MULTIMOORA ile En İyi Makine Öğrenimi Algoritmasının Seçimi ve Covid-19 Pandemisi için Dünya Çapında Ülke Kümelerinin Belirlenmesi

Öz

Bu çalışmada, çok amaçlı karar vermeye dayalı kümeleme analizine entegre bir yaklaşım sunmak amacıyla, 27 iç geçerlilik kriterinin tamamı MULTIMOORA yöntemi ile eş zamanlı olarak değerlendirilerek 11 farklı kümeleme algoritması arasından en iyi kümeleme algoritmasının belirlenmesi amaçlanmıştır. Çalışmada öncelikle iki veri kümesi için en uygun küme sayısı ve bu küme sayısına bağlı olarak en iyi kümeleme algoritması belirlenmiştir. Daha sonra, belirlenen ülke kümelerinin insani gelişmişlik sınıflarıyla ilişkisinin belirlenmesine odaklanılmıştır. Yapılan analizler sonucunda COVID-19 salgınından etkilenen ülkeler, Öklid uzaklığı aracılığıyla hesaplanan yakınlıklarına göre CLARA ve SOM algoritmaları ile kümelenmiştir. Her iki veri kümesi için de en uygun küme sayısı olarak üç küme belirlenmiştir. Vaka-ölüm oranına kıyasla insidans oranının kümeler arasındaki gerçek farkta daha baskın faktör olduğu bulunmuştur. Bir diğer dikkat çekici bulgu ise, ekonomik gücü ve insani gelişmişlik düzeyi yüksek ülkelerin, aşılama öncesinde pandemiden daha az etkilenmesi beklenirken, insani gelişmişlik düzeyi yüksek olan ülkelerin pandemiden etkilenme düzeyinin her değişken bakımından da yüksek olmasıdır.

Anahtar Kelimeler

• Makine Öğrenimi
• Kümeleme
• İç geçerlilik kriterleri
• MULTIMOORA
• COVID-19

Determination of Worldwide Country Clusters by Selecting the Best Machine Learning Algorithm via MULTIMOORA for Covid-19 Pandemic

Abstract

In this study, to present an integrated approach to clustering analysis based on multi-objective decision making, it is aimed to determine the best clustering algorithm among 11 different clustering algorithms by evaluating all 27 internal validity criteria simultaneously with MULTIMOORA method. In the study, initially, the best clustering algorithm was determined according to the optimal number of clusters for two COVID-19 datasets. Then, it focuses on determining the relationship of the country clusters with the classes determined according to the human development index. In the result of the analyses, countries affected by the COVID-19 pandemic have clustered via the CLARA and SOM algorithms according to their proximity calculated from the Euclidean distance. Three optimal number of clusters were determined for both datasets. The incidence rate variable is the more dominant factor than case fatality rate in the real difference between clusters. Another remarkable finding is that while countries with economic power and a high level of human development are expected to be less affected by the pandemic before the vaccination, the level of being affected by the pandemic increases in terms of both variables as the level of human development increases.

Keywords

• Machine learning
• Clustering
• Internal validation criteria
• MULTIMOORA
• COVID-19

References

1. Ahmad, K., Erqou, S., Shah, N., Nazir, U., Morrison, A.R., Choudhary, G., Wu, W. C. (2020). Association of poor housing conditions with COVID-19 incidence and mortality across US counties. PloS One, 15(11), e0241327.
2. Asem, N., Ramadan, A., Hassany, M., Ghazi, R.M., Abdallah, M., Ibrahim, M., Gamal, E. M. Hassan, S., Kamal, N., & Zaid, H. (2021). Pattern and determinants of COVID-19 infection and mortality across countries: An ecological study. Heliyon, 7(7).
3. Aydın, N. & Seven, A. N. (2015). İl nüfus ve vatandaşlik müdürlüklerinin iş yoğunluğuna göre hibrid kümeleme ile sınıflandırılması. Journal of Management and Economics Research, 13 (2), 181-201.
4. Berkhin, P. Survey of Clustering Data Mining Techniques, Accrue Software Inc., San Jose, California, USA (2002).
5. Bezdek, J., & Hathaway, R.J. (2002). VAT: A tool for visual assessment of (cluster) tendency. Proceedings of the International Joint Conference on Neural Networks, 3, 2225 - 2230. https://doi.org/10.1109/IJCNN.2002.1007487.
6. Bolshakova, N. Azuaje, F.J. (2003). Cluster validation techniques for genome expression data, Signal Process. 83 825-833. https://doi.org/10.1016/S0165-1684(02)00475-9.
7. Bradley, P. S., Mangasarian, O. L. and Street, W. N. Clustering via Concave Minimization, in Advances in Neural Information Processing Systems 9, M. C. Mozer, M. I. Jordan, and T. Petsche (Eds.) (1997) 368- 374, MIT Press.
8. Brauers, K.W.M., Zavadskas, E.K., Turskis, Z., Vilutienė, T. (2008). Multi-objective contractor's ranking by applying the MOORA method. Journal of Business Economics and Management, 9(4) 245-255.

