Novel strategy for effective selection of characteristic spectra of milk minerals

Accurate selection of characteristic spectra is essential to improving the predictive accuracy of spectral models. While conventional spectral selection methods moderately enhance predictive capabilities, they often exhibit limited correlation and precision between the selected wavelengths and the target substance (e.g., minerals in milk), thereby constraining the model's predictive performance. In response, this study introduces a novel Multi-Characteristic Random Frog (MCRF) strategy, designed to enhance the accuracy and robustness of spectral selection through a dual criterion based on the significance (contribution rate) and selection probability of spectral bands relative to the target substances. This study focuses on five essential macrominerals (Ca, K, Na, Mg, P) and five trace minerals (Cu, Fe, Mn, Sr, Zn) present in milk. Using the MCRF strategy alongside three established spectral selection techniques—Competitive Adaptive Reweighted Sampling (CARS), Uninformative Variable Elimination (UVE), and RF—we identified the characteristic spectra for each mineral. These spectra, combined with preprocessed infrared spectra of milk and Partial Least Squares Regression (PLSR) modeling, were employed to establish predictive models for the mineral concentrations. Compared to the three conventional selection methods, the MCRF strategy significantly enhanced the predictive precision of the mineral content models. Specifically, the Ca content predictive model, constructed using the SNV spectral preprocessing + MCRF strategy + PLSR algorithm, demonstrated high predictive performance, achieving an R 2 of 0.96, RMSE of 38.14 mg/kg, and RPD of 4.82—optimizing the model by 5.49 %, 32.23 %, and 47.85 % over the full-spectrum model. Similarly, the P content model (SNV + MCRF + PLSR) exhibited an R 2 of 0.76, RMSE of 66.04 mg/kg, and RPD of 2.04, improving predictive accuracy by 8.57 %, 10.71 %, and 12.09 %, respectively. Predictive models for the other eight mineral contents established with MCRF-selected characteristic spectra also displayed strong predictive capabilities (R 2 ranging from 0.57 to 0.68). The findings demonstrate that the MCRF strategy provides a marked improvement in spectral authenticity and predictive precision. This novel approach offers an effective strategy for the selection of characteristic spectra and the development of accurate predictive models for mineral and other compositional contents in milk. • This is the first time that 9 mineral prediction models have been established using mineral content data from dairy cattle in China. • This is the first time that the Multi-Characteristic Random Frog (MCRF) strategy has been used in the establishment of a prediction model for milk minerals. • Ca content predictive model using the SNV spectral preprocessing + MCRF strategy + PLSR algorithm, achieving an R2 of 0.957.