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SpaceX
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NASA
СпутникиРНSpaceXРоскосмосNASASpatial clustering is important for identifying regions with similar spatial patterns in spatial datasets. This study focuses on selecting the optimal tuning parameter for the generalized lasso in spatial clustering analysis. Common approaches for selecting the tuning parameter in the generalized lasso include generalized cross-validation (GCV) and approximate leave-one-out cross-validation (ALOCV). However, these methods often produce substantially different tuning parameter values, which may lead to inconsistent clustering results and misinterpretation. In general, ALOCV tends to select larger tuning parameters, whereas GCV tends to select smaller ones. To address this issue, we propose an ensemble learning cross-validation (ELCV) approach that combines the validation errors from ALOCV and GCV using arithmetic, geometric, and harmonic means to obtain a more balanced tuning parameter selection. In addition, an analytical justification of the proposed ensemble framework is provided to demonstrate its theoretical relationship with ALOCV and GCV. A simulation study was conducted under four spatial clustering scenarios, namely three separated clusters, three connected clusters, five separated clusters, and five connected clusters, combined with three noise standard deviation levels to evaluate the robustness of the proposed methods. The Index of Edge Detection Accuracy (IEDA) was used as the primary criterion for assessing clustering performance. The simulation results showed that the proposed methods based on the geometric mean, and the harmonic mean, consistently achieved better and more stable performance across different scenarios and noise levels, as indicated by higher IEDA values and lower estimation errors compared to ALOCV and GCV. Finally, the proposed methods were applied to cluster the productivity of oil palm fresh fruit bunches (FFB) across several planting blocks in oil palm concessions in Kalimantan, Indonesia.
Spatial clustering is important for identifying regions with similar spatial patterns in spatial datasets. This study focuses on selecting the optimal tuning parameter for the generalized lasso in spatial clustering analysis. Common approaches for selecting the tuning parameter in the generalized lasso include generalized cross-validation (GCV) and approximate leave-one-out cross-validation (ALOCV). However, these methods often produce substantially different tuning parameter values, which may lead to inconsistent clustering results and misinterpretation. In general, ALOCV tends to select larger tuning parameters, whereas GCV tends to select smaller ones. To address this issue, we propose an ensemble learning cross-validation (ELCV) approach that combines the validation errors from ALOCV and GCV using arithmetic, geometric, and harmonic means to obtain a more balanced tuning parameter selection. In addition, an analytical justification of the proposed ensemble framework is provided to demonstrate its theoretical relationship with ALOCV and GCV. A simulation study was conducted under four spatial clustering scenarios, namely three separated clusters, three connected clusters, five separated clusters, and five connected clusters, combined with three noise standard deviation levels to evaluate the robustness of the proposed methods. The Index of Edge Detection Accuracy (IEDA) was used as the primary criterion for assessing clustering performance. The simulation results showed that the proposed methods based on the geometric mean, and the harmonic mean, consistently achieved better and more stable performance across different scenarios and noise levels, as indicated by higher IEDA values and lower estimation errors compared to ALOCV and GCV. Finally, the proposed methods were applied to cluster the productivity of oil palm fresh fruit bunches (FFB) across several planting blocks in oil palm concessions in Kalimantan, Indonesia.
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Program in Statistics and Data Science, School of Data Science, Mathematics, and Informatics, IPB University, Bogor, Indonesia
Septian Rahardiantoro, Sachnaz Desta Oktarina, Gerry Alfa Dito, Indahwati Indahwati & Anang Kurnia
Program in Statistics, Universitas Negeri Jakarta, Jakarta, Indonesia
Dian Handayani
Authors
Correspondence to Septian Rahardiantoro or Anang Kurnia.
This research is supported by The Directorate General of Higher Education, Research and Technology of the Ministry of Education, Culture, Research and Technology the Republic of Indonesia based on contract number 027/E5/PG.02.00.PL/2024 for the Fundamental Research schema. This research was also supported by the IPB University research grant “Penelitian Dosen Muda” 2024 under Contract Number 23445/IT3/PT.01.03/P/B/2024.
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Rahardiantoro, S., Oktarina, S.D., Dito, G.A. et al. The Ensemble Learning to Determine Optimal Tuning Parameter of the Generalized Lasso in Spatial Clustering Analysis. J Stat Theory Pract 20, 102 (2026). https://doi.org/10.1007/s42519-026-00627-7
Received: 15 April 2025
Accepted: 11 July 2026
Published: 22 July 2026
Version of record: 22 July 2026
DOI: https://doi.org/10.1007/s42519-026-00627-7