## 3 The Proposed Algorithm
Similarly, the value for normalized accuracy according to the MAE error metric is obtained using the same normalization formula:

\[normAcc(s)=\frac{MAE\_reduction(s)-\min(MAE\_reduction(s))}{s\in all\ settings\ combinations} \tag{8}\]

An analogous formula is employed to obtain the value for normalized accuracy according to the RMSE error metric. Figure 3 illustrates the results of the HM of the normalized coverage and accuracy increase measures for the candidate settings presented above, when using the PCC as the similarity metric. In Figure 3, we can observe that the third setting ({\(\text{thr}_{\text{NN}}=3\), \(\text{thr}_{\text{sim}}=0.0\), \(\text{w}_{\text{dr}}=1.0\)}) is the best performer across both error metrics, with its harmonic mean being equal to 0.84 under both error metrics. The fourth setting ({\(\text{thr}_{\text{NN}}=3\), \(\text{thr}_{\text{sim}}=2.5\), \(\text{w}_{\text{dr}}=0.8\)}) is the runner up, scoring an HM equal to 0.82 under the MAE error metric and 0.80 under the RMSE error metric. Similarly, Figure 4 illustrates the results of the HM of the normalized coverage and accuracy increase measures for the eight candidate settings, when using the CS as the similarity metric. Again, the performance of the plain CF algorithm is used as a baseline. In Figure 4, we can observe that again the third setting ({\(\text{thr}_{\text{NN}}=3\), \(\text{thr}_{\text{sim}}=0.0\), \(\text{w}_{\text{dr}}=1.0\)}) attains the highest harmonic means under both error metrics (0.83 under both the MAE and RMSE), closely followed by the fourth setting (0.82 under the MAE and 0.81 under the RMSE). The fifth setting ({\(\text{thr}_{\text{NN}}=2\), \(\text{thr}_{\text{sim}}=1.0\), \(\text{w}_{\text{dr}}=1.0\)}) follows, with its HM under the MAE being 0.81 and its HM under the RMSE being 0.80. Taking into account that the third setting ({\(\text{thr}_{\text{NN}}=3\), \(\text{thr}_{\text{sim}}=0.0\), \(\text{w}_{\text{dr}}=1.0\)}) achieves the best performance under both similarity metrics and under both error metrics, for the rest of this paper we adopt this setting for all experiments. This practically means that (a) any prediction with at least 3 NNs taking part in its formulation is considered robust and hence produces a DR and (b) the importance of

Figure 3: Harmonic Mean of the normalized accuracy and coverage increase measures for the candidate setting, when using the PCC as the similarity metric. DRs in the prediction formulation process is equal to that of an explicitly entered (real) user rating. This aspect is also exploited for optimization purposes, since no additional information needs to be entered to the user-rating matrix in order to discriminate between real ratings and DRs. In the next subsection, we present the results obtained in the experiments in more detail, per individual dataset. As noted above, the CF\({}_{\text{DR}}\) algorithm parameters were set to the values proven to be optimal (i.e., \(\{\text{thr}_{\text{NN}}=3\), \(\text{thr}_{\text{sim}}=0.0\), \(\text{w}_{\text{dr}}=1.0\}\)). ### Performance Evaluation

Following the identification of the optimal parameter values for the operation of the CF\({}_{\text{DR}}\) algorithm, we evaluated the performance of the algorithm in terms of dataset density increase, prediction coverage increase, and prediction accuracy improvement using the seven datasets listed in Table 4.

#### 4.2.1 Density Increase

Figure 5 illustrates the densities of the seven datasets listed in Table 4: (a) in their initial form and (b) after the enrichment with the DRs produced by the CF\({}_{\text{DR}}\) algorithm's preprocessing step. Note that a base-10 logarithmic scale is used for the Y axis. Under the PCC similarity metric, the incorporation of the DRs achieves an increase of the average density from 0.6% that the initial datasets averaged, to 18.54%.