## 3 Methodology
### Steps in Pattern Recognition
The PCA removes any redundancy between the components of the projected vectors, since the covariance matrix in the transformed space becomes diagonal as shown in Equation (1):  
\[\sum y=diag[\lambda_{1}\,\lambda_{2}\ldots\,\lambda_{n}] \tag{1}\]  
where, \(\{\lambda_{i}\}_{i=1...n}\) represent for the eigenvalues of the covariance matrix. The PCA performs the vector projection without any knowledge of their labels. This transformation is defined in such a way that the first principal component has as high a variance as possible and each succeeding component in turn has the highest variance possible under the constraint that it be orthogonal to the preceding components. It is therefore known as an unsupervised data analysis method or algorithm since it \"ignores\" class labels [50; 51; 52]. In this research, PCA was used to remove any redundancy between the components of the projected vectors and reduce the dimension of the original dataset. The result is explained in term of the \"total variance explained\" table. The table shows the number of the principal component (PC) that has been extracted with eigenvalue and how much information (variance) can be attributed to each component. Only a few components will be selected based on \"eigenvalue-one criterion\". In PCA, one of the most commonly-used criteria for solving the number of components problem is the eigenvalue-one criterion, also known as the Kaiser criterion [53]. With this approach, any component with an eigenvalue greater than 1.00 will be selected, and thus it will reduce the dimension of original datasets which have nine dimensions. Table 6 shows the total variance explained for the raw (RW) feature after being analyzed via PCA. The table clearly shows that most of the variance (31.77%) can be explained by the first principal component (PC1) alone. The second principal component (PC2) still bears some information (23.42%) while the third (PC3) and fourth principal components (PC4) bear least information with variance of 14.59% and 11.16%. respectively. Based on \"eigenvalue-one criterion\", four components (PC1, PC2, PC3 and PC4) have been selected because they display an eigenvalue greater than 1.00 and hold the greater amount of variance. Together, the selected components explain 80.88% of the information. The dimensionality reduction based on PCA has also been performed to other features. Table 7 illustrates the overall results for all features. According to Table 7, it is clear that most features can be explained based on four dimensions, except for vector array normalization (VAN), which can be explained by two dimensions only. VAN also gave the highest total variance explained at 93.70%. All other features are being dimensionally reduced from nine dimensions to four dimensions, with differential (DIFF) being the second-highest total variance explained at 84.48%, while SN was the lowest total variance explained at 73.99% only. Other features gave a similar result to raw (RW) at 80.88%, and relative (REL) and fractional (FRACT) shared the same percentage at 80.85%. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**PC**} & \multicolumn{4}{c}{**Initial Eigenvalues**} & \multicolumn{4}{c}{**Extraction Sums of Squared Loadings**} \\ \cline{2-7}  & **Total** & **Variance (\%)** & **Cumulative (\%)** & **Total** & **Variance (\%)** & **Cumulative (\%)** \\ \hline
1 & 2.854 & 31.711 & 31.711 & 2.854 & 31.711 & 31.711 \\
2 & 2.108 & 23.420 & 55.131 & 2.108 & 23.420 & 55.131 \\
3 & 1.313 & 14.590 & 69.720 & 1.313 & 14.590 & 69.720 \\
4 & 1.005 & 11.162 & 80.882 & 1.005 & 11.162 & 80.882 \\
5 & 0.833 & 9.251 & 90.133 & & & \\
6 & 0.407 & 4.526 & 94.659 & & & \\
7 & 0.278 & 3.085 & 97.744 & & & \\
8 & 0.152 & 1.685 & 99.429 & & & \\
9 & 0.051 & 0.571 & 100.000 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Total variance explained for raw (RW) feature.