###### Abstract
Then, the recommendation algorithm would either refrain from formulating a recommendation or use the mean database rating value for items \(i_{4}\) and \(i_{5}\), which is 5 for both items, and therefore would arbitrarily choose among them. In the DR-enriched rating matrix context, the recommendation algorithm has a prediction for rating \(r_{U3,i4}\) at its disposal and can therefore knowledgably select and recommend \(i_{4}\) to \(U_{3}\). In the DR-enriched item rating matrix, already existing near neighbours of a user \(U\) can contribute more ratings when rating predictions for user \(U\) are calculated, therefore it is possible to compute predictions regarding \(U\)'s ratings on items, which could not have been computed on the basis of the original user-item rating matrix. Indeed, we can observe that, due to the addition of DR \(r_{U3,i3}\), user \(U_{2}\), who was formerly a NN of \(U_{1}\), can now contribute to the computation of a rating prediction for \(r_{U3,i3}\). Regarding the recommendation formulation stage, when the RS utilises the DR-enriched rating matrix the recommendation algorithm, having at its disposal a prediction for rating \(r_{U3,i3}\), it can knowledgeably refrain from recommending item \(i_{3}\) to \(U_{1}\), rather than relying on the database rating mean value for this item. Regarding user \(U_{4}\), who had no common ratings with any other user in the user-item rating matrix, still no near-neighbours can be identified for him/her in the context of the DR-enriched user-item rating matrix. Similarly, in the same context, no personalized prediction can be computed for item \(i_{5}\). These cases mainly correspond to the cold start problem [4; 5]. The cold start problem can be tackled using content-based algorithms [6; 7], context-based algorithms [8], and social network-based algorithms [9; 10]. Each class of such algorithms requires additional information, while it is also possible that such algorithms are combined with the approach presented in this paper. In the example presented above, for simplicity, each rating prediction was considered to be robust and hence produced a DR. However, this setting may not be the optimal one. The optimal setting for tuning the algorithm operation, regarding the characterization of predictions as robust, is presented in Section 4. Notably, the procedure employed in Section 4 follows a grid search approach to hyperparameter tuning. Since hyperparameters moderate the importance of various robustness \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**User/Item** & \(\mathbf{i_{1}}\) & \(\mathbf{i_{2}}\) & \(\mathbf{i_{3}}\) & \(\mathbf{i_{4}}\) & \(\mathbf{i_{5}}\) \\ \hline U\({}_{1}\) & 1 & 5 & 5 & \\ U\({}_{2}\) & 1 & 5 & 1 & 5 \\ U\({}_{3}\) & 1 & 5 & 1 & \\ U\({}_{4}\) & & & & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: User-item rating database excerpt after the execution of the preprocessing step of CFDR. estimators (e.g., number and similarity of contributing NNs), alternative methods can be employed for combining the partial estimators to optimize the prediction model, such as merging estimators [11; 12; 13]. In order to validate the CF\({}_{\text{DR}}\) algorithm, an extensive evaluation is conducted, assessing (1) the degree of density enrichment, (2) the prediction coverage increase, and (3) the prediction accuracy increase, achieved by the proposed algorithm. In this evaluation, we use seven contemporary and widely used CF datasets from various domains (videogames, music, movies, food, etc.). We consider the two most widely used CF similarity metrics, namely the Pearson correlation coefficient and the cosine similarity and the two most widely used CF error metrics, namely the mean average error and the root mean square error.