## 4 Results and Discussion
### ML Classification
#### 4.3.1 Receiver Operating Characteristic Curve (ROC) and Area under Curve (AUC)  
To depict how well the meta-models are able to predict the probability of intrinsic compression index belonging to the different soil classes across some decision thresholds, the AUC-ROC are used. ROC plots the true positive rate (TPR) or sensitivity against false positive rate (FPR) or one less specificity given under various thresholds therefore separating \"noise\" from \"signals\" (Figure 12). Higher values on the horizontal axis, indicates higher number of the false positives compared to the true negatives. On the other hand, higher values on the vertical axis, indicate a higher number of true positives compared to false negatives. Hence, balancing between false positive and false negatives remains the choice of a chosen threshold. Meanwhile, AUC measures the actual capability of a model to differentiate between class labels. Hence, the higher the larger of AUC, the better the classifier at being able to distinguish between the positive and negative classes. When AUC equals 1, it therefore means that the model has been able to perfectly distinguish between the classes. However, a zero value would mean that the model has predicted all the positives as negatives and all the negativesas positives. When AUC is between 0.5 and 1, it means there is a higher chance that the model is capable of detecting more numbers of true positives and negatives than false negatives and positives. If AUC is exactly 0.5, then it means that the classifier is not able to differentiate between classes, in which case, it is just predicting constant or random class. Figure 11: Distribution of residuals. It could be observed from the ROC (Figures 13 and 14) that the meta-ensembles all demonstrate the ability to discriminate between positive and negative classes. This also means that using the meta-ensembles in the multinomial class prediction has enabled a reduction in both type 1 and 2 prediction errors. Figure 14: ROC plot for VE model. Figure 12: Typical ROC plots. Figure 13: ROC plot for SE model. The dataset training and testing performed using the TVS appears to show perfect classification with an alignment of ROC with the top horizontal and left vertical axes. This again indicates an overfitting of the dataset given that the application of iterative cross validation techniques (kFCV and MCCV) results in slightly lower sensitivity compared to the TVS method. A closer examination of the corresponding Tables 6 and 7 for both voting and stacking methods of model aggregation indicates that ML training and validation done by utilising the kFCV has the most sensitivity in distinguishing between the soil categories but with the 5-fold validation case having the highest overall AUC. Further analysis of sensitivity as given by Table 8 indicates that the kFCV method has the best accuracy, recall rate and precision. When compared with the TVS method (with 20% of the dataset) originally used for testing of the algorithm, it could be observed that when using 5-fold cross validation multiclass predictions are higher by approximately 10-25% in terms of accuracy, rate of recall and precision. It is also interesting to observe that the kFCV method does also performs slightly better than MCCV on a multiclass problem such as that considered in this research. In this case, the disadvantage of using MCCV seems to weigh more heavily on multiclass prediction than on non-linear regression. Table 8 also indicate that the assignment of uniform weights to cater for any under-represented class instances does clearly improves the individual multiclass accuracy compared to the overall accuracy metric. Further, it is also worth noting that the averaging of each class instances (i.e., micro-averaging), presents higher scores compared to the averaging that considers all equal class instances (i.e., macro-averaging) with respect to the most frequently occurring labels.