Semi-supervised LIBS quantitative analysis method based on co-training regression model with selection of effective unlabeled samples

The accuracy of laser-induced breakdown spectroscopy (LIBS) quantitative method is greatly dependent on the amount of certified standard samples used for training. However, in practical applications, only limited standard samples with labeled certified concentrations are available. A novel semi-supervised LIBS quantitative analysis method is proposed, based on co-training regression model with selection of effective unlabeled samples. The main idea of the proposed method is to obtain better regression performance by adding effective unlabeled samples in semi- supervised learning. First, effective unlabeled samples are selected according to the testing samples by Euclidean metric. Two original regression models based on least squares support vector machine with different parameters are trained by the labeled samples separately, and then the effective unlabeled samples predicted by the two models are used to enlarge the training dataset based on labeling confidence estimation. The final predictions of the proposed method on the testing samples will be determined by weighted combinations of the predictions of two updated regression models. Chromium concentration analysis experiments of 23 certified standard high-alloy steel samples were carried out, in which 5 samples with labeled concentrations and 11 unlabeled samples were used to train the regression models and the remaining 7 samples were used for testing. With the numbers of effective unlabeled samples increasing, the root mean square error of the proposed method went down from 1.80% to 0.84% and the relative prediction error was reduced from 9.15% to 4.04%.