Clustering for Mapping Food Insecurity in the Land of Papua: A Five-Year Multiyear Analysis with Spatial Interpretation (2020-2024)

Ishak Semuel Beno, Alvian M Sroyer, Felix Reba, Remuz M. B. Kmurawak, Antonius A. P. Tama

Abstract


Food insecurity in the Land of Papua remains a critical issue due to extreme geographical conditions, limited infrastructure, and unstable food distribution systems. This study aims to map food vulnerability across 42 districts/cities in Papua using insufficient food consumption data from 2020 to 2024. Clustering was performed using five methods—Single Linkage, Complete Linkage, Ward, K-Means, and Gaussian Mixture Model (GMM)—and evaluated using three validation indices: Silhouette, Davies–Bouldin Index (DBI), and Calinski–Harabasz Index (CHI). To obtain a balanced and comprehensive model selection, a Performance-Based Weighting (PBW) framework was applied. In this framework, the DBI was first transformed to ensure a consistent higher-is-better orientation, and all validation indices were normalized to the [0,1] range prior to computing variance-based weights. This normalization step mitigates potential scale dominance, particularly from the unbounded CHI metric, ensuring proportional contribution from each validation criterion in the aggregated score. Although individual validation indices exhibited varying optimal values of k, the integrated PBW evaluation consistently identifies the two-cluster configuration as the most stable and interpretable overall structure. Specifically, Complete Linkage with k = 2 achieved the highest combined PBW score (0.8658), reflecting strong cluster separation and consistency across validation measures. Spatial interpretation of the resulting clusters reveals that the first cluster predominantly consists of high-risk mountainous districts with persistently elevated levels of food consumption inadequacy, particularly during 2021–2022, while the second cluster represents coastal and urban regions with comparatively lower and improving prevalence in 2023–2024. These findings provide a multiyear clustering perspective with geographic insight into regional disparities in food insecurity across Papua. Overall, this study presents a data-driven and reproducible multiyear clustering framework that integrates multiple validation criteria to enhance robustness in model selection and support evidence-based regional policy formulation.


Keywords


food insecurity; clustering; multiyear analysis; spatial interpretation; Silhouette; Davies–Bouldin Index; Calinski–Harabasz Index.

Full Text:

PDF

References


[1] UNICEF, The State of Food Security and Nutrition in the World 2023. UNICEF, 2023.

[2] World Food Programme, “Asia and the pacific–regional overview of food security and nutrition 2022,” WFP, 2023.

[3] S. K. Dermoredjo, U. Mu’awanah, A. S. Hidayat, R. P. Hidayat, W. Estiningtyas, and S. M. Pasaribu, “National food development policies in indonesia: An analysis of food sustainability and security,” in BIO Web of Conferences, vol. 119, EDP Sciences, 2024, 381 p. 05 006. doi: 10.1051/bioconf/202411905006.

[4] I. Tjolli, M. Karuniasa, A. B. Rehiara, S. Jance, and I. Lestari, “Development of the sustainable human development index model in west papua,” in IOP Conference Series:Earth and Environmental Science, vol. 716, IOP Publishing, 2021, p. 012 106. doi: 10.1088/1755-1315/716/1/012106.

[5] K. Kim, S. Kim, and C. Y. Park, Food Security in Asia and the Pacific amid the COVID-19Pandemic. Mandaluyong, Philippines: Asian Development Bank, 2020, vol. 6.

[6] S. Fan, P. Teng, P. Chew, G. Smith, and L. Copeland, “Food system resilience and covid-19–lessons from the asian experience,” Global Food Security, vol. 28, p. 100 501, 2021. doi:10.1016/j.gfs.2020.100501.

[7] R. Virtriana et al., “Development of spatial model for food security prediction using remotesensing data in west java, indonesia,” ISPRS International Journal of Geo-Information,vol. 11, no. 5, p. 284, 2022. doi: 10.3390/ijgi11050284.

[8] W. A. Teniwut, “Challenges in reducing seaweed supply chain risks arising within andoutside remote islands in indonesia: An integrated mcdm approach,” in SustainabilityModeling in Engineering: A Multi-Criteria Perspective, Springer, 2020, pp. 271–291.

