📄 chemistry

A Comparative Evaluation of Sample Selection Algorithms for Multivariate Calibration in Near-Infrared Spectroscopic Analysis of Pharmaceutical Formulations

This study demonstrates that the Kennard–Stone algorithm, evaluated via Gaussian process regression on paracetamol tablet NIR spectra, outperforms other sample selection methods in generating robust multivariate calibration models, as confirmed by superior predictive statistics and rigorous non-parametric testing.

Original authors: Amanita Sow, Harouna Sangaré, Fadaba Danioko, Tidiane Diallo

Published 2026-09-09

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CC BY 4.0

Original authors: Amanita Sow, Harouna Sangaré, Fadaba Danioko, Tidiane Diallo

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the world of pharmaceutical manufacturing, ensuring that every pill contains the exact right amount of medicine is a matter of safety and trust. For decades, chemists have relied on a technique called near-infrared spectroscopy to check this quality. Imagine shining a special kind of light onto a pile of crushed medicine powder; the way the powder bounces that light back creates a unique fingerprint that reveals its chemical makeup. This method is fast, does not destroy the sample, and requires very little preparation. However, turning these light patterns into a reliable tool for measuring drug strength is not as simple as pointing a camera and taking a picture. The computer needs to learn how to read these fingerprints, a process called building a model. To teach the computer, scientists must show it a collection of samples with known drug amounts. The critical challenge lies in deciding which specific samples to show the computer for learning and which to save for a final test. If the learning group is chosen poorly, the computer might memorize the training examples perfectly but fail completely when it encounters a new, unseen pill.

A team of researchers in Bamako, Mali, set out to solve this specific puzzle of sample selection. They worked with fifty-eight commercial paracetamol tablets, representing different batches from pharmacies across the city. Their goal was to test four different computer strategies for splitting these fifty-eight tablets into a learning group and a testing group. One strategy, known as the Kennard–Stone algorithm, works by picking samples that are as different from each other as possible, ensuring the computer sees the full range of variations. Another, called the Honigs method, picks samples that add the most new information at each step. A third approach, Duplex, tries to build the learning and testing groups at the same time to keep them balanced, while the fourth, Naes, groups similar tablets together and picks a representative from each group. To see which strategy worked best, the researchers used a sophisticated mathematical approach called Gaussian process regression to build their models, a method they had previously found to be highly effective for this type of data.

The results were clear and decisive. When the researchers compared the performance of these four strategies, the Kennard–Stone algorithm emerged as the most reliable, followed closely by the Honigs method. The models built using these two strategies predicted the drug content with near-perfect accuracy, achieving a score of 0.99999 on a scale where one is perfect, and making errors so small they were measured in millionths. In contrast, the Duplex and Naes strategies, while showing excellent results during the training phase, performed significantly worse when tested on new data. This indicated that those methods had likely led the computer to memorize the training set rather than learn the underlying patterns, a problem known as overfitting. The researchers also tested a simple random selection method, where tablets were split into groups by chance, and found it produced the poorest results of all, confirming that a thoughtful, systematic approach is essential.

To ensure these findings were not just a lucky fluke, the team subjected the data to rigorous statistical testing. The analysis confirmed that the superior performance of the Kennard–Stone and Honigs methods was statistically significant and not due to random chance. Interestingly, the statistical tests showed that the Kennard–Stone and Honigs methods were effectively equivalent in their ability to produce accurate models, giving scientists flexibility in choosing between them. The researchers also investigated how the size of the learning group affected the outcome. They found a steady, predictable relationship: as the learning group grew larger, taking up more of the total samples, the model's accuracy improved. The best results were seen when the learning group comprised between 80 and 90 percent of the total samples, suggesting that for this specific type of medicine, a large training set yields the most robust predictions.

The study also examined the mathematical tools used to measure how different the samples were from one another. For the top-performing Kennard–Stone algorithm, using a specific type of distance measurement that accounts for how the different parts of the light spectrum relate to each other proved superior to a simpler measurement. This nuance mattered, as it allowed the algorithm to better understand the complex structure of the data. The researchers concluded that for anyone developing these rapid testing methods for pharmaceuticals, using a systematic selection strategy like Kennard–Stone or Honigs is far better than guessing or picking samples at random. Their work provides a clear, evidence-based guide for ensuring that the computer models used to check our medicine are built on the strongest possible foundation, ensuring that the pills we take are exactly what they are supposed to be.

