# Applying Recommender Systems to Predict Personalized Film Age Ratings for Parents
## 5 Experimental Results
### Performance Evaluation  
We performed a wide range of experiments to evaluate the performance of the proposed system. All RMSE values reported are the average of five identical runs per value, with only minor differences between the averaged values observed in the second decimal digits. We first performed several experiments on the shapes of the functions that generated the values \(r_{i}(p,f)\). We employed three different types of functions, namely, the aforementioned linear function shown in Equation (3), a normal (Gaussian) distribution-like  
Figure 3: The distribution of age ratings in the Common Sense Media dataset test file. function, and a Laplace distribution-like function. In the last two cases, the maximum value was set to 1 (as in the linear function), while the variance and diversity parameters, respectively, were set to \(1/\lambda\), which led to similar behavior of the \(\lambda\) parameter in all three cases (i.e., the larger the value, the wider the range of non-zero values). We performed several experiments, using only the information contained in the original training set, in order to find the most efficient function to employ, as well as the optimal value of \(\lambda\). The results of those experiments are shown in Figure 4. As expected, the Laplace and Gaussian functions performed similarly, with the Laplacian one yielding the best result for a \(\lambda\) value of 0.9. One can also observe that both high and low values of \(\lambda\) behaved poorly, which is to be expected. Low values of \(\lambda\) do not differentiate the different age categories enough (due to a wide range of consecutive age categories receiving \(r_{i}(p,f)\) values close to the highest one, whereas high \(\lambda\) values lead to just one age category receiving a high \(r_{i}(p,f)\) value, while the values of the rest will be almost zero (similar to Equation (2)). Having non-zero \(r_{i}(p,f)\) values for age categories adjacent to \(c(p,f)\) helps the recommender systems used in the following step to more easily \"locate\" the most accurate prediction. Using the aforementioned parameter values, we then performed extensive experiments using two collaborative filtering recommender systems, namely ScoR [15] and NeuMF [16]. The experiments can be divided into the following three groups:  
1. In the first group (MRSs--multiple recommender systems), the approach used was the one described in this paper (see Figure 2). 2. The second group (SRS--single recommender system) was a variation of the first, where only one recommender system was used, which was trained on the data of all age categories, instead of a separate independent recommender system per age category (see Figure 5a). 3. Finally, the \"RS\" group corresponds to the experiments performed without any dataset transformation, where both recommender systems used (SCoR and NeuMF) were trained on the original age values (see Figure 5b). Those experiments were performed in order to demonstrate the necessity of the data transformation in the first phase. One can see in the results shown in Table 1 that the MRS-SCoR combination outperforms the rest of the cases. In addition, it is noteworthy that the RMSE values between the SRS and MRS cases while using the same recommender system, which was expected. It is also important to note that not both recommender systems enjoyed similar improvements while employing the data transformation. At the same time, however, in both cases, those improvements are significant. To gain deeper insight into the functioning of the suggested method, on each of the two recommender systems used, we also demonstrate the mean average error for all entries in the test file, per the \"correct\" age category. The results are presented in Figure 6. One can see that ScoR outperformed NeuMF in most age categories except for a narrow range in the middle of the entire age category range. One can also see that most expediencies  
Figure 4: The RMSEs of the MRS-SCoR system for different values of the slope parameter \(\lambda\).