# Unsupervised 3D Motion Summarization Using Stacked Auto-Encoders
## 7 Conclusions  
In this paper, we propose a deep stacked auto-encoder scheme followed by a hierarchical Sparse Modelling for Representative Selection (H-SMRS) summarization algorithm for performing accurate synopses of dance sequences. The sequences have been recorded through a motion capturing framework such as of VICON which produces 3D point joint of the dancers. The originality of this paper lies in the fact that our recorded dance sequences consist of two dancers performing simultaneously. This causes severe and intense errors in capturing the humans' joints in 3D coordination space. Thus, we adopt a stacked auto-encoder (SAE) scheme to reduce the redundant information of the 3D  
Figure 12: A representation of the decompressed data (**a**) relative to the original skeletal data (**b**), for the same time frame as for Syrtos (2b) dance sequence. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dance** & **Minimum Difference** & **Maximum Difference** & **Sampling Summarization Algorithm** \\ \hline Makedonikos & 0.06 s & 5.20 s & KenStone \\  & 0.04 s & 6.71 s & K-OPTICS \\  & 0.04 s & 6.66 s & SMRS \\  & 0 s & 0.72 s & H-SMRS \\ \hline Syrtos (2-beats) & 0.008 s & 4.45 s & KenStone \\  & 0.016 s & 3.88 s & K-OPTICS \\  & 0.016 s & 0.5 s & SMRS \\  & 0 s & 0.74 s & H-SMRS \\ \hline Syrtos (3-beats) & 0.041 s & 0.54 s & KenStone \\  & 0.116 s & 0.808 s & K-OPTICS \\  & 0.033 s & 0.541 s & SMRS \\  & 0 s & 0.55 s & H-SMRS \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The minimum (best) and maximum (worst) time deviation (\(\mu_{max}\)) among the key frames extracted using a summarization algorithm and the ground truth data. The comparison is carried out using four summarization algorithms, K-OPTICS, Kennard Stone, SMRS and H-SMRS and for the three dances.The values are in seconds. point joints and thus improve the performance of the summarization than applying the summary algorithms directly on the raw captured data. Regarding summarization, this paper compares the results using four key frame extraction algorithms. The K-OPTICS scheme, the Kennard Stone, the conventional SMRS and its hierarchical representation called H-SMRS. Our approach has been evaluated over three real-world dance sequences, each executing by two dancers. The results achieved show that the H-SMRS outperforms the other three algorithms for all the examined dance sequences. More specifically, the average time deviation is less than 0.3 s compared to ground truth selected frames being annotated by dance experts. Even in its worst performance, H-SMRS yields at least 0.72 s time deviations which is an excellent result. The proposed SAE approach also reduces the time required for executing the summarization algorithms than applying the summarization schemes directly on the raw data. This way, summarization become applicable to many engineering scenarios. Conceptualization, E.P., I.R. and N.D.; Formal analysis, E.P. and A.V. ; Funding acquisition, N.D. and A.D.; Investigation, I.R. ; Methodology, E.P. and A.V. ; Resources, N.D.; Software, I.R. and E.P. ; Supervision, A.V., N.D. and A.D.; Validation, A.D. and I.R. ; Visualization, I.R. ; Writing--original draft, I.R. and E.P. ; Writing--review & editing, N.D., A.D. and A.V. All authors have read and agreed to the published version of the manuscript. The research was funded by the Hellenic Foundation for Research Innovation grant No. HFRI-FM17-2972. This paper is supported by the research project 4 DBeyond: 4D Analysis Beyond the Visible Spectrum in Real-Life Engineering Applications'. This paper is supported by the research project 4 DBeyond: 4D Analysis Beyond the Visible Spectrum in Real-Life Engineering Applications, project No. HFRI-FM17-2972 funded by the Hellenic Foundation for Research Innovation. The authors declare no conflict of interest. The following abbreviations are used in this manuscript: