## 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{8}{c}{**AMCR (Avg. Dim.) [AMFI-Score]**} \\ \cline{3-10}  & & **PCA** & **HQ-PCA** & **\(I_{1}\)-PCA** & **RPCA** & **OM-RPCA** & **AM-PCA** & **TC-PCA** \\ \hline \multirow{4}{*}{**1**} & \multirow{2}{*}{**Overall**} & 0.670 & 0.654 & 0.635 & 0.651 & 0.641 & 0.657 & 0.654 & **0.681** \\  & & ( – ) & (43.10) & (47.70) & (42.70) & (39.60) & (40.80) & (43.10) & **(32.50)** \\  & & [0.681] & [0.669] & [0.642] & [0.666] & [0.648] & [0.67] & [0.667] & **[0.684]** \\ \hline \multirow{2}{*}{**1**} & \multirow{2}{*}{Non-standard} & 0.470 & 0.443 & 0.413 & 0.439 & 0.422 & 0.448 & 0.443 & **0.487** \\  & & **[0.429]** & [0.408] & [0.37] & [0.399] & [0.379] & [0.41] & [0.407] & **[0.429]** \\ \hline \multirow{2}{*}{Standard} & \multirow{2}{*}{Standard} & **1.000** & **1.000** & **1.000** & **1.000** & **1.000** & **1.000** & **1.000** & **1.000** \\  & & **[1.000]** & **[1.000]** & **[1.000]** & **[1.000]** & **[1.000]** & **[1.000]** & **[1.000]** & **[1.000]** \\ \hline \multirow{4}{*}{2} & \multirow{2}{*}{Overall} & 0.750 & 0.744 & 0.731 & 0.742 & 0.731 & 0.742 & 0.746 & **0.763** \\  & & ( – ) & (34.70) & (33.40) & (38.80) & (34.10) & (43.60) & (38.90) & **(18.7)** \\  & & [0.761] & [0.756] & [0.739] & [0.753] & [0.74] & [0.753] & [0.756] & **[0.77]** \\ \hline \multirow{2}{*}{2} & \multirow{2}{*}{Non-standard} & 0.443 & 0.430 & 0.404 & 0.426 & 0.400 & 0.430 & 0.435 & **0.483** \\  & & [0.386] & [0.372] & [0.353] & [0.377] & [0.346] & [0.371] & [0.378] & **[0.425]** \\ \hline \multirow{2}{*}{Standard} & \multirow{2}{*}{Standard} & **0.993** & **0.993** & 0.990 & **0.993** & **0.993** & 0.990 & **0.993** & 0.986 \\  & & **[0.993]** & **[0.993]** & [0.989] & **[0.993]** & **[0.993]** & [0.989] & **[0.993]** & [0.986] \\ \hline \multirow{4}{*}{3} & \multirow{2}{*}{Overall} & **0.809** & **0.809** & 0.800 & 0.801 & 0.796 & 0.803 & **0.809** & **0.809** \\  & & **( – )** & **[39.20]** & (36.20) & (44.90) & (37.20) & (41.70) & **(44.90)** & **(35.20)** \\  & & **[0.821]** & **[0.821]** & [0.81] & [0.813] & [0.805] & [0.815] & [0.82] & [0.814] \\ \hline \multirow{2}{*}{3} & \multirow{2}{*}{Non-standard} & **0.470** & 0.457 & 0.435 & 0.448 & 0.426 & 0.452 & 0.461 & 0.457 \\  & & **[0.414]** & [0.405] & [0.382] & [0.399] & [0.375] & [0.409] & [0.405] & [0.393] \\ \hline \multirow{2}{*}{Standard} & 0.986 & **0.993** & 0.991 & 0.986 & 0.989 & 0.986 & 0.991 & **0.993** \\  & & [0.986] & **[0.993]** & [0.991] & [0.985] & [0.988] & [0.986] & [0.991] & [0.985] \\ \hline \multirow{4}{*}{4} & \multirow{2}{*}{Overall} & **0.816** & **0.816** & 0.809 & 0.813 & 0.813 & 0.812 & 0.813 & **0.816** \\  & & **( – )** & **[50.700]** & (37.60) & (51.70) & (32.00) & (43.40) & (48.70) & **(30.60)** \\ \cline{1-1}  & & **[0.826]** & [0.825] & [0.817] & [0.823] & [0.823] & [0.82] & [0.822] & **[0.826]** \\ \hline \multirow{2}{*}{4} & \multirow{2}{*}{Non-standard} & **0.400** & **0.400** & 0.387 & 0.396 & 0.378 & **0.400** & 0.391 & **0.400** \\  & & **[0.375]** & [0.368] & [0.351] & [0.365] & [0.352] & [0.371] & [0.363] & [0.37] \\ \hline \multirow{2}{*}{Standard} & 0.978 & 0.978 & 0.973 & 0.976 & **0.983** & 0.973 & 0.978 & 0.978 \\  & & [0.978] & [0.978] & [0.972] & [0.976] & **[0.983]** & [0.973] & [0.978] & [0.978] \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparative Classification Performance for Yale Face Database. Next, we compare the classification performance of all methods using AR face database. In this database, we perform three experiments. The first experiment (Normal + Lighting) uses all normal face images and images under lighting conditions. Similarly, the second and third experiments use all normal face images and images with sunglasses (Normal + Sunglasses) and scarves (Normal + Scarves), respectively.