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. 2022 Sep 20;12:15687. doi: 10.1038/s41598-022-19365-4

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© The Author(s) 2022

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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A plot of simulation results for the two clusters problem. All four clustering methods (GMM, K-means(C), K-means(E), and SASA) were tested on synthetic data with two clusters. The performance of clustering methods is monitored based on their adjusted rand index (ARI) value. In the above figure, the ‘Scenarios’ represent the number of variables with updated mean values in synthetic data, such as VarMod_0, all variables in synthetic data with zero mean; VarMod_10, 10 variables in synthetic data with mean value 0.5; VarMod_5, 5 variables in synthetic data with mean value 0.5. And the ‘Type’ represents the nested conditions with scenarios (0, all variables with mean 0; 1, variables with updated means in single cluster (VarMod_0_5, VarMod_0_10); 2, variables with updated means in both clusters (VarMod_5_5, VarMod_10_10); 3, simulation with added noise (VarMod_5_5_addnoise, VarMod_10_10_addnoise). The details of the statistical and spatial parameters modified are given in Fig. 2.