# A Location-Time-Aware Factorization Machine Based on Fuzzy Set Theory for Game Perception
## 4 Experiments and Results in Discussion
### Experimental Analysis  
We consider training time and convergence speed to choose the batch size. A larger batch size will speed up training per epoch time, but convergence is relatively slow. To cope with this problem, L2 regularization, discarding, and early stopping are introduced. The early stopping strategy for training is executed when the F1 score increases for five consecutive epochs on the test set. The convergence speed of the model is examined through experiments, as shown in Figure 3a. We summarize the loss convergence of each model under the same epoch, and we find that the convergence speed of the proposed LTFM is the fastest and most stable among FM and its variants. We can also see LTFM has been higher than others in ROC curves, which means LTFM is more stable. \begin{table}
\begin{tabular}{c c} \hline \hline
**Evaluation Metric** & **Formula** \\ \hline Precision & \(\frac{TP}{TP+TP}\) \\ Recall & \(\frac{TP}{TP+FN}\) \\ F-measure & \(\frac{2\times precision\times recall}{precision+recall}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance metrics to compare prediction models. In addition, we verify the effect of learning rate on the prediction performance of perceptual evaluation of LTFM games through extensive experiments in this paper, and the results are shown in Table 4. For trade-off considerations, we chose \(lr=10^{-2}\) in LTFM. The experimental results of the model performance comparison are shown in Table 5.  
The proposed LTFM model performs better than all baseline models in the experimental results, which indicates the projection (considering both the location information \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Lr** & **AUC** & **Precision** & **Recall** & **F-Measure** & **Time (s)** \\ \hline
0.1 & 0.7572 & 0.7901 & 0.7975 & 0.776 & 16.225 \\
0.3 & 0.7862 & 0.7842 & 0.7595 & 0.7867 & 14.15 \\
0.5 & 0.7493 & 0.7903 & 0.7835 & 0.7848 & 14.4 \\
0.01 & 0.8093 & 0.8328 & 0.8228 & 0.8178 & 16.4 \\
0.03 & 0.7796 & 0.8235 & 0.7848 & 0.7867 & 15.025 \\
0.05 & 0.7862 & 0.8089 & 0.7848 & 0.7837 & 15.025 \\
0.001 & 0.7843 & 0.8256 & 0.7342 & 0.753 & 15.4 \\
0.003 & 0.7777 & 0.8213 & 0.7468 & 0.7595 & 14.825 \\
0.005 & 0.7701 & 0.827 & 0.7848 & 0.7735 & 15.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Learning rate effect. Figure 3: The performance for comparison FMs (**a**) comparison of model convergence (**b**) ROC curves of different comparison algorithms. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Model** & **AUC** & **Precision** & **Recall** & **F-Measure** & **Time (s)** \\ \hline RF & 0.7302 & 0.7385 & 0.7595 & 0.7444 & — \\ DTree & 0.722 & 0.7087 & 0.7215 & 0.7133 & — \\ MLP & 0.7422 & 0.7526 & 0.7608 & 0.7538 & — \\ Lightgbm & 0.7164 & 0.7197 & 0.7595 & 0.7283 & — \\ Xgboost & 0.7258 & 0.7324 & 0.7646 & 0.7428 & — \\ Catboost & 0.7319 & 0.7259 & 0.7722 & 0.7174 & — \\ \hline Standard FM & 0.7549 & 0.7189 & 0.7215 & 0.7008 & 16.91 \\ NFM & 0.7721 & 0.7789 & 0.7595 & 0.7778 & 14.6 \\ AFM & 0.7862 & 0.8052 & 0.7848 & 0.7972 & 184.82 \\ IFM & 0.7908 & 0.8158 & 0.7975 & 0.801 & 56.31 \\ LDFM & 0.7288 & 0.796 & 0.7975 & 0.7802 & 18.24 \\ LTFM (time) & 0.8014 & 0.8207 & 0.7975 & 0.8010 & — \\ LTFM (time + location) & 0.8017 & 0.8259 & 0.8101 & 0.8069 & — \\ Proposed & 0.8093 & 0.8328 & 0.8228 & 0.8178 & 16.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Model performance comparison. and time information) is very beneficial for the overall performance improvement. We experimentally confirm that LTFM, considering projection information, obtains better performance than the baseline and improves performance than models that do not consider feature interactions (RF, MLP, etc.). These results demonstrate the importance of modeling feature interactions for perception prediction. Compared with AFM, IFM, etc., which consider the importance of feature interactions, LTFM shows better performance improvement and trains faster.