2.4.3. Partial Least Square Discriminant Analysis (PLS-DA)

PLS-DA was applied to HSI data to build a predictive model able to classify tile and cement mortar. This classification technique combines the properties of partial least squares regression with the ability of a classification technique. It is a classification method used to find a model able to predict the known classes in an unknown image [52,53,54]. Prior knowledge of the data was required. Starting from known samples, a distinguishing function is built to predict the new unknown object in the HSI image, made of the same materials of the known classes.

PLS-DA is used to classify samples into predefined groups by forming discriminant functions from input variables (i.e., wavelengths) to yield a new set of transformed values that provides more accurate discrimination than any single variable (i.e., wavelength). A discriminant function is then built using samples with known groups to be employed later to classify samples with an unknown group set. Therefore, once the model is obtained, it can be applied to an entire hypercube and for the classification of a new hypercube. The same pre-processing algorithms used in the PCA step were applied. The result of PLS-DA, applied to the hypercubes, is a “prediction map”, where the classes (i.e., tile and cement mortar) are defined by different colors.

Classification models were then evaluated using the following parameters: Sensitivity and Specificity in calibration (Cal) and cross-validation (CV):

where TP are true positive, TN true negative and FN false negatives. The best models are obtained when similar values are obtained for Sensitivity and Specificity in Cal and CV, thus demonstrating the robustness of the developed model [55]. Receiver Operating Characteristics (ROC) curves were adopted to evaluate the classification capability of the model. A perfect classification method would yield a point in the upper left corner of the ROC space, representing maximum sensitivity and specificity, while a random classification gives points along the diagonal line from the left bottom to the top right corner [52].

Finally, the prediction results, in terms of pixel percentage (i.e., tile and cement mortar presence in each fragment), obtained by the PLS-DA model were compared with those coming from the micro-XRF map obtained by class set on PC1-PC2 score plot.