## 3 The Proposed Algorithm
Finally, for each dataset, the algorithm performance under the best-performing hyperparameter setting determined for the specific dataset was assessed, through the experiment described in Section 4.2. In this experiment, the training portion was again used to compute the user similarities and the NN sets for the baseline algorithm (plain CF algorithm) as well as the DR-enriched user-item rating matrix for the CF\({}_{\text{DR}}\) algorithm, while accuracy was measured against the ratings in the holdout portion. The parameters for the plain CF algorithm were set as follows: user \(V\) was considered an NN of \(U\) if \(sim(U,V)>0\) and a prediction \(p_{U,i}\) was formulated when at least one NN of \(U\) had entered a rating for item \(i\). For our experiments, we used a machine equipped with six Intel Xeon [EMAIL_ADDRESS] GHz CPUs with 256 GB of RAM and a 900 GB HDD with a transfer rate of 200 MBps. The aforementioned machine hosted the seven CF datasets and ran the rating prediction algorithms. ### Determining the Algorithm's Parameters

The goal of the first experiment is to determine the optimal values for the parameters \(thr_{\text{NN}}\), \(thr_{\text{sim}}\), and \(w_{dr}\), used in the CF\({}_{\text{DR}}\) algorithm. In order to find the optimal setting for these parameters, we explored different combinations of values for them. In total, more than 30 candidate setting combinations were examined. For conciseness, our presentation is confined to the most indicative settings. For each of the parameter combinations, we present the coverage increase and the improvement of the rating prediction accuracy that were achieved (expressed as reduction to the MAE and RMSE metrics). The results were found to be relatively consistent across the seven datasets tested (for the majority of tests, the parameter value combinations were ranked in the same order across all datasets). Consequently, in this subsection, only the average values of the respective coverage increase and error metrics for the seven datasets are presented. Figure 1 illustrates the coverage increase and the rating prediction error reduction (using both the MAE and the RMSE error metrics) under different settings for parameters \(thr_{\text{NN}}\), \(thr_{\text{sim}}\) and \(w_{dr}\), when similarity is measured using the PCC metric and using the performance of the plain CF algorithm as a baseline. Similarly, Figure 2 depicts the respective measures under the same parameter value combinations, when similarity is measured using the CS metric, again using the performance of the plain CF algorithm as a baseline. In Figures 1 and 2, we can observe that prediction accuracy improvement does not present maxima and minima under the same parameter combinations. Hence, to determine the best choice regarding the optimal setting of parameters, we synthesize the coverage and accuracy metrics into a single score by computing their harmonic mean (HM). This is analogous to the combination of the precision and recall measures into the F1-measure in the information retrieval domain [55]. Notably, the HM is also used in other RS research works for synthesising coverage and error metrics, e.g., [50]. More specifically, the HM is given by the following formula:

\[\text{HM(s)}=2*\frac{normCovInc(s)\times normAccInc(s)}{normCovInc(s)+normAccInc (s)} \tag{6}\]where the normalized value for the coverage increase of the setting \(s\), denoted as _normCovInc(s)_, is obtained using the standard normalization formula [55]:

\[normCovInc(s)=\frac{\text{coverage\_incr}(s)-\text{min}(\text{coverage\_incr}(s))}{s \in\text{all settings combinations}} \tag{7}\]

Figure 1: Prediction error reduction and coverage increase under different parameter value combinations, when using the PCC as the similarity metric. Figure 2: Prediction error reduction and coverage increase under different parameter value combinations, when using the CS as the similarity metric.