## 3 The Proposed Algorithm
Regarding the dense dataset \"MovieLens 100 K\", the proposed algorithm was found to surpass the performance of the CF\({}_{\text{FOAF}}\) algorithm by a margin of 0.21% in absolute figures, while, in terms of relative improvement, the edge of the proposed algorithm is quantified to 15.2%. #### 4.2.3 Prediction Accuracy Increase

In this subsection, we present detailed results on the algorithm performance evaluation in terms of rating prediction error reduction, where the error is measured using the MAE and the RMSE metrics, for the same seven datasets. As before, besides obtaining absolute metrics regarding the prediction accuracy achieved by the CF\({}_{\text{DR}}\) algorithm, we also compare its performance to the performance of the CF\({}_{\text{VNN}}\) algorithm introduced in [27] and the CF\({}_{\text{FOAF}}\) algorithm introduced in [29]. Figure 8 illustrates the results obtained regarding the prediction accuracy, in terms of the MAE, when the metric used to quantify similarity between users is the PCC. The considerable differences observed for the values of the MAE metric between the MovieLens dataset on the one hand and the Amazon datasets on the other is that, in the former dataset, the ratings range from 0 to 9, whereas in the Amazon datasets, ratings range from 1 to 5. \[\text{HM(s)}=2*\frac{normCovInc(s)\times normAccInc(s)}{normCovInc(s)+normAccInc (s)} \tag{6}\]3 Coverage increase for the datasets summarized in Table 4, when the CS user similarity metric is used. We can observe that the CF\({}_{\text{DR}}\) algorithm, presented in this paper, achieves an average prediction MAE reduction equal to 2.06% (in absolute terms 0.877 versus 0.895, the plain CF achieves), exceeding the performance of the CF\({}_{\text{VNN}}\) algorithm [27] (which is measured at 1.42%) by 0.64% in absolute figures, or 45.1% as a relative improvement. When compared with the CF\({}_{\text{FOAF}}\) algorithm [29], the CF\({}_{\text{DR}}\) algorithm outperforms CF\({}_{\text{FOAF}}\) (whose MAE reduction was measured at 1.17%) by a margin of 76.3%. On the individual dataset level, the performance edge of the proposed algorithm against the CF\({}_{\text{VNN}}\) algorithm (which achieves a higher MAE reduction than the CF\({}_{\text{FOAF}}\) algorithm), ranges from 25.9% (for the Amazon \"Digital Music\" dataset) to 84.4% (for the Amazon \"Videogames\" dataset). Similarly, Figure 9 illustrates the results obtained regarding the prediction accuracy increase, in terms of the MAE, when the CS metric is used to quantify similarity between users. \[\text{HM(s)}=2*\frac{normCovInc(s)\times normAccInc(s)}{normCovInc(s)+normAccInc (s)} \tag{6}\]4 Rating prediction MAE for the datasets summarized in Table 4, when the PCC user similarity metric is used. \[\text{HM(s)}=2*\frac{normCovInc(s)\times normAccInc(s)}{normCovInc(s)+normAccInc (s)} \tag{6}\]5 Rating prediction MAE for the datasets summarized in Table 4, when the CS user similarity metric is used. In Figure 9, we notice that the CF\({}_{\text{DR}}\) algorithm, presented in this paper, achieves an average prediction MAE reduction equal to 2.19% (in absolute terms 0.814 versus 0.832, the plain CF achieves), exceeding the performance of the CF\({}_{\text{VNN}}\) algorithm [27] (which is measured at 1.65%) by 0.54% in absolute figures, or 32.1% as a relative improvement. The CF\({}_{\text{DR}}\) algorithm also surpasses the performance of the CF\({}_{\text{FOAF}}\) algorithm [29] (which is measured at 1.55%) by 41.4%. On the individual dataset level, the performance edge of the proposed algorithm against the CF\({}_{\text{VNN}}\) algorithm (which achieves higher MAE reduction than the CF\({}_{\text{FOAF}}\) algorithm), ranges from 8.12% (for the Amazon \"Digital Music\" dataset) to 79.7% (for the Amazon \"Office Supplies\" dataset). Figure 10 illustrates the results obtained regarding the prediction accuracy increase, in terms of the RMSE, when the PCC was used to quantify similarity between users.