9. Brauers, W.K.M., & Zavadskas, E. K. (2011). MULTIMOORA optimization used to decide on a bank loan to buy property, Technological and Economic Development of Economy 17(1) 174-188.
10. Brauers, W.K.M. & Ginevičius R., (2010). The Economy of the Belgian Regions tested with MULTIMOORA, Journal of Business Economics and Management. 11(2), 173–209. http://doi.org/10.3846/jbem.2010.09.
11. Cebeci, Z. (2020). fcvalid: an r package for internal validation of probabilistic and possibilistic clustering. Sakarya University Journal of Computer and Information Sciences, 3(1). https://doi.org/10.35377/saucis.03.01.664560
12. Charrad, M. Ghazzali, N. Boiteau, & V. Niknafs, A. (2014). NbClust: an R package for determining the relevant number of clusters in a data set. Journal of Statistical Software, 61 (6) 1–36. https://doi.org/10.18637/jss.v061.i06.
13. Chu, J. (2021). A statistical analysis of the novel coronavirus (COVID-19) in Italy and Spain. PLoS ONE, 16(3), e0249037. https://doi.org/10.1371/journal.pone.0249037.
14. Couvreur, C. The EM algorithm: a guided tour. In: Kárný M., Warwick K. (eds) Computer Intensive Methods in Control and Signal Processing. Birkhäuser, Boston, MA (1997). https://doi.org/10.1007/978-1-4612-1996-5_12.
15. Dalton, L. Ballarin, V., & Brun, M. (2009). Clustering algorithms: on learning, validation, performance, and applications to genomics, Current Genomics. 10 430-445. https://dx.doi.org/10.2174/138920209789177601.
16. Dempster, A.P., Paird, N.M. & Rubin, D.B. (1977) Maximum likelihood from incomplete data via the EM algorithm, Journal of the Royal Statistical Society. 39(1),1–38.
17. Desgraupes, B. (2012). ClusterCrit: Clustering Indices. Available online: https://cran.r-proje ct.org/web/packages/clusterCrit/.
18. Desgraupes, B. (2016). ClusterCrit: clustering indices R package version 1.2.8. https://cran.r-proje ct.org/web/packages/clusterCrit/.
19. Dopazo, J. Carazo, J.M. Phylogenetic reconstruction using an unsupervised growing neural network that adopts the topology of a phylogenetic tree, J Mol Evol. 44(2) (1997) 226-33. http://dx.doi.org/10.1007/pl00006139. Dunham, M.H. Data Mining Introductory and Advanced Topics, Prentice Hall, USA (2003).
20. Fraley, C. Raftery, A.E. How many clusters? Which clustering method? Answers via model-based cluster analysis, Computer Journal. 41(8) (1998) 578–588.
21. Flexer, A. On the use of self-organizing maps for clustering and visualization, Intelligent Data Analysis, 5(5) (2001) 373-384.
22. Gagolewski, M., Bartoszuk, M., & Cena, A. (2016). Genie: A new, fast, and outlier-resistant hierarchical clustering algorithm. Inform Sci, 363, 8–23. http://dx.doi.org/10.1016/j.ins.2016.05.003.
23. Gokmen, Y., Baskici, C., & Ercil, Y. (2021). The impact of national culture on the increase of COVID-19: A cross-country analysis of European countries. International Journal of Intercultural Relations, 81, 1-8. https://doi.org/10.1016/j.ijintrel.2020.12.006.
24. Gupta, M. R. &Chen, Y. (2011). Theory and use of the EM algorithm, Foundations and Trends in Signal Processing. 4(3), 223-296. http://dx.doi.org/10.1561/2000000034.
25. Halkidi M., Batistakis Y., & Vazirgiannis M., On clustering validation techniques, Journal of Intelligent Information Systems. 17 (2001) 107–145. https://doi.org/10.1023/A:1012801612483.
26. Han, J. Kamber M., Pei, J. Data mining: Concepts and techniques, (3rd ed.). Morgan Kaufmann Publishers (2012). Harapan, H., Itoh, N., Yufika, A. Winardi, W., Keam, S. Te, H., Megawati, Hayati, D. Z., Wagner, A.L., & Mudatsir, M. (2020). Coronavirus disease 2019 (COVID-19): A literature review. J Infect Public Health, 13(5), 667-673. doi: 10.1016/j.jiph.2020.03.019.
27. Hartigan, J.A & Wong, M.A., Algorithm AS 136: A k-means clustering algorithm, Journal of the Royal Statistical Society. Series C (Applied Statistics). 28 (1979) 100-108. http://dx.doi.org/10.2307/2346830.
28. Hasell, J., Mathieu, E., Beltekian, D., Macdonald, B., Giattino, C., Ortiz-Ospina, E., Roser, M., & Ritchie, H. (2020). A cross-country database of COVID-19 testing. Scientific Data, 7(1), 345. https://doi.org/10.1038/s41597-020-00688-8.
