## 4 Evaluation
### Experimental Setup
This was the same configuration used in experiment A3. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**ID** & **Dropout** & **LSTM \#** & \
\begin{tabular}{c} **LSTM** \\ **Size** \\ \end{tabular} & **Dense \#** &
\begin{tabular}{c} **Dense** \\ **Size** \\ \end{tabular} & **Sequence** & **Length** & **Coding** \\ \hline A1 & 0.4 & 1 (Standard) & 512 & 1 & 1024 & 5 & Embedding \\ A2 & 0.8 & 1 (Standard) & 512 & 1 & 1024 & 5 & Embedding \\ A3 & 0.8 & 1 (Standard) & 512 & 2 & 1024 & 5 & Embedding \\ A4 & 0.8 & 2 (Standard) & 512 & 2 & 1024 & 5 & Embedding \\ A5 & 0.2 & 1 (Standard) & 512 & 5 & 50 & 5 & Embedding \\ A6 & 0.8 & 1 (Bidirectional) & 512 & 2 & 1024 & 5 & Embedding \\ A7 & 0.8 & 1 (Standard) & 512 & 2 & 1024 & 5 & One-hot vector \\ A8 & 0.8 & 1 (Standard) & 512 & 1 & 1024 & 5 & One-hot vector \\ A9 & 0.8 & 2 (Standard) & 512 & 2 & 1024 & 5 & One-hot vector \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Architecture experiments. _Dropout_ is the value of the dropout regularizations. _LSTM No._ is the number of long short-term memory network (LSTM) layers in the architecture. _LSTM size_ is the size of the LSTM layers. _Dense No._ is the number of fully connected layers with a rectified linear unit (ReLU) activation (all the architectures have a final fully connected layer with a softmax activation). _Dense size_ is the size of the fully connected layers with a ReLU activation. _Sequence length_ is the length of the input action sequence. _Coding_ is the codifying strategy used for the actions, either embeddings or a one-hot vector. Finally for the time experiments (see Figure 4), we tried different ways of taking into account the timestamps of the actions in the input sequence. We analysed three different options. In the first configuration (T1), we used two parallel LSTM layers, one for the action embeddings and the other for the timestamps, concatenating the results of both layers before the fully connected layers (late fusion strategy [44]). In the second configuration (T2), we concatenated the action embeddings and the timestamps before a single LSTM layer (early fusion strategy [44]). In the third configuration (T3), the embeddings were connected to an LSTM layer, whose output was concatenated with the timestamps and sent to another LSTM layer (slow fusion strategy [44]). All the configurations used a dropout regularization of 0.8, a LSTM layer size of 512, two fully connected layers with ReLU activation with a size of 1024 and one final fully connected layer with softmax activation, as in experiment A3. In all three architectures, the timestamps were represented as a two-position vector (\([x_{t},y_{t}]\)), representing the time in a circle with a radius of 1 and centred at the (0,0) coordinate. The \(x_{t}\) and \(y_{t}\) values were calculated respectively as the cosine and sine of the angle \(ang_{sec}\):  
\[ang_{sec}=\frac{secs_{timestamp}*2*\pi}{secs_{day}} \tag{2}\]  
where \(secs_{timestamp}\) is the timestamp expressed as seconds since midnight and \(secs_{day}\) are the total seconds in a day. Using \(ang_{sec}\), \(x_{t}\) is expressed as  
\[x_{t}=\cos(ang_{sec}) \tag{3}\]  
and \(y_{t}\) is expressed as  
\[y_{t}=\sin(ang_{sec}) \tag{4}\]