## 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** & \(I_{4}\)-PCA & **RPCA** & **OM-RPCA** & **AM-PCA** & **TC-PCA** \\ \hline \multirow{4}{*}{**1**} & \multirow{2}{*}{**Overall**} & 0.588 & 0.556 & 0.580 & 0.564 & 0.552 & 0.556 & 0.564 & **0.680** \\  & & ( –) & (32.30) & (52.80) & (36.10) & (32.80) & (27.40) & (32.50) & **(20.80)** \\  & & [0.605] & [0.573] & [0.598] & [0.581] & [0.57] & [0.578] & [0.581] & **[0.692]** \\ \cline{2-10}  & \multirow{2}{*}{Non-standard} & 0.333 & 0.267 & 0.320 & 0.287 & 0.253 & 0.273 & 0.287 & **0.467** \\  & & [0.325] & [0.248] & [0.318] & [0.275] & [0.24] & [0.268] & [0.274] & **[0.446]** \\ \cline{2-10}  & \multirow{2}{*}{Standard} & 0.970 & 0.990 & 0.970 & 0.980 & **1.000** & 0.980 & 0.980 & **1.000** \\  & & [0.96] & [0.987] & [0.96] & [0.973] & **[1.000]** & [0.973] & [0.973] & **[1.000]** \\ \hline \multirow{4}{*}{2} & \multirow{2}{*}{Overall} & 0.674 & 0.666 & 0.657 & 0.663 & 0.669 & 0.671 & 0.666 & **0.726** \\  & & ( –) & (31.60) & (26.10) & (33.90) & (31.10) & (29.10) & (36.70) & **(27.70)** \\  & & [0.693] & [0.687] & [0.684] & [0.682] & [0.692] & [0.693] & [0.685] & **[0.744]** \\ \hline \multirow{2}{*}{2} & \multirow{2}{*}{Non-standard} & 0.273 & 0.260 & 0.207 & 0.253 & 0.227 & 0.260 & 0.260 & **0.380** \\  & & [0.282] & [0.277] & [0.222] & [0.252] & [0.223] & [0.276] & [0.269] & **[0.367]** \\ \cline{2-10}  & \multirow{2}{*}{Standard} & 0.975 & 0.970 & 0.995 & 0.970 & **1.000** & 0.980 & 0.970 & 0.985 \\  & & [0.973] & [0.965] & [0.995] & [0.968] & **[1.000]** & [0.979] & [0.968] & [0.984] \\ \hline \multirow{4}{*}{3} & \multirow{2}{*}{Overall} & 0.758 & 0.742 & 0.749 & 0.742 & 0.751 & 0.751 & 0.744 & **0.773** \\  & & ( –) & (33.40) & (32.80) & (33.10) & (39.20) & (35.30) & (35.40) & **(20.90)** \\  & & [0.766] & [0.75] & [0.76] & [0.751] & [0.761] & [0.76] & [0.753] & **[0.776]** \\ \cline{2-10}  & \multirow{2}{*}{Non-standard} & 0.347 & 0.313 & 0.293 & 0.307 & 0.280 & 0.333 & 0.313 & **0.373** \\  & & [0.319] & [0.291] & [0.279] & [0.278] & [0.259] & [0.312] & [0.292] & **[0.361]** \\ \cline{2-10}  & \multirow{2}{*}{Standard} & 0.963 & 0.957 & 0.977 & 0.960 & **0.987** & 0.960 & 0.960 & 0.973 \\  & & [0.962] & [0.955] & [0.976] & [0.958] & [0.985] & [0.958] & [0.969] \\ \hline \multirow{4}{*}{4} & \multirow{2}{*}{Overall} & 0.782 & 0.775 & 0.776 & 0.776 & **0.793** & 0.784 & 0.771 & 0.784 \\  & & ( –) & (26.30) & (28.40) & (28.50) & **(23.90)** & (25.20) & (23.00) & (23.90) \\ \cline{1-1}  & \multirow{2}{*}{Overall} & 0.786 & [0.779] & [0.785] & [0.781] & **[0.799]** & (0.789) & [0.776] & [0.79] \\ \cline{1-1}  & \multirow{2}{*}{Non-standard} & **0.313** & 0.293 & 0.273 & 0.300 & 0.267 & 0.300 & 0.280 & 0.293 \\ \cline{1-1}  & \multirow{2}{*}{Non-standard} & **0.329** & [0.299] & [0.287] & [0.305] & [0.265] & [0.308] & [0.28] & [0.286] \\ \cline{1-1}  & \multirow{2}{*}{Standard} & 0.958 & 0.955 & 0.965 & 0.955 & **0.990** & 0.965 & 0.955 & 0.968 \\ \cline{1-1}  & \multirow{2}{*}{Standard} & 0.956 & [0.953] & [0.964] & [0.954] & **[0.99]** & [0.964] & [0.953] & [0.967] \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparative Classification Performance for AR Face Database (Normal + Lighting). we select AR (Normal + Light) as an example. It is obvious that the projected data consists of two compact clusters with some outliers. The proposed TC-PCA can ignore the negative impact of the non-standard images and successfully identify the two clusters, in which the data objects in the same cluster belong to the same classes. No data objects from the same classes are assigned to the two different clusters. Moreover, the vector difference between the two cluster centers, which is the projection vector estimated by the TC-PCA, provides the inter-class information. This is important for classification and clustering problems.