## 4 Results
### AD Definition as a Data Preprocessing Method (Substudy 1)
#### 4.1.1 Outlier Detection  
X-outliers, y-outliers and Model-outliers are detected on the preprocessed data via the different methods presented in Section 3.3. Figure 3a-c show a visual representation of the preprocessed data for the enthalpy only, according to the different categories of outliers, as well as according to the three studied methods for X-outlier detection. In particular, the x-axis corresponds to an anomaly score specific to each X-outlier detection method, while the y-axis corresponds to the standardized residual between the reference response value (DIPPR) and the predicted one by the Lasso model trained on the whole preprocessed data. Points identified as y-outliers are colored in red. Note that the implementation of the leverage method for X-outlier detection is not presented here due to the occurrence of numerical issues in the calculation of the hat values, probably due to existing multicollinearitiesbetween the descriptors (more than 2000 descriptors) that resulted in negative eigenvalues of the matrix \(X^{T}X\)[26; 61]. This is evidence of the limitations of the leverage method when applied to high-dimensional data. In addition, tSNE was preferred over PCA for projecting the descriptor space into a lower-dimensional space, since the number of PCs necessary to describe 95% of the data variance exceeds 200, with the first component containing only 20% of the variance (the numbers given are for the enthalpy, but the situation is similar for the entropy). For all three X-outlier detection methods, similar behavior can be observed in Figure 2(a)-c. Points showing a high score in the abscissa metric (i.e., considered as the \"most abnormal\" in descriptor space) tend to be better predicted (i.e., with lower absolute standardized residual values) than some points with lower abscissa values. It seems as if, even though these points are located \"further away\" in the descriptor space (i.e., in terms of the employed metric) than the majority of data, the model succeeds in \"extending\" the response hypersurface to include them [33]. The molecules displaying the highest absolute standardized residuals (Model-outliers) and the highest anomaly scores (X-outliers), according to the three investigated detection methods, are shown in Tables A1 and A2, respectively. The first category (i.e., Model-outliers) mainly includes molecules containing halogen, polyfunctional and silicon compounds, while in the second category (i.e., X-outliers) it is seen that _iForest_ and _RF confidence_ identify some common molecules, such as large silicon or halogen compounds. All these identified families share a common element of being poorly represented, as there is a lack of molecules containing the characteristic heteroatoms of these families in the database. This could be one of the reasons for their identification as outliers; for example, they can be easily isolated (_iForest_) or display high standard deviations in the individual trees' predictions (_RF confidence_). Note also that polyfunctional compounds combine several functional groups,  
Figure 3: Comparison of three X-outlier detection methods on the preprocessed data for **enthalpy**: (**a**) _iForest_, (**b**) _tSNE2D/kNN_, (**c**) _RF confidence_, (**d**) _RF confidence_ combined with H values. y-outliers are identified via the IQR method. thus conferring to these molecules a partial similarity, in terms of some descriptor values, to other species that also contain these groups, despite their overall different structures and enthalpy and/or entropy values. Additionally, for the two first molecules of Table 11, with chemid n\({}^{\circ}\)3608 and 2628, another explanation for their outlier behavior could be related to the significant difference (i.e., of 700 and 600 kJ/mol, respectively) that is observed in their enthalpy values with their counterparts with the same formula. Finally, concerning X-outlier detection, _tSNE2D/ANN_ does not seem to share any molecule in common with the two other methods.