[9] U. Maulik and S. Bandyopadhyay, “Performance evaluation of some clustering algorithmsand validity indices,” IEEE Transactions on Pattern Analysis and Machine Intelligence,vol. 24, no. 12, pp. 1650–1654, 2003. doi: 10.1109/TPAMI.2002.1114856.

[10] M. Mittal, L. M. Goyal, D. J. Hemanth, and J. K. Sethi, “Clustering approaches forhigh-dimensional databases: A review,” WIREs Data Mining and Knowledge Discovery,vol. 9, no. 3, e1300, 2019. doi: 10.1002/widm.1300.

[11] L. Kaufman and P. J. Rousseeuw, Finding Groups in Data: An Introduction to ClusterAnalysis. John Wiley & Sons, 2009.[12] B. S. Everitt, S. Landau, M. Leese, and D. Stahl, Cluster Analysis. Wiley, 2011.

[13] F. Murtagh and P. Legendre, “Ward’s hierarchical agglomerative clustering method: Whichalgorithms implement ward’s criterion?” Journal of Classification, vol. 31, no. 3, pp. 274–295, 2014. doi: 10.1007/s00357-014-9161-z.

[14]F. Murtagh and P. Contreras, “Algorithms for hierarchical clustering: An overview,” WIREsData Mining and Knowledge Discovery, vol. 2, no. 1, pp. 86–97, 2012. doi: 10.1002/widm.53.

[15] I. Assent, “Clustering high dimensional data,” WIREs Data Mining and Knowledge Dis413covery, vol. 2, no. 4, pp. 340–350, 2012. doi: 10.1002/widm.1062.

[16] S. Lloyd, “Least squares quantization in pcm,” IEEE Transactions on Information Theory,vol. 28, no. 2, pp. 129–137, 1982. doi: 10.1109/TIT.1982.1056489.

[17] J. A. Hartigan and M. A. Wong, “Algorithm as 136: A k-means clustering algorithm,”Journal of the Royal Statistical Society: Series C (Applied Statistics), vol. 28, no. 1, pp. 100–108, 1979. doi: 10.2307/2346830.

[18] A. Ashabi, S. B. Sahibuddin, and M. Salkhordeh Haghighi, “The systematic review ofk-means clustering algorithm,” in Proceedings of the 2020 9th International Conference onNetworks, Communication and Computing, 2020, pp. 13–18.

[19] C. M. Bishop and N. M. Nasrabadi, Pattern Recognition and Machine Learning. New York:Springer, 2006.

[20] G. J. McLachlan, S. X. Lee, and S. I. Rathnayake, “Finite mixture models,” Annual Reviewof Statistics and Its Application, vol. 6, no. 1, pp. 355–378, 2019. doi: 10.1146/annurev-statistics-031017-100325.

[21] V. E. Neagoe and V. Chirila-Berbentea, “Improved gaussian mixture model with expectation428maximization for clustering of remote sensing imagery,” in IEEE International Geoscienceand Remote Sensing Symposium (IGARSS), IEEE, 2016, pp. 3063–3065. doi: 10.1109/IGARSS.2016.7729856.

[22] P. J. Rousseeuw, “Silhouettes: A graphical aid to the interpretation and validation ofcluster analysis,” Journal of Computational and Applied Mathematics, vol. 20, pp. 53–65,1987. doi: 10.1016/0377-0427(87)90125-7.

[23] A. K. Jain and R. C. Dubes, Algorithms for Clustering Data. Prentice-Hall, 1988.

[24] O. Arbelaitz, I. Gurrutxaga, J. Muguerza, J. M. Pérez, and I. Perona, “An extensivecomparative study of cluster validity indices,” Pattern Recognition, vol. 46, no. 1, pp. 243–256, 2013. doi: 10.1016/j.patcog.2012.07.021.




DOI: https://doi.org/10.18860/cauchy.v11i1.40366

Refbacks

  • There are currently no refbacks.


Copyright (c) 2026 Ishak Semuel Beno

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Gajayana Street 50 Malang, East Java, Indonesia 65144
Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.