## 3 Results  
The results of the optimization of the pairs of elementary metrics confirm the validity of the proposed approach since a significant increase of the SROCC may be observed for the best combinations in comparison to IL-NIQE shown in Table 1. The best five combinations for the NA subset are presented in Table 3 together with the absolute values of the KROCC and PLCC values, although [PERSON]'s correlation has been assumed as the objective function during the optimization. Similar results obtained for the whole TID2013 database are shown in Table 4. Due to very low values of the Pearson's correlation (below 0.1) for some metrics, their precise values have not been presented. The results provided in Tables 3 and 4 illustrate some interesting properties of the combined metrics. Firstly, all five \"best\" combinations for the NA subset contain the IL-NIQE metric, however, the situation for the whole TID2013 database is a bit different, particularly for the \(CM_{2}^{+}\) family of metrics. Secondly, the elementary metrics combined with IL-NIQE are not the \"best\" among the elementary metrics listed in Table 1. It confirms that the combination of various types of metrics leads to better performance the use of those based on similar assumptions. Starting from the combinations listed in Tables 3 and 4, the respective \(CM_{3}\). and \(CM_{3}^{+}\) families of the combined metrics have been optimized, as well as similar combinations of more elementary metrics. The obtained \"best\" combinations for the NA subset are presented in Table 5. As it may be observed for the combinations of five elementary metrics three of them are the same for both types of combined metrics whereas two of them are different. After a further increase of the number of elementary metrics (\(N>5\)) there are no significant improvements in the performance, however, it leads to noticeably higher computational complexity. Table 6 illustrates the best results obtained using the combinations of 3 to 5 elementary metrics using formulas (1) and (2), for the whole TID2013 database. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**\#** & **Pre-Processing Rule** & **Number of Metrics** & **List of Metrics** \\ \hline
1 & All metrics & 42 & - \\
2 & Using Lasso (NNZ \(>\) 20) & 37 & - \\
3 & Using Lasso (NNZ \(>\) 30) & 35 & - \\
4 & Using Lasso (NNZ \(>\) 40) & 32 & - \\
5 & Using Lasso (NNZ \(>\) 50) & 27 & - \\
6 & Using Lasso (NNZ \(>\) 60) & 19 & - \\
7 & Using Lasso (NNZ \(>\) 63) & 15 & - \\
8 & Using Lasso (NNZ \(>\) 68) & 10 & CORNIA, HOSA, LPSI, MSGF, TCLT, IL-NIQE, QAC, SISBLIM\_SM, SISBLIM, SFB, DESIQUE, \\
9 & Using Lasso (NNZ \(>\) 70) & 8 & CORNIA, QAC, HOSA, LPSI, TCLT, SISBLIM, SFB, NIQMC, IL-NIQE \\
10 & Using Lasso (NNZ \(>\) 75) & 5 & CORNIA, QAC, HOSA, LPSI, IL-NIQE \\
11 & Using Lasso (NNZ \(>\) 80) & 3 & CORNIA, LPSI, IL-NIQE \\
12 & Custom set 1 & 5 & CORNIA, LPSI, HOSA, QAC, IL-NIQE \\
13 & Custom set 2 & 5 & SISBLIM\_SM, HOSA, QAC, IL-NIQE, BRISQUE \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The combinations of metrics considered in the NN-based experiments (with the lists of metrics presented only when less than 10 metrics have been applied). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metric** & **SROCC** & **KROCC** & **PLCC** \\ \hline \(CM_{3}\) (IL-NIQE, HOSA, TCLT) & 0.5765 & 0.4140 & \textless{}0.1 \\ \(CM_{4}\) (IL-NIQE, LPCSI, TCLT, WNJE) & 0.5995 & 0.4305 & \textless{}0.1 \\ \(CM_{5}\) (IL-NIQE, HOSA, TCLT, LPCSI, WNJE) & 0.6235 & 0.4521 & \textless{}0.1 \\ \hline \(CM_{3}^{+}\) (PSI, LPCSI, CORNIA) & 0.5967 & 0.4252 & \textless{}0.1 \\ \(CM_{4}^{+}\) (PSI, LPCSI, IL-NIQE, BIBLE) & 0.6274 & 0.4492 & 0.1301 \\ \(CM_{5}^{+}\) (HOSA, LPCSI, IL-NIQE, OG\_IQA, WNJE) & 0.6442 & 0.4648 & 0.5052 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Performance of the best combinations of NR elementary metrics (\(N>2\)) for the whole-TID2013 database assuming the use of the weighted product (\(CM\)) and weighted sum (\(CM^{+}\)).