## 4 Experiments
### Image Classification
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{\(r\)} & \multirow{2}{*}{**All Dim.**} & \multicolumn{8}{c}{**AMCR (Avg. Dim.) [AMF1-Score]**} \\ \cline{3-10}  & & & **PCA** & **HQ-PCA** & **\(l_{1}\)-PCA** & **RPCA** & **OM-RPCA** & **AM-PCA** & **TC-PCA** \\ \hline \multirow{4}{*}{**1**} & \multirow{2}{*}{**Overall**} & 0.588 & 0.592 & 0.576 & 0.592 & 0.572 & 0.592 & 0.588 & **0.816** \\  & & ( –) & (31.70) & (40.10) & (28.30) & (36.30) & (24.40) & (29.30) & **(15.10)** \\  & & [0.595] & [0.598] & [0.582] & [0.599] & [0.588] & [0.599] & [0.597] & **[0.817]** \\ \hline \multirow{4}{*}{**1**} & \multirow{2}{*}{Non-standard} & 0.333 & 0.333 & 0.313 & 0.333 & 0.300 & 0.333 & 0.333 & **0.693** \\  & & [0.312] & [0.309] & [0.28] & [0.312] & [0.284] & [0.31] & [0.316] & **[0.665]** \\ \cline{2-10}  & \multirow{2}{*}{Standard} & 0.97 & 0.980 & 0.970 & 0.980 & 0.980 & 0.980 & 0.970 & **1.000** \\  & & [0.96] & [0.973] & [0.96] & [0.973] & [0.973] & [0.973] & [0.96] & **[1.000]** \\ \hline \multirow{4}{*}{2} & \multirow{2}{*}{Overall} & 0.694 & 0.669 & 0.691 & 0.680 & 0.663 & 0.680 & 0.671 & **0.840** \\  & & ( –) & (20.90) & (31.30) & (25.60) & (38.50) & (24.80) & (27.90) & **(18.10)** \\  & & [0.708] & [0.69] & [0.711] & [0.697] & [0.685] & [0.696] & [0.691] & **[0.845]** \\ \hline \multirow{4}{*}{2} & \multirow{2}{*}{Non-standard} & 0.32 & 0.253 & 0.287 & 0.280 & 0.220 & 0.287 & 0.260 & **0.647** \\  & & [0.329] & [0.266] & [0.308] & [0.277] & [0.235] & [0.292] & [0.271] & **[0.597]** \\ \cline{2-10}  & \multirow{2}{*}{Standard} & 0.975 & 0.980 & **0.995** & 0.980 & **0.995** & 0.975 & 0.980 & 0.985 \\  & & [0.973] & [0.979] & [0.995] & [0.979] & [0.995] & [0.973] & [0.979] & **[0.984]** \\ \hline \multirow{4}{*}{3} & \multirow{2}{*}{Overall} & 0.744 & 0.738 & 0.742 & 0.736 & 0.753 & 0.744 & 0.736 & **0.869** \\  & & ( –) & (28.60) & (45.80) & (35.60) & (35.80) & (37.20) & (34.60) & **(16.10)** \\  & & [0.749] & [0.744] & [0.748] & [0.74] & [0.761] & [0.751] & [0.741] & **[0.871]** \\ \hline \multirow{4}{*}{3} & \multirow{2}{*}{Non-standard} & 0.307 & 0.287 & 0.293 & 0.273 & 0.273 & 0.300 & 0.300 & **0.660** \\  & & [0.286] & [0.267] & [0.284] & [0.248] & [0.274] & [0.278] & [0.285] & **[0.614]** \\ \cline{2-10}  & \multirow{2}{*}{Standard} & 0.963 & 0.963 & 0.967 & 0.967 & **0.993** & 0.967 & 0.953 & 0.973 \\  & & [0.962] & [0.962] & [0.965] & [0.965] & **[0.993]** & [0.965] & [0.948] & [0.973] \\ \hline \multirow{4}{*}{4} & \multirow{2}{*}{Overall} & 0.794 & 0.776 & 0.780 & 0.771 & 0.795 & 0.789 & 0.776 & **0.815** \\  & & ( –) & (30.60) & (29.90) & (32.70) & (31.80) & (26.10) & (33.50) & **(26.70)** \\ \cline{1-1}  & & [0.788] & [0.785] & [0.787] & [0.779] & [0.799] & [0.785] & [0.777] & **[0.822]** \\ \hline \multirow{4}{*}{**4**} & \multirow{2}{*}{Non-standard} & 0.32 & 0.280 & 0.300 & 0.280 & 0.273 & 0.307 & 0.287 & **0.38** \\  & & [0.314] & [0.312] & [0.297] & [0.292] & [0.259] & [0.293] & [0.282] & **[0.38]** \\ \hline \multirow{4}{*}{Standard} & 0.958 & 0.963 & 0.960 & 0.955 & **0.990** & 0.970 & 0.960 & 0.978 \\  & & [0.956] & [0.959] & [0.962] & [0.957] & **[0.99]** & [0.964] & [0.956] & [0.977] \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparative Classification Performance for AR Face Database (Normal + Sunglasses).