# Learning and Mining Player Motion Profiles in Physically Interactive Robogames
## 6 Experimental Results
### Feature Extraction  
The first question we need to answer concerns the size of the sliding window. This parameter regards the definition of the GASF images used as building blocks for the dictionary learning. The window size should be large enough to capture motion patterns relevant for the player characterization, but not so large to confound their interpretation. We tried different window sizes, and in the end, we followed [13] and decided to consider half a second of data per window without overlap, which allows for a fine-grained data representation.  
We applied no preprocessing to the signal, since we were interested in observing how an autoencoder would perform using the unfiltered input. The expectation was that it would naturally compensate for the differences in the images, decisively choosing to capture important features (the main signal characteristic) and disregarding non-representative ones (the small noise associated). We defined an architecture composed by dropout and dense layers where only hyperbolic tangent activation functions where used, except in the last layer, where a linear activation function was used instead. The best performing architecture was composed by the following layers: dropout (0.1 drop fraction), dense (size = 256), dropout (0.2) and dense (size = 64). The same layers (in reversed order) were used for the decoder part.  
A window of half a second corresponded to 32 samples given our accelerometer average frequency of 48.8 Hz. As a consequence, we obtain GASF images (without using PAA) with a total of 1024 pixels. Using the autoencoder, we manage to reduce the representation down to a 64-dimensional input, resulting in the reconstruction presented in Figure 13. The choice of a 64-dimensional representation is empirical, meaning that we were in principle searching for an undercomplete representation of the data and, upon testing with different configurations, we have chosen the one with the lowest reconstruction error. As it turned out, a 64-dimensional vector representation was the best result, given our dataset.  
It is possible to notice from the reconstruction result that, despite such a large compression (from 1024 to only 64 values), the input image structures are captured. This can also be seen in the reconstructed time series. A closer look reveals that the autoencoder practically smoothed the time series while preserving the overall shape, this being a nice property that can help to prevent overfitting.  
Figure 13: Autoencoder reconstruction for five input segments corresponding to half a second of data (linear combination of the acceleration axis). (Top line) Input GASF images. (Second line) Original time series for each GASF input. (Third line) The autoencoder reconstruction for the input images. (Forth line) Time series from the reconstructed GASF images.  
From Figure 13, we can also see that the obtained time series reconstruction presents some holes. This seems to be caused by the information loss in the reconstruction and demands further investigation. However, in our experimentation, it did not seem to affect performance.