# On the Quality of Deep Representations for Kepler Light Curves Using Variational Auto-Encoders
## 2 Materials and Methods
### Light Curve Representation Methods
#### 2.1.2 Self-Generated Representations  
While most of the representations focus on using astrophysical knowledge to ease a specific task (task-based), e.g., classifying star variability or vetting transits, only a few of them tried different representation approaches without direct human intervention or being especially designed for some task (task-free), which may have the advantage of using unlabeled data and being used for different purposes. [PERSON] et al. [9] used an unsupervised learning algorithm known as affinity propagation with a custom distance function to build a new representation from light curves and then use it on a linear support vector machine to classify variable stars. The representation is based on the similarity between fragments of the light curves and cluster exemplars or centroids. [PERSON] et al. [20] also used an unsupervised learning algorithm to build a new representation on the Kepler mission, and in a second phase, used supervised learning to classify true planets. The principal component analysis (PCA) to extract features on the frequency domain representation of light curves, based on a discrete Fourier transform, was used in [20].  
In the work of [PERSON] et al. [21], an image representation (i.e., grid) was obtained from the variations of magnitude through time from light curves with missing values. This work used the variable star data from the CRTS dataset and completed the classification task using two-dimensional convolutional neural networks (2D CNN), which are models that learn local spatial dependencies [22]. [PERSON] et al. [14] also obtained variations in magnitude from variable stars light curves and the delta times of each sample. These were used as different input channels to train a 1D CNN classifier with shared-weights through novel data augmentation techniques.  
In the work of [PERSON] et al. [10], time was used as an additional input channel but through recurrent neural network (RNN) models, which are models that learn temporal dependencies [23]. [PERSON] et al. [10] presented a recurrent auto-encoder (RAE) that learned how to embed and then reconstruct a light curve by setting the original times using RNN models in the encoder and decoder phase--which we named \"RAE\({}_{t}\)\" (RAE _plus time information_). The authors in [10,15] showed that learned representations are useful for classifying variable stars, thus improving the results obtained using statistical features [12]. It also explores the use of the folded light curve representation which further improves the obtained results.  
Other types of research have been performed to characterize noisy signals. The most common approach is to estimate the missing values. [PERSON] et al. [24] presented the principal techniques used to analyze the correlation on irregularly sampled time series. [PERSON] & [PERSON] [25] proposed an estimator for wavelet variance for time series with missing data. There is also the Lomb-Scargle periodogram [13] for period analysis on data with missing values and the previously discussed Mandel-Agol model.  
[PERSON] & [PERSON] [26] included _delta times_ (time differences between two adjacent samples) to obtain a spectral analysis from time series. However, to the best of our knowledge, including delta times as an input in neural networks models of noisy times series was first explored by [PERSON] et al. [27]. This study presents a modification of a gated recurrent unit (GRU) model [28], namely GRU-D, which uses a binary mask for missing values and the delta times as input channels. The objective was to impute (fill) the missing values to improve the predictions on medical problems.