29. Herrero, J. Valencia A., Dopazo, J. A hierarchical unsupervised growing neural network for clustering gene expression patterns, Bioinformatics. 17(2) (2001) 126-36. https://doi.org/10.1093/bioinformatics/17.2.126.
30. Hezam, I.M. (2021). COVID-19 Global Humanitarian Response Plan: An optimal distribution model for high-priority countries. ISA Transactions. https://doi.org/10.1016/j.isatra.2021.04.006.
31. HDR. (2020). Human Development Reports. http://hdr.undp.org/en/2020-report (google Scholar).
32. Itoh, H. Market area analysis of ports in Japan: an application of fuzzy clustering, in: The IAME2013 Annual Conference, Marseille, France. (2013) 1-21. hal-00918672
33. Karmakar, M. Lantz, P. M., & Tipirneni, R. (2021). Association of social and demographic factors with COVID-19 incidence and death rates in the US. JAMA network open, 4(1), e2036462.
34. Kaufman, L., Rousseeuw, P. J. Finding Groups in Data: An Introduction to Cluster Analysis. John Wiley & Sons (2005).
35. Khafaie, M.A., & Rahim, F., (2020). Cross-country comparison of case fatality rates of COVID-19/SARS-COV-2. Osong. Public Health Res Perspect, 11(2), 74-80. https://dx.doi.org/10.24171/j.phrp.2020.11.2.03.
36. Kiang M.Y., Extending the Kohonen self-organizing map networks for clustering analysis, Computational Statistics and Data Analysis. 38 (2001) 161–180. https://doi.org/10.1016/S0167-9473(01)00040-8.
37. Kurniawan, R. Sheikh Abdullah, S. N. H. Lestari, F. Nazri, M. Z. A. Mujahidin, A. and Adnan, N. (2020) Clustering and correlation methods for predicting coronavirus COVID-19 risk analysis in pandemic countries, 8th International Conference on Cyber and IT Service Management (CITSM). 1-5. htpps://doi.org/ 10.1109/CITSM50537.2020.9268920.
38. Kuster, A.C., & Overgaard, H.J. (2021). A novel comprehensive metric to assess effectiveness of COVID-19 testing: Inter-country comparison and association with geography, government, and policy response. PLoS One, 16(3), e0248176. doi: 10.1371/journal.pone.0248176
39. Kucukefe, B. (2020). Clustering macroeconomic impact of COVID-19 in OECD countries and China, Ekonomi Politika Ve Finans Araştırmaları Dergisi. 5 (2020) 280–291. https://doi.org/10.30784/epfad.811289.
40. Kvålseth, T.O. (2017). An alternative measure of ordinal association as a value-validity correction of the Goodman–Kruskal gamma. Communications in Statistics - Theory and Methods, 46 (21), 10582-10593. http://doi.org/ 10.1080/03610926.2016.1239114
41. Li, M., Zhang, Z., Cao, W., Liu, Y., Du, B., Chen, C., Liu, Q., Uddin, M.N., Jiang, S., Chen, C., Zhang, Y., & Wang, X. (2021). Identifying novel factors associated with COVID-19 transmission and fatality using the machine learning approach. Sci Total Environ, 764, 142810. doi: 10.1016/j.scitotenv.2020.142810.
42. Liu, K., He, M., Zhuang, Z., He, D., & Li, H. (2020). Unexpected positive correlation between human development index and risk of infections and deaths of COVID-19 in Italy. One Health, 10, 100174. DOI: https://doi.org/10.1016/j.onehlt.2020.100174
43. Maechler, M., Rousseeuw, P., Struyf, A., Hubert, M., & Hornik, K. (2021). cluster: Cluster Analysis Basics and Extensions. R package version 2.1.2 — For new features, see the 'Changelog' file (in the package source). https://CRAN.R-project.org/package=cluster.
44. Marziali, E.M., Hogg, R.S., Oduwole, O.A. & Card, K.G. (2021). Predictors of COVID-19 testing rates: A cross-country comparison. International Journal of Infectious Diseases, 104, 370-372.
45. McKenzie, G., & Adams, B. (2020). A country comparison of place-based activity response to COVID-19 policies. Applied geography, 125, 102363.https://doi.org/10.1016/j.apgeog.2020.102363.
46. McLachlan, G.J. Krishnan, T. & Ng, S.K. (2004). The EM algorithm, Working Paper No. 2004, 24, Humboldt-Universität zu Berlin, Center for Applied Statistics and Economics (CASE), Berlin http://hdl.handle.net/10419/22198.
47. Milligan, G.W. (1981). A monte carlo study of thirty internal criterion measures for cluster analysis, Psychometrika. 46(2), 187–199.