Technical Summary: Comparative Evaluation of Sample Selection Algorithms for NIR Multivariate Calibration

Problem Statement
The development of robust multivariate calibration models for Near-Infrared (NIR) spectroscopic analysis in pharmaceutical quality control faces a critical methodological challenge: the rational partitioning of available samples into calibration (training) and validation sets. Inadequate sample selection leads to model overfitting, where excellent calibration statistics mask poor predictive performance on novel samples, while unnecessarily large calibration sets increase analytical costs without proportional gains in accuracy. Although several algorithms exist to optimize this partitioning, the literature lacks rigorous statistical validation of their relative performance, systematic investigation into the influence of distance metrics (Euclidean vs. Mahalanobis) on correlated spectral data, and comprehensive analysis of training set proportions across multiple split ratios.

Methodology
This study conducted a systematic comparative analysis of four established sample selection algorithms applied to NIR spectral data from 58 commercial paracetamol tablets (500 mg) acquired from pharmacies in Bamako, Mali.

Data Acquisition: Samples were analyzed using a reflectance spectrometer (800–1700 nm), with spectra preprocessed using Savitzky–Golay smoothing.
Modeling Framework: Gaussian Process Regression (GPR) with a radial basis function kernel served as the modeling framework, chosen for its demonstrated efficacy in previous studies on this dataset.
Algorithms Evaluated:
1. Kennard–Stone: Selects samples to maximize multivariate space coverage.
2. Honigs: Iteratively selects spectrally distinct samples based on residual projection.
3. Duplex: Simultaneously constructs balanced calibration and validation sets.
4. Naes: A clustering-based approach ensuring representation of all sample subtypes.
Experimental Design: Each algorithm was tested with both Euclidean and Mahalanobis distance metrics. Performance was evaluated across training set proportions ranging from 60% to 90%.
Statistical Analysis: Model performance was quantified using the coefficient of determination ( $R^2$ ) and Root Mean Square Error of Prediction (RMSEP). Differences between algorithms were validated using non-parametric Kruskal–Wallis tests followed by post-hoc Mann–Whitney U tests with Bonferroni correction to avoid distributional assumptions.

Key Results

Algorithm Performance: The Kennard–Stone algorithm employing the Mahalanobis distance metric demonstrated superior predictive accuracy, yielding a validation $R^2$ of 0.99999 and an RMSEP of $1.74 \times 10^{-6}$ . The Honigs algorithm showed comparable performance ( $R^2 = 0.999996$ , RMSEP = $1.76 \times 10^{-6}$ ).
Statistical Significance: Non-parametric testing confirmed highly significant differences among the algorithms ( $p < 0.001$ ). Post-hoc analysis revealed that both Kennard–Stone and Honigs significantly outperformed Duplex, Naes, and random splitting methods. Crucially, no statistically significant difference was found between Kennard–Stone and Honigs ( $p = 1.000$ after correction), indicating statistical equivalence for this dataset.
Overfitting in Other Methods: Naes and Duplex algorithms produced excellent calibration statistics but degraded validation performance, suggesting they selected calibration samples that inadequately represented the variability of the validation set.
Training Set Size: A monotonic relationship was observed between training set size and predictive accuracy. Performance improved as the training proportion increased from 60% to 90%, with diminishing returns observed beyond the 80–90% threshold.
Distance Metrics: For the Kennard–Stone algorithm, the Mahalanobis distance yielded superior validation results compared to the Euclidean distance, attributed to its ability to account for inter-wavelength correlations in NIR data. For the Honigs algorithm, both metrics performed comparably.

Significance and Claims
The authors assert that this work provides evidence-based guidance for optimizing sample selection protocols in pharmaceutical NIR applications. The study claims to fill specific gaps in the literature by:

Establishing the statistical equivalence of Kennard–Stone and Honigs methods through rigorous hypothesis testing, offering practitioners flexibility in algorithm selection based on computational or implementation preferences.
Demonstrating the critical importance of using the Mahalanobis distance metric for Kennard–Stone applications involving correlated spectral data.
Reinforcing the necessity of external validation over calibration metrics alone, as evidenced by the overfitting tendencies of Naes and Duplex methods.
Providing a validated workflow for paracetamol quantification, recommending the Kennard–Stone algorithm with Mahalanobis distance as a robust approach for sample set partitioning.

The paper concludes that while future work could explore diverse pharmaceutical classes and advanced optimization techniques (e.g., genetic algorithms), the current findings offer a methodologically sound foundation for developing NIR-based pharmaceutical assays.

Technical Summary: Comparative Evaluation of Sample Selection Algorithms for NIR Multivariate Calibration

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