## 3 Results
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metric** & **SROCC** & **KROCC** & **PLCC** \\ \hline \(CM_{2}\) (LPCSI, IL-NIQE) & 0.5352 & 0.3783 & 0.0553 \\ \(CM_{2}\) (HOSA, IL-NIQE) & 0.5255 & 0.3732 & 0.4040 \\ \(CM_{2}\) (TCLT, IL-NIQE) & 0.5225 & 0.3690 & 0.1829 \\ \(CM_{2}\) (WINE, IL-NIQE) & 0.5191 & 0.3728 & 0.3092 \\ \(CM_{2}\) (HOSA, LPCSI) & 0.5154 & 0.3615 & \textless{}0.1 \\ \hline \(CM_{2}^{+}\) (PSI, CORNIA) & 0.5631 & 0.3978 & 0.4922 \\ \(CM_{2}^{+}\) (PSI, IL-NIQE) & 0.5571 & 0.3955 & \textless{}0.1 \\ \(CM_{2}^{+}\) (HOSA, IL-NIQE) & 0.5425 & 0.3877 & \textless{}0.1 \\ \(CM_{2}^{+}\) (SBSBLIM\_WM, IL-NIQE) & 0.5384 & 0.3804 & \textless{}0.1 \\ \(CM_{2}^{+}\) (CORNIA, Blur Metric) & 0.5372 & 0.3801 & \textless{}0.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance of the five best combinations of two NR elementary metrics (\(N=2\)) for the whole-TID2013 dataset assuming the use of the weighted product (\(CM_{2}\)) and weighted sum (\(CM_{2}^{+}\)). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metric** & **SROCC** & **KROCC** & **PLCC** \\ \hline \(CM_{3}\) (ARISM, IL-NIQE, BIBLE) & 0.7839 & 0.5856 & 0.2993 \\ \(CM_{4}\) (ARISM, IL-NIQE, BIBLE, WNJE) & 0.8056 & 0.6129 & 0.2769 \\ \(CM_{5}\) (ARISMC, IL-NIQE, BIBLE, WNJE, GM\_LOG) & 0.8132 & 0.6243 & 0.5847 \\ \hline \(CM_{3}^{+}\) (ARISMC, IL-NIQE, CORNIA) & 0.8089 & 0.6122 & 0.7024 \\ \(CM_{4}^{+}\) (ARISMC, IL-NIQE, CORNIA, WNJE) & 0.8315 & 0.6406 & 0.7922 \\ \(CM_{5}^{+}\) (ARISMC, IL-NIQE, CORNIA, WNJE, QAC) & 0.8406 & 0.6522 & 0.8320 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Performance of the best combinations of NR elementary metrics (\(N>2\)) for the NA subset assuming the use of the weighted product (\(CM\)) and weighted sum (\(CM^{+}\)). The results obtained for neural networks with 5, 10, and 15 inputs selected by the Lasso algorithm are shown in Table 7. In its description 1 L-4 L denote the number of hidden layers, whereas \"equal\" and \"half\" stand for the number of neurons. The number of neurons in the first hidden layer was equal to the number of elementary metrics. There were two variants for determining the number(s) of neurons in the next hidden layers. The first option was to set the same number(s) of neurons whilst the second was to reduce the number of neurons approximately twice in each next hidden layer. A graphical illustration of the obtained performance for some of the \"best\" combinations is presented on the scatter plots shown in Figure 2 and discussed in Section 4. The dependence of the accuracy of the neural network (considered as the SROCC values calculated for the NA subset) on the number of input metrics is shown in Figure 3. For different configurations of networks, fairly similar results have been obtained. For this task, the most critical factors are the list of the used metrics, their number, whereas the specific network configuration is less crucial. In terms of the totality of all stages of networks training, it can be noted that a single-layer network does not always provide the necessary computing capacity, and the use of 4 hidden layers does not lead to a visible advantage. Hence, a stable result with a low complexity cascade network is ensured when 2-3 hidden layers are used and, basically, with an equal number of neurons in the layers. The results of the verification of the universality of the proposed NN-based metric are presented in Table 8. The results obtained for the whole LIVE database are not the best. The NN-based metric is better than some elementary metrics and worse than other ones, however, the obtained SROCC for this database is considered large enough. It should be noted here that some elementary metrics have been obtained just for a limited set of distortion types present in the LIVE database and this explains the aforementioned observations. For different subsets of the TID2013, the results for the designed NN-based metric are either the best or close to the best.