# Enhancing Recommendation Accuracy of Item-Based Collaborative Filtering via Item-Variance Weighting
## 4 Experiments and Evaluation
### Experimental Setup and Evaluation Metrics  
Here, we used two popular real-world datasets that are often used to evaluate RSs. One is the MovieLens10M dataset [30], which was collected by the GroupLens Research Project from January 1995 to January 2009 (168 months). This dataset contains 10,681 movies, 69,878 users and a total of 10 million ratings on a scale of \(\{0.5,1,1.5,2,2.5,3,3.5,4,4.5,5\}\). In this dataset, each user has rated at least 20 movies. The other dataset is the Netflix dataset obtained from the Netflix Prize website ([[http://www.netflixprize.com](http://www.netflixprize.com)]([http://www.netflixprize.com](http://www.netflixprize.com))). This dataset was collected between October 1998 and December 2005 (85 months) and it contains a total of 100 million ratings of 17,770 movies from 480,189 users. The ratings are on a \(\{1,2,3,4,5\}\) scale and each user has rated a different number of movies. In this paper, considering the huge number of items and users in the MovieLens10M and Netflix dataset, to obtain a manageable size, for each dataset, we randomly selected 2000 items as the experimental data. In our experiment, in order to mimic real-world conditions, we utilized one of the most popular rating orders: the user-centered and time-dependent ordering conditions combination to build the training and test sets [20]. For each item, we ordered the ratings by timestamps separately and the most recent 20% of the ratings were treated as test data and the remaining 80% were treated as training data. We used the training data to compute the item-item similarity and predicted rating scores for the test data and the test data were used to evaluate the performance of the proposed approach. As the MovieLens10M dataset was collected over 168 months, we used two months period (60 days) as the time decay rate. As the Netflix data were collected over 85 months, we utilized a month period (30 days) as the time decay rate. To avoid the impact of accidental phenomena, we repeated experiments for each dataset 20 times and computed the average values as the results. In RSs, the customer's confidence in the system depends on both the predictive accuracy and classification accuracy. Therefore, in our experiments, we used the mean absolute error (_MAE_) and root-mean-square error (_RMSE_) to represent the predictive accuracy of recommendations. In addition, we used precision, recall and _F1_ measures to represent the classification accuracy of recommendations. The MAE and RMSE metrics demonstrate the average error between predictions and real values; therefore, lower values represent higher accuracy. The MAE and RMSE are expressed as follows:  
\[MAE=\ \frac{1}{card(U)}\sum_{u\in U}\left(\frac{1}{card(O_{u})}\sum_{x\in O_{u }}\left|p_{u,x}-\ r_{u,x}\right|\right) \tag{10}\]  
\[RMSE=\ \frac{1}{card(U)}\sum_{u\in U}\sqrt{\frac{1}{card(O_{u})}\sum_{x\in O_{ u}}\left(p_{u,x}-\ r_{u,x}\right)^{2}} \tag{11}\]  
where \(O_{u}=\{x\in I\big{|}p_{u,x}\
eq\star\wedge r_{u,x}\
eq\star\}\) indicates a set of items rated by user u with prediction values. Precision refers to the proportion of relevant recommended items from the total number of recommended items for the target user. Here, higher values indicate better performance. Assuming that \(N_{s}\) is the number of recommended items for the target user, \(N_{rs}\) denotes the amounts of items the target user likes that appear in the recommended list. The precision metric is defined as follows:  
\[Precision=\frac{N_{rs}}{N_{s}} \tag{12}\]Recall indicates the proportion of relevant recommended items from all relevant items for the target user. Similar to precision, higher recall values indicate better performance. Here, \(N_{r}\) denotes the number of items preferred by the target user.