Analysis of the Global Gender Gap Index Using the Time Series Clustering Method

Abstract

This study aims to cluster analyse the countries of the world based on the Global Gender Gap Index (GGGI). In this context, GGGI data covering the years 2006-2024 were compiled and clustering analysis of 99 countries was carried out using time series data for 18 years. Dynamic Time Warping (DTW) method was used as a distance measure to determine the similarities between countries. In clustering analysis, hierarchical clustering (single linkage, full linkage and Ward's method), k-medoids clustering (Partitioning Around Medoids - PAM) and spectral clustering techniques were applied. The average silhouette method was used to determine the optimum number of clusters. Mean silhouette score, Dunn's index, Calinski-Harabasz criterion and coophenetic correlation coefficient were calculated to evaluate the clustering performances. As a result of the analyses, it was determined that the countries of the world were grouped into two main clusters based on the GGGI index. While an increasing trend is observed in the GGGI values of the countries in the first cluster, it is determined that there is a decreasing trend in the index values of the countries in the second cluster.

Keywords

• time series clustering
• machine learning
• global gender gap index

Zaman Serisi Kümeleme Yöntemi ile Küresel Cinsiyet Uçurumu Endeksinin Analizi

Öz

Bu çalışma, dünya ülkelerinin Küresel Cinsiyet Uçurumu Endeksi (Global Gender Gap Index- GGGI) temelinde kümeleme analizini amaçlamaktadır. Bu kapsamda, 2006-2024 yıllarını kapsayan GGGI verileri derlenmiş ve 18 yıllık döneme ait zaman serisi verileri kullanılarak 99 ülkenin kümeleme analizi gerçekleştirilmiştir. Ülkeler arasındaki benzerliklerin belirlenmesi için uzaklık ölçütü olarak Dinamik Zaman Bükmesi (Dynamic Time Warping-DTW) yöntemi kullanılmıştır. Kümeleme analizinde hiyerarşik kümeleme (tek bağlantı, tam bağlantı ve Ward’s yöntemi), k-medoid kümeleme (Partitioning Around Medoids - PAM) ve spektral kümeleme teknikleri uygulanmıştır. Optimum küme sayısının belirlenmesinde ortalama silüet yöntemi kullanılmıştır. Kümeleme performanslarının değerlendirilmesi amacıyla ortalama silüet skoru, Dunn endeksi, Calinski-Harabasz kriteri ve kofenetik korelasyon katsayısı hesaplanmıştır. Analizler sonucunda, dünya ülkelerinin GGGI endeksine dayalı olarak iki temel kümede toplandığı tespit edilmiştir. İlk kümede yer alan ülkelerin GGGI değerlerinde artış eğilimi gözlemlenirken, ikinci kümede yer alan ülkelerin endeks değerlerinde azalan bir trendin olduğu belirlenmiştir.

Anahtar Kelimeler

• Zaman serisi kümeleme
• makine öğrenmesi
• küresel cinsiyet farkı endeksi

References

1. Ayabakan, B. Ç. (2022). OECD Ülkelerinin Küresel Cinsiyet Uçurumu Endeksi Verilerinin Kümeleme Analizi ile Değerlendirilmesi. Sosyal Bilimler Araştırmaları Dergisi, 15(3), 85-98.
2. Caliński T, Harabasz J. A (1974). Dendrite method for cluster analysis. Communications in Statistics-theory and Methods, 3(1), 1-27.
3. Davies DL, Bouldin, DW. A (1979). Cluster separation measure. IEEE transactions on pattern analysis and machine intelligence, 1(2), 224-227.
4. Dunn, J. C. (1973). A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters. Journal of Cybernetics, 3(3), 32–57. https://doi.org/10.1080/01969727308546046
5. Fransiska, H., Agustina, D., Setyorini, D., Sumartajaya, I. M., & Kurnia, A. (2024, June). Time Series Clustering Analysis Using Dynamic Time Warping Technique of Daily Rainfall in Bengkulu Province. IOP Conference Series: Earth and Environmental Science. 1359(1), 012026. Access address: https://conference.ipb.ac.id/index.php/fisaed/article/view/316
6. Gençoğlu, P., & Kuşkaya, S. (2016). Global Gender Gap Index Analysis in Europe and Central Asia: A Statistical Approach. Journal of International Social Research, 9(46), 696-702.
7. Hair, Joseph F., et al. (2014) Multivariate data analysis. Essex: Pearson Education Limited.
8. Hervada-Sala, C., & Jarauta-Bragulat, E. (2004). A program to perform Ward's clustering method on several regionalized variables. Computers & Geosciences, 30(8), 881-886.

