## 7 Experimental Studies
### Result and Analysis  
In this section, we show the experimental comparison between different metrics/divergences within our proposed methods, as well as a comparison of our proposed methods and seven SPD-based comparison algorithms. Since the feature curves we proposed were based on SPD geometry, the choice of metric/divergence in the SPD manifold, which derived the distance metric in DTW, was especially important. Hence, the AIRM, the LEM introduced in Section 2.2, and the Stein and Jeffrey divergences introduced in Section 2.3 combined with the KNN classifier were applied for the comparative experiments. Table 1 shows the average accuracies using these four metrics/divergences on the SPD manifold. It is obvious that our method with AIRM achieved the highest recognition accuracies on two databases. It should be noted that the AIRM defines a true geodesic distance. Although the LEM was confirmed to be much more efficient than the AIRM in [21], the LEM did not perform well in our proposed method. This might have been the case because the LEM is not an affine invariant. In addition, the LEM does not really reflect the geometric relationship between two points on an SPD manifold. Moreover, as we introduced in Section 5, we utilized global spatial features (global faces) as the companion to regional spatial features (ROIs). To prove the improvement made by the global spatial features, we compared three situations in our method, namely, regional spatial features (ROIs) only, global spatial features (global faces) only, and the combination of both. As shown in Table 2, extracting regional spatial features only and \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{3}{c}{**Database**} \\ \cline{2-4}  & **YTC**[51] & **ICT-BBT**[52] & **ICT-PB**[52] \\ \hline Ours—[PERSON] & 44.50\% & 65.40\% & 36.83\% \\ Ours—LEM & 62.67\% & 73.20\% & 48.60\% \\ Ours—[PERSON] & 79.00\% & 86.80\% & **71.17\%** \\ Ours—AIRM & **82.33\%** & **87.80\%** & 68.20\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Recognition result on our proposed method with different metrics/divergences. global spatial features only from short videos underperformed in most cases. However, the combination of ROIs and global faces provided more plentiful information and achieved better accuracy than the first two. The face recognition tests compared with seven SPD-based algorithms on three internet video face databases are summarized in Table 3. As can be seen from Table 3, our framework with AIRM performed best on both ICT-BBT and ICT-PB databases and highly approached CREML on the YTC database. The DR methods LEML, SPDML and SPDSL showed similar performance, maybe because set-based SPD matrix representations encode approximate information of global variations of videos. In contrast, the DALG, the CERML, and our proposed method were generally outperformed by the other SPD-based video recognition methods on the both databases. This may have been because the DALG utilized the geometry of LGs, which provides high-order information, and the CERML fuses the Euclidean representation and Riemannian representation from videos while our proposed method fuses both major spatial features and temporal features of video. However, the accuracy sharply decreased in the ICT-PB database, which may have been due to complex imaging conditions and facial occlusion. Only the CERML, the AidCovDs, and our proposed method performed most consistently. This further demonstrates the effectiveness and robustness of fusing temporal and spatial features by temporal mod