48. Moshtaghi M., Bezdek, J. CErfani, S.M., Leckie, C. & Bailey, J. (2019). Online cluster validity indices for performance monitoring of streaming data clustering, International Journal of Intelligent Systems. 34, 541 - 563. https://dx.doi.org/10.1002/int.22064.
49. OWD. (2022). COVID-19 Data, https://ourworldindata.org/coronavirus-testing#testing-for-covid-19-background-the-our-world-in-data-covid-19-testing-dataset.
50. Pérez, L.A., García-Vico, Á.M., González, P., & Carmona, C.J. (2020). Techniques for evaluating clustering data in R, The Clustering Package. https://cran.r-project.org/web/packages/Clustering/vignettes/Clustering.pdf
51. Estivill-Castro, V&Yang., J. (2000), Fast and Robust General Purpose Clustering Algorithms. In: Mizoguchi R., Slaney J. (eds) PRICAI 2000 Topics in Artificial Intelligence. PRICAI 2000. Lecture Notes in Computer Science. vol 1886. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44533-1_24.
52. Rendón, E., Abundez, I., Arizmendi, A., & Quiroz, E.M. (2011). Internal versus external cluster validation indexes. International Journal of Computers and Communications, 5(1).
53. Rocha, R., Atun, R., Massuda, A., Rache, B., Spinola, P., Nunes, L., Lago, M., & Castro, M.C. (2021). Effect of socioeconomic inequalities and vulnerabilities on health-system preparedness and response to COVID-19 in Brazil: a comprehensive analysis. Lancet Glob Health, 9, e782–92.
54. RStudio Team. (2021). RStudio: Integrated Development Environment for R. RStudio, PBC, Boston, MA http://www.rstudio.com/.
55. Sekula, M., Datta, S., & Datta, S. (2017). optCluster: An R package for determining the optimal clustering algorithm. Bioinformation, 13(3), 101-103. http://doi.org/:10.6026/97320630013101
56. Shahbazi, F., & Khazaei, S. (2020). Socio-economic inequality in global incidence and mortality rates from coronavirus disease 2019: an ecological study. New Microbe and New Infect, 38, 100762.
57. Sharma, A., Borah, S. B., & Moses, A.C. (2021). Responses to COVID-19: The role of governance, healthcare infrastructure, and learning from past pandemics. Journal of Business Research, 122, 597-607. https://doi.org/10.1016/j.jbusres.2020.09.011
58. Siddik, N. A. (2020). Economic stimulus for COVID-19 pandemic and its determinants: evidence from cross-country analysis. Heliyon, 6 (12). https://doi.org/10.1016/j.heliyon.2020.e05634.
59. Tosepu, R., Gunawan, J., Effendy, D. S., Lestari, H., Bahar, H., & Asfian, P. (2020). Correlation between weather and COVID-19 pandemic in Jakarta, Indonesia. Science of the Total Environment, 725, 138436.
60. Van Craenendonck, T., & Blockeel, H. (2015). Using Internal Validity Measures to Compare Clustering Algorithms. ICML 2015 AutoML Workshop.
61. Virgantari, & Faridhan, Y.E. K-means clustering of COVID-19 cases in Indonesia’s provinces, in: Proceedings of the International Conference on Global Optimization and Its Applications Jakarta, Indonesia (2020).
62. VoPham, T., Weaver, M.D., Hart, J. E., Ton, M., White, E., Newcomb, P. A. (2020). Effect of social distancing on COVID-19 incidence and mortality in the US. MedRxiv: the preprint server for health sciences. https://doi.org/10.1101/2020.06.10.20127589
63. Yuan, J., Wu, Y., Jing, W., Liu, J., Du, M., Wang, Y., & Liu, M. (2021). Association between meteorological factors and daily new cases of COVID-19 in 188 countries: A time series analysis, Science of The Total Environment, 780. https://doi.org/10.1016/j.scitotenv.2021.146538.
64. Wani, M.A. & Riyaz, R. A (2016). new cluster validity index using maximum cluster spread based compactness measure, International Journal of Intelligent Computing and Cybernetics. 9(2) 179-204. https://doi.org/10.1108/IJICC-02-2016-0006.
65. Wickham, H., Hester, J., & Chang, W. (2021). devtools: Tools to make developing R packages Easier. R package version 2.4.2. https://CRAN.R-project.org/package=devtools
66. Wu, J.T., Leung, K., & Leung, G.M. (2020). Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: A modeling study. The Lancet, 395 (10225), 689-697.