Rapid quantitative analysis of calcium in infant formula powder assisted by long short-term memory with variable importance using laser-induced breakdown spectroscopy

Calcium is the main mineral responsible for healthy bone growth in infants. In this study, LIBS was combined with a variable importance-based long short-term memory (VI-LSTM) for the quantitative analysis of calcium in infant formula powder. Firstly, the full spectra were used to establish PLS (partial least square) and LSTM models. The R2 and root-mean-square error (RMSE) of the test set (R2P and RMSEP) were 0.1460 and 0.0093 in the PLS method, respectively, and 0.1454 and 0.0091 in the LSTM model, respectively. To improve the quantitative performance, variable selection based on variable importance was introduced to evaluate the contribution of input variables. The variable importance-based PLS (VI-PLS) model had R2P and RMSEP of 0.1454 and 0.0091, respectively, whereas the VI-LSTM model had R2P and RMSEP of 0.9845 and 0.0037, respectively. Compared with the LSTM model, the number of input variables in the VI-LSTM model was reduced to 276, R2P was improved by 114.63%, and RMSEP was reduced by 46.38%. The mean relative error of the VI-LSTM model was 3.33%. This study confirms the predictive ability of the VI-LSTM model for calcium element in infant formula powder. Thus, combining VI-LSTM modeling and LIBS has great potential for the quantitative elemental analysis of dairy products.