Improving Grading Accuracy by Optimizing the Logistic Loss Function in PLS Modelling

Abstract

The prediction results from Partial Least Squares (PLS) model are commonly used to assess whether a product meets quality standards, or whether adjustments are needed in production process parameters. It's easy to understand that misgrading is mostly occurred for marginal samples (samples near the threshold). We propose Logistic-Enhanced PLS (LE-PLS) model, which defines a logistic loss function and minimizes it via gradient descent to optimize the PLS projection vector. The prediction result of LE-PLS for marginal samples tends to be far away from the threshold value. This optimization enables LE-PLS to enhance grading capability while largely maintaining the regression accuracy of the PLS. LE-PLS was evaluated on two real-world datasets (bean pulp and corn gluten meal) and one simulated dataset, correcting 10 out of 19 misgraded samples, 6 out of 7, and 6 out of 12, respectively. Statistical analysis using paired t-tests confirmed that these improvements were significant. Although RMSEP increased slightly, the change remained within an acceptable range considering the substantial enhancement in grading performance. The algorithm has a computational complexity of $O\left(\text{iteration}*\text{samples}*\text{variables}\right)$ during modeling training. However, its prediction-phase complexity is only $O\left(\text{samples}*\text{variables}\right)$. Given these advantages, LE-PLS is well-suited for practical applications in NIR-based quality grading of products.