling is the detection of block boundaries and clustering can be used as a tool for this. Cluster analysis assigns data to similar groups based on similarities and differences in the data subject to clustering. In this study, Türkiye was determined as the study area. In this context, we utilized the ensemble clustering algorithm to cluster recent Global Navigation Satellite Systems (GNSS) velocity field in Türkiye and determine block boundaries. Current GNSS velocity field, which consists of 78% survey and 22% continuous type GNSS data processed together, used for clustering analysis for the first time in this study. Before clustering, we employed three different methods - Davies-Bouldin, Gap statistics, and Silhouette - to determine the optimal number (cluster number that best fit to GNSS velocity field) of clusters. Then, k-means, HAC, and spectral clustering techniques were then applied to cluster current GNSS velocities. Finally, we utilized the Meta-Clustering Algorithm (MCLA) as an ensemble clustering technique to cluster the horizontal components of the current velocity domain and present our findings.

Keywords

Determining block boundaries, GNSS, Current velocity field, Clustering, Meta-Clustering

GNSS hızlarında kümelemeden topluluk kümelemesine: Meta-kümeleme odaklı bir yaklaşım

Abstract

Kıtasal deformasyonları anlayabilmek ve yorumlayabilmek için farklı yaklaşımlar ve modeller bulunmakta olup, bunlardan biri de blok modelleme yöntemidir. Blok modelleme yardımıyla plaka hareketleri, kayma hızları, faylardaki kilitlenme derinlikleri, Euler kutbu gibi parametreler belirlenebilmektedir. Ancak, blok sınırları ne kadar iyi belirlenirse, modelleme sonuçları o kadar gerçeğe yaklaşmaktadır. Blok modellemenin en önemli adımlarından biri blok sınırlarının tespiti olup, kümeleme işlemi bunun için bir araç olarak kullanılabilmektedir. Kümeleme analizi, kümelemeye konu verideki benzerlik ve farklılıklara dayanarak veriyi benzer gruplara atamaktadır. Bu çalışmada, çalışma alanı olarak Türkiye belirlenmiştir. Bu kapsamda Türkiye'nin en güncel Küresel Navigasyon Uydu Sistemi (Global Navigation Satellite Systems – GNSS) hız alanı topluluk kümeleme algoritması ile kümelenmiş ve bu hız alanına uygun blok sınırları belirlenmiştir. Türkiye için %22’si sürekli ve %78’i kampanya tipi verilerden oluşan GNSS gözlemlerinin birarada değerlendirilerek güncellenmiş hız alanı ilk defa bu çalışma ile kümelenmiştir. Kümeleme öncesinde üç ayrı yöntemle, Davies-Bouldin, Gap (gap istatistiği) ve Silhouette ile, veriye en iyi uyum sağlayan optimum küme sayısı (GNSS hız alanına en uygun küme sayısı) tespit edilmiştir. Daha sonra, k-ortalamalar, HAC ve spektral kümeleme teknikleri kullanılarak güncel GNSS hızları kümelenmiştir. Son olarak, Meta-Kümeleme Algoritması (Meta-CLustering Algorithm - MCLA) olan topluluk kümeleme tekniği ile güncel hız alanı yatay bileşenleri kümelenmiş ve sonuçlar paylaşılmıştır.

