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Peer-reviewedCC BYPLOS One

Comparative study of quadratic regression, Lasso, random forest, and multilayer perceptron for modeling optimal solid density in offset printing

  • Bingzhong Qiu1
  • Liangfei Li2,3
  • Xiaoli Liu1
  • Xiaolei Sheng1
  • Yujun Jiang1
  • Xiaomei Liu1
  • Ying-Leh Ling4
4 affiliations
  1. 1General Education Department, Qilu Medical University, Zibo, Shandong, China.
  2. 2College of Vocational Education, Tianjin University of Technology and Education, Tianjin, China.
  3. 3Academic Affairs Office, Zibo Polytechnical Vocational School, Zibo, Shandong, China.
  4. 4Department of Mathematics, Science and Computer, Politeknik Kuching Sarawak, Sarawak, Malaysia.
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Abstract

This study compares four modeling methods, namely quadratic regression (QR), Lasso, random forest (RF), and multilayer perceptron (MLP), to determine the optimal solid density for four-color offset printing. Based on 110 valid samples for each ink color, random 5-fold cross-validation (CV) and paired t-tests were employed to evaluate model predictive accuracy (R2, RMSE) and the stability of the estimated optimal solid density (CV%). Under random 5-fold CV, non-parametric approaches (RF and MLP) outperformed parametric counterparts (QR and Lasso) for black, cyan, and magenta inks, and MLP yielded the optimal performance for yellow ink (R2 = 0.9770). Pairwise statistical tests showed no significant differences between RF and MLP for black, cyan, and magenta inks (p > 0.05), while MLP was statistically superior for yellow ink under random 5-fold CV (p = 0.0296). However, this ranking cannot be generalized to blocked cross‑validation (blocked‑CV). Two blocked‑CV strategies, temporal-block and spatial-block CV, were further implemented to mitigate data leakage arising from high lag-1 autocorrelation (0.96–0.98) in sequentially collected process data. Under blocked-CV, mean R2 values were negative across most models and ink colors, limiting the interpretability of inter-model rankings. While surfaces fitted under random 5-fold CV revealed nonlinear features including broad high-quality plateaus for cyan and magenta inks and multi-peak patterns for yellow ink, such features require cautious physical interpretation given validation-strategy dependence. Despite substantial drops in predictive performance metrics under blocked-CV, the estimated optimal solid densities were insensitive to the fold structure, with deviations ranging from 0.0034 to 0.0152 across all four ink colors. The recommended optimal solid densities are 1.67 (RF) for black ink, 1.44 (RF) for cyan ink, 1.42 (RF) for magenta ink, and 0.99 (MLP) for yellow ink. This study shows that although predictive performance metrics are highly sensitive to the validation strategies, the estimated optimal solid densities are insensitive to the fold structure examined here. This consistency is dataset‑specific and does not by itself establish out‑of‑sample validity under different printing conditions. For offset printing process optimization, the stability of the estimated optimal solid density offers greater practical engineering value than raw predictive performance or model ranking consistency.

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Cite

BibTeXRIS
BibTeX
@article{qiu2026comparative,
  title = {{Comparative study of quadratic regression, Lasso, random forest, and multilayer perceptron for modeling optimal solid density in offset printing}},
  author = {Bingzhong Qiu and Liangfei Li and Xiaoli Liu and Xiaolei Sheng and Yujun Jiang and Xiaomei Liu and Ying-Leh Ling},
  journal = {PLOS One},
  year = {2026},
  month = oct,
  doi = {10.1371/journal.pone.0361203},
  url = {https://doi.org/10.1371/journal.pone.0361203},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Comparative study of quadratic regression, Lasso, random forest, and multilayer perceptron for modeling optimal solid density in offset printing
AU  - Bingzhong Qiu
AU  - Liangfei Li
AU  - Xiaoli Liu
AU  - Xiaolei Sheng
AU  - Yujun Jiang
AU  - Xiaomei Liu
AU  - Ying-Leh Ling
PY  - 2026
DA  - 2026/10/21
JO  - PLOS One
DO  - 10.1371/journal.pone.0361203
UR  - https://doi.org/10.1371/journal.pone.0361203
AB  - This study compares four modeling methods, namely quadratic regression (QR), Lasso, random forest (RF), and multilayer perceptron (MLP), to determine the optimal solid density for four-color offset printing. Based on 110 valid samples for each ink color, random 5-fold cross-validation (CV) and paired t-tests were employed to evaluate model predictive accuracy (R2, RMSE) and the stability of the estimated optimal solid density (CV%). Under random 5-fold CV, non-parametric approaches (RF and MLP) outperformed parametric counterparts (QR and Lasso) for black, cyan, and magenta inks, and MLP yielded the optimal performance for yellow ink (R2 = 0.9770). Pairwise statistical tests showed no significant differences between RF and MLP for black, cyan, and magenta inks (p > 0.05), while MLP was statistically superior for yellow ink under random 5-fold CV (p = 0.0296). However, this ranking cannot be generalized to blocked cross‑validation (blocked‑CV). Two blocked‑CV strategies, temporal-block and spatial-block CV, were further implemented to mitigate data leakage arising from high lag-1 autocorrelation (0.96–0.98) in sequentially collected process data. Under blocked-CV, mean R2 values were negative across most models and ink colors, limiting the interpretability of inter-model rankings. While surfaces fitted under random 5-fold CV revealed nonlinear features including broad high-quality plateaus for cyan and magenta inks and multi-peak patterns for yellow ink, such features require cautious physical interpretation given validation-strategy dependence. Despite substantial drops in predictive performance metrics under blocked-CV, the estimated optimal solid densities were insensitive to the fold structure, with deviations ranging from 0.0034 to 0.0152 across all four ink colors. The recommended optimal solid densities are 1.67 (RF) for black ink, 1.44 (RF) for cyan ink, 1.42 (RF) for magenta ink, and 0.99 (MLP) for yellow ink. This study shows that although predictive performance metrics are highly sensitive to the validation strategies, the estimated optimal solid densities are insensitive to the fold structure examined here. This consistency is dataset‑specific and does not by itself establish out‑of‑sample validity under different printing conditions. For offset printing process optimization, the stability of the estimated optimal solid density offers greater practical engineering value than raw predictive performance or model ranking consistency.
SN  - 1932-6203
ER  -