DOI: 10.1371/journal.pone.0361203 ISSN: 1932-6203

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

Bingzhong Qiu, Liangfei Li, Xiaoli Liu, Xiaolei Sheng, Yujun Jiang, Xiaomei Liu, Ying-Leh Ling
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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 (

R 2
, 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 (
R 2
= 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
R 2
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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