Keywords

Blok sınırlarının belirlenmesi, GNSS, Güncel hız alanı, Kümeleme, Meta-Kümeleme

References

• Abbasi, S. O., Nejatian, S., Parvin, H., Rezaie, V., & Bagherifard, K. (2019). Clustering ensemble selection considering quality and diversity. Artificial Intelligence Review, 52(2), 1311-1340. https://doi.org/10.1007/s10462-018-9642-2
• Alqurashi, T., & Wang, W. (2019). Clustering ensemble method. International Journal of Machine Learning and Cybernetics, 10, 1227-1246. https://doi.org/10.1007/s13042-017-0756-7
• Arbelaitz, O., Gurrutxaga, I., Muguerza, J., Pérez, J. M., & Perona, I. (2013). An extensive comparative study of cluster validity indices. Pattern Recognition, 46(1), 243-256. https://doi.org/10.1016/j.patcog.2012.07.021
• Davies, D. L., & Bouldin, D. W. (1979). A cluster separation measure. IEEE Transactions on Pattern Analysis and Machine Intelligence, PAMI-1(2), 224-227. https://doi.org/10.1109/TPAMI.1979.4766909
• Driver, H. E., & Kroeber, A. L. (1932). Quantitative expression of cultural relationships. University of California Publications in American Archaeology and Ethnology, 31(4), 211-256.
• Emre, Ö., Duman, T.Y., Özalp, S., Elmacı, H., Olgun, Ş., & Şaroglu, F. (2013). Açıklamalı Türkiye Diri Fay Haritası, Ölçek 1:1.250.000. Maden Tetkik ve Arama Genel Müdürlüğü, Özel Yayın Serisi, 30, Ankara, Türkiye. ISBN: 978-605- 5310-56-1
• Ergintav, S., Reilinger, R. E., Çakmak, R., Floyd, M., Cakir, Z., Doğan, U., King, R. W., McClusky, S., & Özener, H. (2014). Istanbul’s earthquake hot spots: Geodetic constraints on strain accumulation along faults in the Marmara seismic gap. Geophysical Research Letters, 41(16), 5783-5788. https://doi.org/10.1002/2014GL060985
• Ghaemi, R., Sulaiman, M. N., Ibrahim, H., & Mustapha, N. (2009). A survey: clustering ensembles techniques. International Journal of Computer and Information Engineering, 3(2), 365-374. https://doi.org/10.5281/zenodo.1329276
• Ghosh, J., & Acharya, A. (2011). Cluster ensembles. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 1(4), 305-315. https://doi.org/10.1002/widm.32
• Golalipour, K., Akbari, E., Hamidi, S. S., Lee, M., & Enayatifar, R. (2021). From clustering to clustering ensemble selection: A review. Engineering Applications of Artificial Intelligence, 104, 104388. https://doi.org/10.1016/j.engappai.2021.104388
• Granat, R., Donnellan, A., Heflin, M., Lyzenga, G., Glasscoe, M., Parker, J., Pierce, M., Wang, J., Rundle, J., & Ludwig, L. G. (2021). Clustering analysis methods for GNSS observations: A data‐driven approach to identifying California's major faults. Earth and Space Science, 8(11), e2021EA001680. https://doi.org/10.1029/2021EA001680
• Jain, A. K., Murty, M. N., & Flynn, P. J. (1999). Data clustering: a review. ACM Computing Surveys (CSUR), 31(3), 264-323. https://doi.org/10.1145/331499.331504
• Karypis, G., & Kumar, V. (1998). A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM Journal on Scientific Computing, 20(1), 359-392. https://doi.org/10.1137/S106482759528799
• Kaufman, L., & Rousseeuw, P. J. (1990). Finding groups in data: An introduction to cluster analysis. Wiley: New York.
• Kılıç, B., & Özarpacı, S. (2022). Ensemble clustering in GPS velocities: A case study of Turkey. Applied Sciences, 12(24), 12636. https://doi.org/10.3390/app122412636
• Kleinberg, J. (2002). An impossibility theorem for clustering. In S. Becker, S. Thrun, & K. Obermayer (Eds.), Advances in Neural Information Processing Systems (ss. 446-453.). MIT Press.
• Kurt, A. İ., Özbakir, A. D., Cingöz, A., Ergintav, S., Doğan, U., & Özarpaci, S. (2023). Contemporary velocity field for Turkey inferred from combination of a dense network of long term GNSS observations. Turkish Journal of Earth Sciences, 32(SI-3), 275-293. https://doi.org/10.55730/1300-0985.1844
• MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations. In L.M. Le Cam, & J. Neyman (Eds.), Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability (ss. 281-297). University of California Press.
• Mcclusky, S., Balassanian, S., Barka, A., Demir, C., Ergintav, S., Georgiev, I., Gurkan, O., Hamburger, M., Hurst, K., Kahle, H., Kastens, K., Kekelidze, G., King, R., Kotzev, V., Lenk, O., Mahmoud, S., Mishin, A., Nadariya, M., Ouzounis, A., ... Veis, G. (2000). Global Positioning System constraints on plate kinematics and dynamics in the eastern Mediterranean and Caucasus. Journal of Geophysical Research: Solid Earth, 105(B3), 5695-5719. https://doi.org/10.1029/1999JB900351
• Meade, B. J., Hager, B. H., McClusky, S. C., Reilinger, R. E., Ergintav, S., Lenk, O., Barka, A., & Ozener, H. (2002). Estimates of seismic potential in the Marmara Sea region from block models of secular deformation constrained by Global Positioning System measurements. Bulletin of the Seismological Society of America, 92(1), 208-215. https://doi.org/10.1785/0120000837
