## 5 Results Summary and Conclusions  
A comparison between the results of 8 clusters and 10 clusters can be summarized in Table 7. As shown in Table 7, different criteria values are slightly better for 8 clusters than 10 clusters. Silhouette coefficients and Calinski-Harabasz clustering evaluation criterion values are higher for eight clusters, while Davies-Bouldin values are lower. For the population audiograms, the Silhouette and the Davies-Bouldin values are better for eight clusters, but the Calinski-Harabasz value is better for 10 clusters. This could be explained as Calinski-Harabasz is the most sensitive parameter to the number of observations considered to calculate this criterion [45]. The number of audiograms considered for 8 clusters in stage 3 is 20,957 while it is 22,002 audiograms for 10 clusters in stage 3 (as shown in \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**[PERSON] Standard Level**} & **Cluster Number in the** & **Cluster Number in the** \\  & **Generated 8 Clusters** & **Generated 10 Clusters** \\ \hline N1 & 1 & 8 \\ N2 & 1 & 4 \\ N3 & 5 & 1 \\ N4 & 4 & 5 \\ N5 & 4 & 6 \\ N6 & 6 & 3 \\ N7 & 6 & 3 \\ S1 & 1 & 4 \\ S2 & 2 & 10 \\ S3 & 8 & 2 \\  & 3 & 7 \\  & 7 & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Standard levels chosen by [PERSON] mapped to the generated clusters. Figure 7: Standard set chosen by [PERSON] [15] mapped to the generated clusters. Table 7). Eigenvalues are small, but no gap is indicated to confirm selection between 8 and 10 clusters. The number of audiograms' population considered in the last stage for 10 clusters is higher than those in 8 clusters. The 10 clusters can be preferred as more patients' audiogram shapes are considered using 10 clusters. The Silhouette coefficients of the audiogram population are higher than 0.5 for both number of clusters, which suggests good clustering. The trial to classify audiograms by [PERSON] [20] to adjust hearing aid, has low accuracy. 68% when they assigned one configuration to each audiogram. We believe that their accuracy might have increased if they considered higher number of clusters as the data has a nature of high overlap. This matches with the results found in this research to cluster data into 8 or 10 classes. This work can be considered the first step to change the way of designing hearing aid filter banks. The existing filter bank designs use digital filters with different techniques to divide the entire frequency band (125 Hz-8 KHz) non-uniformly. It then applies gain controls to configure the hearing aid to match patient's audiogram. The current practice aims to design digital filters that can match multiple patients' audiograms which leads to very complex designs as conducted in [6; 7; 8; 9]. These designs lower the cost of manufacturing hearing aids as they can be produced on a large scale since they accommodate multiple users. However, complex designs require high operating power and big chip area, which leads to an improper fitted hearing aid. When there is a reduction in complexity, the hearing aid prototype can match a limited number of audiograms effectively. On the other hand, a low complex hearing aid design makes it properly fitted as it does not require large area to be implemented since it has a small number of filter coefficients [4; 8]. Normally, hardware complexity when designing filter bank structures is measured by the components needed to realize these filters (which are multipliers, adders, and shifters). However, in many researches, only multipliers are considered as they are the most power-consuming elements in the digital signal processing (DSP) hardware [46]. Hence, to summarize, the