## 4 Experiments
### Image Classification
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{\(r\)} & \multirow{2}{*}{**All Dim.**} & \multicolumn{6}{c}{**AMCR (Avg. Dim.) [AMF1-Score]**} \\ \cline{3-10}  & & & **PCA** & **HQ-PCA** & \(t_{1}\)**-PCA** & **RPCA** & **OM-RPCA** & **AM-PCA** & **TC-PCA** \\ \hline \multirow{3}{*}{1} & \multirow{3}{*}{Overall} & **1.000** & **1.000** & **1.000** & **1.000** & **1.000** & **1.000** & **1.000** \\  & & (\(-\)) & **(34.30)** & **(40.40)** & **(29.50)** & **(26.80)** & **(30.50)** & **(31.60)** & **(34.80)** \\  & & **[1.000]** & **[1.000]** & **[1.000]** & **[1.000]** & **[1.000]** & **[1.000]** & **[1.000]** \\ \hline \multirow{3}{*}{2} & \multirow{3}{*}{Overall} & 0.975 & 0.980 & **0.990** & 0.980 & **0.990** & 0.980 & 0.980 & **0.990** \\  & & (\(-\)) & (32.80) & **(31.40)** & (27.70) & **(21.50)** & (25.30) & (30.50) & **(31.80)** \\  & & [0.973] & [0.979] & **[0.989]** & [0.979] & **[0.989]** & [0.979] & [0.979] & **[0.989]** \\ \hline \multirow{3}{*}{3} & \multirow{3}{*}{Overall} & 0.983 & 0.987 & **0.990** & 0.987 & **0.990** & 0.987 & 0.983 & **0.990** \\  & & (\(-\)) & (21.50) & **(35.80)** & (28.00) & **(30.90)** & (27.90) & (22.40) & **(30.20)** \\  & & [0.983] & [0.986] & **[0.99]** & [0.986] & **[0.991]** & [0.986] & [0.983] & **[0.991]** \\ \hline \multirow{3}{*}{4} & \multirow{3}{*}{Overall} & **0.995** & **0.995** & **0.995** & **0.995** & **0.995** & **0.995** & **0.995** & **0.995** \\  & & (\(-\)) & **(31.30)** & **(48.00)** & **(28.40)** & **(34.30)** & **(34.30)** & **(30.30)** & **(35.10)** \\  & & **[0.995]** & **[0.995]** & **[0.995]** & **[0.995]** & **[0.995]** & **[0.995]** & **[0.995]** & **[0.995]** \\ \hline \multirow{3}{*}{5} & \multirow{3}{*}{Overall} & 0.994 & **0.996** & **0.996** & **0.996** & **0.996** & **0.996** & **0.996** & **0.996** \\  & & (\(-\)) & **(31.70)** & **(44.00)** & **(32.60)** & **(38.90)** & **(31.30)** & **(24.00)** & **(36.00)** \\  & & [0.994] & [0.994] & [0.994] & [0.994] & [0.994] & [0.996] & [0.994] & **[0.996]** & **[0.998]** \\ \hline \multirow{3}{*}{6} & \multirow{3}{*}{Overall} & 0.983 & 0.987 & **0.993** & 0.988 & 0.992 & 0.988 & 0.987 & **0.993** \\  & & (\(-\)) & (30.20) & **(37.00)** & (30.90) & (36.70) & (35.20) & (27.10) & **(37.50)** \\  & & (\(-\)) & (0.983) & [0.987] & [0.992] & [0.987] & [0.992] & [0.988] & [0.987] & **[0.993]** \\ \hline \multirow{3}{*}{7} & \multirow{3}{*}{Overall} & 0.981 & 0.986 & 0.986 & 0.983 & 0.984 & 0.983 & 0.984 & **0.987** \\  & & (\(-\)) & (25.00) & (48.10) & (34.00) & (33.10) & (26.90) & (30.20) & **(32.90)** \\  & & [0.981] & [0.981] & [0.985] & [0.981] & [0.985] & [0.984] & [0.981] & **[0.988]** \\ \hline \multirow{3}{*}{8} & \multirow{3}{*}{Overall} & 0.984 & 0.989 & **0.990** & 0.988 & 0.993 & 0.988 & 0.986 & 0.984 \\  & & (\(-\)) & (28.40) & **(44.20)** & (35.20) & (34.50) & (41.80) & (26.80) & (26.30) \\ \cline{1-1}  & & [0.984] & [0.987] & **[0.991]** & [0.99] & [0.989] & [0.987] & [0.986] & [0.985] \\ \hline \multirow{3}{*}{9} & \multirow{3}{*}{Overall} & 0.990 & **0.991** & 0.990 & **0.991** & 0.989 & 0.989 & 0.989 & **0.991** \\  & & (\(-\)) & **(28.00)** & **(46.50)** & **(35.40)** & (36.00) & (28.70) & (29.70) & **(34.30)** \\ \cline{1-1}  & & [0.99] & [0.992] & [0.988] & [0.988] & [0.99] & **[0.991]** & [0.988] & **[0.991]** \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparative Classification Performance for JAFFE Face Database. various lighting conditions. On the other hand, the performance of all methods in classifying standard images are similar (around 97%-100%), which is consistent with the findings of JAFFE face database shown in Table 1.
3. The overall classification accuracy and F1-score vary with the number of testing images for the Yale face database whereas the classification performance is not sensitive to the number of testing images for the JAFFE face database. Such a difference is mainly due to the ability of each methodology in recognizing non-standard images.