I. Made Sumertajaya, Fahrezal Zubedi, Khairil Anwar Notodiputro, Utami Dyah Syafitri
This study proposes a robust generalized principal component analysis (RGPCA) framework that integrates Euler transformation to improve dimensionality reduction in the presence of outliers. Unlike conventional generalized principal component analysis (GPCA), which is sensitive to anomalous observations, the proposed method enhances robustness by transforming the data distribution while preserving its structural characteristics. The effectiveness of RGPCA is evaluated through simulation experiments under varying outlier proportions. The results demonstrate that RGPCA consistently outperforms GPCA in outlier-contaminated datasets, achieving lower reconstruction errors, with Root Mean Square Error (RMSE) values ranging from 2.10 to 3.40 compared to 2.70 to 4.00 for GPCA at a 10% outlier level. Although GPCA shows slightly better performance on clean data, the difference remains marginal. The proposed method is further applied to human development indicator data in Indonesia, where it effectively captures structural patterns and temporal variations across districts. The findings confirm that the integration of Euler transformation significantly enhances the robustness and stability of GPCA, providing a reliable approach for high-dimensional data analysis in the presence of outliers. ©2026 The authors.
Statistics and Data Science Study Program, IPB University, Bogor, 16680, Indonesia; Department of Mathematics, State University of Gorontalo, Gorontalo, 96128, Indonesia
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