## 4 Results
### Selection of Wavelet Family and Decomposition Level  
Table 2 shows the wavelet families selected by the FAPSO algorithm for each of the five folds. Each fold of the data contained eleven wavelet families to represent the eleven nodes in the GPCR protein hierarchy, which are the root, family A, family B, family C, subfamily Amine, subfamily A Hormone, subfamily A Nucleotide, subfamily A Peptide, subfamily A Thyro, subfamily Prostanoid, and subfamily C CalcSense. As a result, for the five folds of the data set, the total number of wavelet families is 55. The wavelet family and decomposition level selected by the FAPSO method were examined at eleven nodes of the hierarchy. Table 2 clearly shows that the wavelet family and decomposition level chosen at different nodes differ significantly. This supports the use of FAPSO, which determines the wavelet family and decomposition level at each class node automatically. Figure 5 shows how often each wavelet family is chosen at every level of the GPCR hierarchy. 15 GPCR proteins were chosen from the Biorthogonal family, 14 were chosen from the Reverse Biorthogonal family, 9 were chosen from the [PERSON] family, 4 were chosen from the [PERSON] family, 5 were chosen from the [PERSON] family, 3 were chosen from the [PERSON] family, 3 were chosen from the [PERSON] family, and 2 were chosen from the Haar  
Figure 4: Representation of PseAAC features for class A GPCR proteins using the Coiflet 4 DWT wavelet family with 3 decomposition level. \begin{table}
\begin{tabular}{l c} \hline
**Class Node** & **Wavelet Family and Decomposition Level** \\ \hline Root & (RBior 3.7,1), (Bior4.4,3), (Bio5.5,3), (Coif5,1), (Bior3.7,1) \\ Family A & (Coif4,2), (FK18.3), (Rbio2.2,2), (Db9,1), (Bior5.5,1) \\ Family B & (Db7,1), (Db2,3), (FK6,1), (Db1,1), (Rbiot4.4,3) \\ Family C & (Dmey, 6), (Db1,1), (Rbio2.6,1), (Coif3.2), (Dmey,6) \\ Subfamily Amine & (Bior3.9,1), (Sym10,2), (Rbio1.1,1), (Bior3.3,5), (Sym5,1) \\ Subfamily A Hormone & (Rbior2.2), (Sym9,2), (Bior 3.7,2), (Bior2.2,7), (Bior1.3,5) \\ Subfamily A Nucleotide & (Db3.5), (FK18.6), (Rbio5.5,5), (FK22.3), (Rbior3.8,3) \\ Subfamily A Peptide & (Db7.1, (Bior2.4,1), (Rbiol1.1), (Db3.1), (FK4,1) \\ Subfamily A Thyro & (Db1.5), (Db3.3,2), (Db6,4), (Bior1.3, 3), (Rbiol1.3,3) \\ Subfamily A Prostanoid & (Bior5.5,3), (Rbio3.7,1), (Biol1.1,2), (Rbiol1.2), (Rbiot4.4,5) \\ Subfamily C CalcSense & (Dmey,3), (Rbio3.8,3), (Bior3.3,4), (Bior1.5,6), (Bior33.4) \\ \hline \end{tabular}
\end{table} 
Table 2: Selected wavelet family and decomposition level at each GPCR node. family. Most protein classes are effectively represented by the Biorthogonal wavelet family since most scaling functions and wavelet functions in this family have a sudden change in shape. This fits with the rough shape and many sharp changes in the shape of PseAAC, as shown in Figure 4a. Furthermore, [76] mentioned that the Biorthogonal wavelet could get rid of redundant information from protein sequences, minimise feature information leakage and aliasing, let feature vectors represent the original sequence information, and improve prediction performance. FAPSO also selects the Daubechies and Fejer-Korovkin wavelets at least five times. Figure 6 depicts the frequency of decomposition levels to represent protein classes. In total, 15 of the 55 wavelet families used decomposition level 1, the highest level of decomposition used in feature representation. Decomposition level 1 yielded 85 approximation and 85 detail coefficients, accounting for half of the 170 PseAAC features. Decomposition level 1 preserved global and local information. Decomposition level 3 was used by 14 wavelet families. Decomposition level 2 was used by 11 wavelet families. Four wavelet families used level decomposition 4, six families used level decomposition 5, and four families used level decomposition 6. Decomposition level 7 was the fewest decomposition level chosen for the feature representation, with only one.