9. Holder, C., Middlehurst, M., & Bagnall, A. (2024). A review and evaluation of elastic distance functions for time series clustering. Knowledge and Information Systems, 66(2), 765-809.
10. Karakas, B., & Çevik, O. C. (2016). Measurement of Gender Inequality: A Critical Approach to the Global Gender Gap Index. Emek ve Toplum, 5(13), 68-74.
11. Kassambara, A. (2017). Practical guide to cluster analysis in R: Unsupervised machine learning. United States:STHDA
12. Kaufman, L., & Rousseeuw, P. (1987). Clustering by means of medoids. Netherlands: Faculty of Mathematics and Informatics. Delft University of Technology.
13. Koca, G. Ş. (2021). The Classification of World Countries in Terms of Global Gender Gap with Using Cluster Analysis. International Journal of Social Research, 14(2), 30-42.
14. Li, H. Y., Lawarence, J. A., Mason, P. J., & Ghail, R. C. (2025). Fast Dynamic Time Warping and Hierarchical Clustering with Multispectral and Synthetic Aperture Radar Temporal Analysis for Unsupervised Winter Food Crop Mapping. Agriculture, 15(1), 82. https://doi.org/10.3390/agriculture15010082
15. Lor, M. (1983) Cluster Analysis for Social Sciences. San Francisco:Jossey-Bass.
16. Maharaj, E. A., Giovanni, L. D., D’Urso, P., & Bhattacharya, M. (2024). Deployment of renewable energy sources: Empirical evidence in identifying clusters with dynamic time warping. Social Indicators Research, 175(3), 741-762.
17. Mishchenko, M., Lukianets-Shakhova, V., Rostetska, S., & Shvets, S. (2022). Constitutional and legal framework for gender equality in Ukraine and world countries. Amazonia Investiga, 11(49), 165-174.
18. Nielsen, F. (2016). Hierarchical Clustering. Introduction to HPC with MPI for Data Science. (s.195–211) içinde. Springer.
19. Niennattrakul, V., & Ratanamahatana, C. A. (2007). Inaccuracies of shape averaging method using dynamic time warping for time series data. In Computational Science–ICCS 2007: 7th International Conference, Beijing, China, May 27-30, 2007, Proceedings, Part I 7 (pp. 513-520). Springer Berlin Heidelberg.
20. OECD (2018). Bridging The Digital Gender Divide Include, Upskill, Innovate. Access address: https://www.researchgate.net/publication/329144162_Bridging_the_digital_gender_divide_Include_upskill_innovate
21. Öztürk, F. E., & Demirel, N. (2023). Comparison of the methods to determine optimal number of cluster. Veri Bilimi, 6(1), 34-45.
22. Prahara, A., Ismi, D. P., & Azhari, A. (2020). Parallelization of Partitioning Around Medoids (PAM) in K-Medoids Clustering on GPU. Knowledge Engineering and Data Science, 3(1), 40-49.
23. Rahkmawati, Y., & Annisa, S. (2023). Clustering Time Series Using Dynamic Time Warping Distance in Provinces in Indonesia Based on Rice Prices. TIERS Information Technology Journal, 4(2), 115-121.
24. Rani, Y., & Rohil, H. (2013). A study of hierarchical clustering algorithm. International Journal of Information and Computation Technology, 3(11), 1225-1232.
25. Rasmussen, E. M. (1992). Clustering algorithms. Information retrieval: data structures & algorithms 1992, 419-442.
26. Rokach, L. (2010). A survey of Clustering Algorithms. Maimon, O., ve Rokach, L. (Eds.), Data Mining and Knowledge Discovery Handbook. Second Edition (s. 269-298) içinde. Springer.
27. 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.
28. Tibshirani, R., Walther, G. ve 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.
29. Von Luxburg, U. (2007). A tutorial on spectral clustering. Statistics and computing, 17, 395-416. WEF, World Economic Forum (2024). Global Gender Gap Report 2024. Access address: https://www.weforum.org/publications/global-gender-gap-report-2024/
30. Xu, R. & Wunsch, D.C. II (2009). Clustering. IEEE Press, John Wıley&Sons
31. Berndt, D. J., & Clifford, J. (1994). Using dynamic time warping to find patterns in time series. In Proceedings of the 3rd international conference on knowledge discovery and data mining (pp. 359-370). Access address: https://cdn.aaai.org/Workshops/1994/WS-94-03/WS94-03-031.pdf
32. Ratanamahatana, C. A., & Keogh, E. (2004). Everything you know about dynamic time warping is wrong. In Third workshop on mining temporal and sequential data. Seattle: Citeseer. Access address: https://www.cs.ucr.edu/~eamonn/DTW_myths.pdf
33. Wang, W., Lyu, G., Shi, Y., & Liang, X. (2018). Time series clustering based on dynamic time warping. In 2018 IEEE 9th international conference on software engineering and service science (ICSESS). IEEE. Access address: https://ieeexplore.ieee.org/document/8663857