• Özarpacı, S., Kılıç, B., Bayrak, O. C., Özdemir, A., Yılmaz, Y., & Floyd, M. (2023). Comparative analysis of the optimum cluster number determination algorithms in clustering GPS velocities. Geophysical Journal International, 232(1), 70-80. https://doi.org/10.1093/gji/ggac326
• Özdemir, S., & Karslıoğlu, M. O. (2019). Soft clustering of GPS velocities from a homogeneous permanent network in Turkey. Journal of Geodesy, 93(8), 1171-1195. https://doi.org/10.1007/s00190-019-01235-z
• Pakhira, M. K. (2012). Finding number of clusters before finding clusters. Procedia Technology, 4, 27-37. https://doi.org/10.1016/j.protcy.2012.05.004
• Reilinger, R., McClusky, S., Vernant, P., Lawrence, S., Ergintav, S., Cakmak, R., Ozener, H., Kadirov, F., Guliev, I., Stepanyan, R., Nadariya, M., Hahubia, G., Mahmoud, S., Sakr, K., ArRajehi, A., Paradissis, D., Al-Aydrus, A., Prilepin, M., Guseva, T., … Karam, G. (2006). GPS constraints on continental deformation in the Africa‐Arabia‐Eurasia continental collision zone and implications for the dynamics of plate interactions. Journal of Geophysical Research: Solid Earth, 111(B5). https://doi.org/10.1029/2005JB004051
• Rendón, E., Abundez, I., Arizmendi, A., & Quiroz, E. M. (2011). Internal versus external cluster validation indexes. International Journal of Computers and Communications, 5(1), 27-34.
• Rousseeuw, P. J. (1987). Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics, 20, 53-65.
• Savage, J. C., & Simpson, R. W. (2013a). Clustering of GPS velocities in the Mojave Block, southeastern California. Journal of Geophysical Research: Solid Earth, 118(4), 1747-1759. https://doi.org/10.1029/2012JB009699
• Savage, J. C., & Simpson, R. W. (2013b). Clustering of velocities in a GPS network spanning the Sierra Nevada Block, the northern Walker Lane Belt, and the central Nevada Seismic Belt, California‐Nevada. Journal of Geophysical Research: Solid Earth, 118(9), 4937-4947. https://doi.org/10.1002/jgrb.50340
• Savage, J. C., & Wells, R. E. (2015). Identifying block structure in the Pacific Northwest, USA. Journal of Geophysical Research: Solid Earth, 120(11), 7905-7916. https://doi.org/10.1002/2015JB012277
• Savage, J. C. (2018). Euler‐vector clustering of GPS velocities defines microplate geometry in southwest Japan. Journal of Geophysical Research: Solid Earth, 123(2), 1954-1968. https://doi.org/10.1002/2017JB014874
• Simpson, R. W., Thatcher, W., & Savage, J. C. (2012). Using cluster analysis to organize and explore regional GPS velocities. Geophysical Research Letters, 39(18). https://doi.org/10.1029/2012GL052755
• Strehl, A., & Ghosh, J. (2000). Value-based customer grouping from large retail data sets. Proceedings SPIE 4057, Data Mining and Knowledge Discovery: Theory, Tools, and Technology II (pp. 33-42), Orlando, FL, United States.
• Strehl, A., & Ghosh, J. (2002). Cluster ensembles – A knowledge reuse framework for combining multiple partitions. Journal of Machine Learning Research, 3, 583-617. https://doi.org/10.1162/153244303321897735
• Takahashi, A., Hashimoto, M., Hu, J. C., Takeuchi, K., Tsai, M. C., & Fukahata, Y. (2019). Hierarchical cluster analysis of dense GPS data and examination of the nature of the clusters associated with regional tectonics in Taiwan. Journal of Geophysical Research: Solid Earth, 124(5), 5174-5191. https://doi.org/10.1029/2018JB016995
• Thatcher, W. (2009). How the continents deform: The evidence from tectonic geodesy. Annual Review of Earth and Planetary Sciences, 37, 237-262. https://doi.org/10.1146/annurev.earth.031208.100035
• Tibshirani, R., Walther, G., & Hastie, T. (2001). Estimating the number of clusters in a data set via the gap statistic. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 63(2), 411-423. https://doi.org/10.1111/1467-9868.00293
• Topchy, A., Jain, A. K., & Punch, W. (2005). Clustering ensembles: Models of consensus and weak partitions. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(12), 1866-1881. https://doi.org/10.1109/TPAMI.2005.237
• Xu, D., & Tian, Y. (2015). A comprehensive survey of clustering algorithms. Annals of Data Science, 2, 165-193. https://doi.org/10.1007/s40745-015-0040-1
• Vega-Pons, S., & Ruiz-Shulcloper, J. (2011). A survey of clustering ensemble algorithms. International Journal of Pattern Recognition and Artificial Intelligence, 25(03), 337-372. https://doi.org/10.1142/S0218001411008683
• Von Luxburg, U. (2007). A tutorial on spectral clustering. Statistics and computing, 17, 395-416. https://doi.org/10.48550/arXiv.0711.0189
• Ward, J. H. (1963). Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 58(301), 236-244. https://doi.org/10.1080/01621459.1963.10500845
• Yan, D., Huang, L., & Jordan, M. I. (2009). Fast approximate spectral clustering. Proceedings of the 15th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 907-916). Paris, France.