# On the Quality of Deep Representations for Kepler Light Curves Using Variational Auto-Encoders
## 4 Discussion  
In Section 3.3.1, we show that the time is needed if a regularization effect and smoothing is desired. We briefly discuss the reasoning behind why time could contribute to phase-space light curves. As [10] introduced, the time information is not only used as input in the first stage (encoder process), as the decoder process needs the space reference where to reconstructs it. Each light curve has its own phase-space based on its period, then the delta times of the bins for different light curves will be different. Even if the delta times are similar for some light curves, the decoder does not know that information. The model will have to learn to reconstruct in each phase-space, since the decoder processes the previous time and its memory with a recurring operation. By having the same vector \(\hat{z}\) repeated at \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Representation** & \multicolumn{3}{c}{**Input**} & \multicolumn{3}{c}{**Non-Exoplanet**} & \multicolumn{3}{c}{**Exoplanet**} & \multicolumn{1}{c}{**Global**} \\  & **Dim** & **P** & **R** & \(\mathbf{F_{1}}\) & **P** & **R** & \(\mathbf{F_{1}}\) & \(\mathbf{F_{1}}\)-Ma** \\ \hline Metadata & 10 & 94.62 & 86.05 & 90.13 & 77.81 & 90.91 & 83.85 & 87.00 \\ Global-Folded & \(T\) & 83.55 & 83.48 & 83.51 & 69.35 & 69.45 & 69.36 & 76.45 \\ \hline \multicolumn{10}{c}{Unsupervised Methods} \\ \hline (Raw) F-PCA & 16 & 77.24 & 75.55 & 76.38 & 59.15 & 61.40 & 60.26 & 68.32 \\ (Fold) F-PCA & 16 & 81.82 & 87.27 & 84.46 & 75.04 & 66.37 & 70.44 & 77.45 \\ RAE\({}_{t}\) & 16 & 85.35 & 82.55 & 83.93 & 71.37 & 75.44 & 73.35 & 78.64 \\
**VRAE\({}_{t}\)** & 16 & 87.37 & 85.75 & 86.55 & 76.06 & 78.51 & 77.27 & 81.91 \\
**S-VRAE\({}_{t}\)** & 16 & 88.88 & 86.93 & 87.89 & 78.17 & 81.14 & 79.63 & 83.76 \\ \hline \multicolumn{10}{c}{Supervised Methods} \\ \hline RNN\({}_{t}\) & \(T\) & 88.88 & 88.45 & 88.67 & 78.73 & 79.43 & 79.09 & 83.87 \\
1D CNN & \(T\) & 91.57 & 87.09 & 89.27 & 78.01 & 85.10 & 81.40 & 85.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: **Classification validation**: Performance of the representation generated by different methods and techniques. The precision (P), recall (R), and \(F_{1}\) score per class and macro averaged are presented. The length of the curve used was \(T=300\). each time-step in the first decoder layer (Figure 3), the temporal information of each point for the different light curves could be beneficial in the reconstruction. Section 3.3.2 shows that the proposed methods offer a good combination of reconstruction and denoising of the light curves. In addition, adding the re-scaling into the model (S-VRAE\({}_{t}\)) seems to produce a smoother reconstructed time series but with the cost of increasing the reconstruction error, but both results are quite similar. The disadvantage in reconstruction is expected because the model needs to learn to simultaneously codify and reconstruct the _F-std_ of the data. These results indicate that the representation learned by the variational proposals allow a smoother version of the light curve reconstruction that is the most similar (except for RAE\({}_{t}\)) to the original curves, these being the methods that perform the best removal of unstructured patterns (noise) on the light curves among all the methods. While the results in Table 3 illustrate that more exclusive information could be stored through the learned variational features of the proposed models (as every feature represent a more different structure) and used for different proposes, as shown in the following. In addition, as shown in [36], a more disentangled representation indicates that the features found are closer to the underlying factors that explain the data behavior. The unsupervised feature extraction methods are useful based on the classification improvement over the raw global-folded representation, as shown in Section 3.3.3. This suggests that it is easier to discriminate using these compact representations than the raw folded measurements (95% compression).