# Unsupervised 3D Motion Summarization Using Stacked Auto-Encoders
## 6 Experimental Results
### Dance Summarization Experiments  
In this sub-section, we present some results of different summarization algorithms on the above-mentioned dance sequences. In particular, Figure 8 demonstrates the results obtained on Sytros (2 beat) dance sequence, consisting of more than 5000 frames, using as summarization algorithm the K-OPTICS. More specifically, we extract 32 key-representatives using the K-OPTICS algorithm and then we calculate the maximum correlation score \(\rho_{i}^{max}\) for each frame of Sytros (2 beat) dance sequence against the 32 key frames extracted [see Equation (5)]. As shown in Figure 8, the average \(\rho_{i}^{max}\) for all 5000 frames (that is for all \(i\in N\)) is 0.5 with a variance of 0.25, which is a relatively low score. However, as we have stated previously, some frames of the dance sequence have been erroneously encoded mainly due to the simultaneous presence of two dancers in the choreography and the dense occlusions this causes. Thus, if we refine the frames of the dance sequence by excluding the ones whose the joint coordinates between two consecutive frames present high differences, greater than a threshold (in our case the threshold is set to 20% rate of change in joint's coordinates, for more than 20% of joints), then the correlation score is significantly improved. In particular, in this case the average \(\rho_{i}^{max}\) for all 5000 frames becomes more than 0.6, indicating a good summarization ability. Additionally, the majority of excluded frames, shown as purple crosses in Figure 8 can be found bellow the average similarity score. Such an outcome suggests that the applied rules for corrupted frames removal are adequate for the problem at hand. Figure 9 illustrates the summarization performance when the Kennard Stone sampling algorithm is applied over Sytros (3 beat) dance sequence. Again, as in Figure 8, the non-corrupted frames achieve a high average similarity score, close to 0.67, indicating that the summarized sequence can adequate describe (correlate) most of the originally captured frames. The fluctuations are also limited, and appear around frame 1500. Table 2 summarizes the maximum correlation coefficients scores before and after the exclusion of the corrupted frames for all the three dances and the four examined sampling algorithms. It can be seen that the correlation scores obtained is about 0.6 revealing a satisfactory performance of the key frames as representatives of the whole dance sequence variation. In this table, we have presented as bold the highest correlation values. Figure 10 demonstrates the average differences in frames (time instances) between a frame selected using a specific sampling approach (i.e., a summarization algorithm) and the experts' selected frames  
(ground truth), for a particular dance. That is, the criterion \(\mu\) of Section 6.3. Since the the frame rate of the system is 120 fps, a value of 50 indicate that the sampling approach generates frames less than half-a-second earlier/latter compared to the experts' selection. The impact of using raw against encoded data is, also, assessed. Results indicate that SMRS based approaches perform better to the other summarization schemes, for both raw and encoded data, when we have a single dancer sequence. Figure 8: The maximum correlation scores \(\rho_{i}^{max}\) for each frame of the original Syrtos at 2 beat dance sequence compared to the summarized one using K-OPTICS. Figure 9: The maximum correlation scores \(\rho_{i}^{max}\) for each frame of the original Syrtos at 3 beat dance sequence compared to the summarized one using Kennard Stone. In this figure, we also compare the performance derived against the four summarization methods; that is, K-OPTICS, Kennard Stone, SMRS, and the proposed hierarchical SMRS, H-SMRS. As we can observe from Figure 10, the H-SMRS gives the best performance for all dances with a deviation around 50 frames (or, approximately, 0.41 s), when encoded frames are used as inputs.