## 6 Results
### Classification of Synthetic 7D Datasets
#### 6.3.1 Cloud Detection over Water Surfaces  
Within the real case experiment involving cloud discrimination using MODIS satellite spectral measurements (Figure 7), the reference quality metrics (ACC = 0.879, \(\kappa\) = 0.723) for the selected classifiers were derived from the Collection 6 AQUA MODIS cloud mask product (MYD35). In this respect, it has to be emphasized that the MYD35 product is globally applicable for all satellite zenith angles, whereas the classifiers selected are applicable close to the satellite nadir (due to an unrepresentative training dataset). Despite this fact, the decision tree classifier produced inferior results to the MYD35 product (ACC = 0.840, \(\kappa\) = 0.627), whereas all other methods with optimized hyper-parameters generated very similar and accurate classifications. As compared to the VEOR algorithm (ACC = 0.888, \(\kappa\) = 0.748), the Naive Bayes (ACC = 0.880, \(\kappa\) = 0.734), Gaussian process (ACC = 0.882, \(\kappa\) = 0.736), QDA (ACC = 0.883, \(\kappa\) = 0.736), nearest neighbor (ACC = 0.884, \(\kappa\) = 0.738), linear SVM (ACC = 0.885, \(\kappa\) = 0.739) and RBF SVM (ACC = 0.886, \(\kappa\) = 0.745) classifiers were slightly less accurate, while the random forest (ACC = 0.889, \(\kappa\) = 0.747), neural net (ACC = 0.890, \(\kappa\) = 0.752) and AdaBoost (ACC = 0.891, \(\kappa\) = 0.753) classifiers were slightly more accurate. It could be noticed that many classifiers discriminated cloud cover over water surfaces with almost the same classification quality metrics. This may indicate that several methods reached almost maximum classification accuracy given the radiometric sensitivity of the MODIS instrument and the collocation inaccuracies with the CALIOP and CPR sensors.  
Regardless of the very similar classification results, the forward feature selection procedure applied to each classifier resulted in different optimal combinations of input features over water surfaces (see Appendix A). In this respect, the VEOR algorithm selected four optimal features ordered according to decreasing importance: B18_936 nm, B32_12020 nm, sumz, B30_9730 nm (for abbreviations, see Table 3). The first two features (the most important) were also selected by the nearest neighbor, neural net, decision tree and random forest classifiers, while linear SVM, Naive Bayes and QDA did not select even one of them. Other features that were often selected were: B29_8550 nm_B31_11030 nm_diff (6 times), B29_8550 nm_B31_11030 nm_diff (3 times), B29_8550 nm_B31_11030 nm_diff (3 times), NDVI (3 times). All of the algorithms apart from the linear SVM required some angular feature, but the type of this information varied significantly. The Sun zenith angle was required only by the VEOR algorithm. The Sun azimuth angle was optimal for the nearest neighbor, decision tree and Naive Bayes classifiers. The scattering angle was selected by the neural network, random forest, AdaBoost, Naive Bayes and QDA algorithms, while the relative azimuth angle was required by the RBF SVM and Gaussian process classifiers. The satellite zenith angle was not selected by any method because collocations of the CALIPSO and CPR profiles with the AQUA MODIS radiometer were only available close to the satellite nadir. The inconsistency in the selected angular features is not easily explainable as it is a combination of physics and data sampling. Based on the VEOR output, the angular information itself is a weak classification feature for cloud discrimination and it slightly improves the overall accuracy over water surfaces close to the satellite nadir. Thus, in the case of the stochastic classifiers, different features (including angular ones) might be selected between consecutive algorithm runs with the same input data.  
Cloud discrimination over water surfaces during daytime is a fairly simple classification task. Therefore, to fully evaluate the performance of the selected classifiers, an analogous experiment over snow/ice surfaces was performed (see next subsection).