###### Abstract
During step (i), for each user \(U\), users computed to have high similarity with \(U\), based on their likings, represented by the ratings they have entered in the rating database (rDB), are labelled as _U's near neighbours_ (NNs) [27]. In order to identify users' NNs, a similarity function is used, such as the Cosine Similarity and the Pearson Correlation Coefficient, which are the dominant ones in CF research [28; 29]. Having found \(U\)'s NNs and having computed their numeric similarities with \(U\), during step (ii) a prediction formula is used that computes the numeric rating value that \(U\) would give to items that he or she has not evaluated, based on the existed ratings in the rDB [30; 31]. The weight/importance of each NN to the prediction value is based only on this similarity with \(U\), calculated during step (i). Finally, having computed the prediction values of the items that user \(U\) has not evaluated yet, during step (iii) the CF system recommends to U the items that obtained the highest prediction values and hence have the highest probability of \(U\) actually liking them [32; 33]. This work focuses on the second step that a CF system encompasses, i.e., the rating prediction computation; in this step, the proposed approach modifies the weight/importance of each NN to the prediction value, complementing the similarity of \(U\) to his/her NNs with a \"black sheep factor\". More specifically, for each item, we classify users into two categories of interest, those who seem to like the item and those who do not, based on their ratings on this item. When an item is generally accepted, it is more probable to find pairs of users that have entered high ratings for this item. Conversely, it is less probable to find pairs of users that have entered low ratings for the same item. As a result, the novelty of this work is that, after the average rating value (given by all users) of each item is computed, which is a simple and straightforward procedure, it modifies the weight/importance of each NN, based on the aforementioned concept, i.e., based on the relative (un-) acceptance of their commonly rated items, in combination with their ratings on these items. The rationale behind the usage of the aforementioned concept derives from the fact that when in real life a human likes a product (e.g., a TV series, a car model, a videogame) that the majority of others do not (and hence this product obtains a relatively low average rating value), and this human finds another one that also likes the exact same product, the probability of valuing his opinion with greater prominence than the opinions of other users, for a future recommendation, is relatively high. This rationale is in line with the use of the inverse document frequency (IDF) metric in information retrieval, where terms occurring less frequently in the document corpus are assigned higher weights [34]. To validate our approach, an extensive evaluation is presented, using (i) two user similarity metrics, (ii) two rating prediction error metrics, and (iii) six datasets that are widely used in CF research. It is worth mentioning, that the proposed approach (i) does not need any kind of supplementary information, apart from users' ratings on items, and hence can be applied in any CF dataset and (ii) can be fused with other CF approaches, aiming to enhance rating prediction accuracy or efficiency, either using supplementary sources of information, such as users' relations in social networks and detailed characteristics of items [35; 36; 37] or not [38; 39; 40]. The rest of the paper is structured as follows: in Section 2 the related work is overviewed, while in Section 3 the proposed algorithm is introduced. In Section 4 the methodology for tuning the algorithm's operation is reported, as well as the presented algorithm is evaluated. Finally, Section 5 concludes the paper and outlines future work.