# Addressing the Cold-Start Problem in Recommender Systems Based on Frequent Patterns
## 3 Proposed Methodology
Therefore, if there are not sufficient extracted (discriminant) itemsets (i.e., high minimum support) the accuracy of the methodology is decreased. However, there is a wide range of minimum support (0-25%) which guarantees the very high accuracy of the proposed methodology. The value

of \(\varphi\) parameter does not affect remarkably the performance while the value of \(\theta\) parameter affects only slightly the performance. Figure 3: Cross-validation results (100% removal, with respect to minimum support). Figure 2: Cross-validation results (100% removal, minimum support = 0.15). Figure 4: Cross-validation results (50% removal, minimum support = 0.15). Figure 5: Cross-validation results (50% removal, with respect to minimum support). \[Positive\ Predictive\ Value-PPV\ (Precision)=\frac{TP}{TP+FP} \tag{6}\]0 Cross-validation results (with respect to remove percentage, minimum support = 0.15). The results in Figure 2 show that the value of plentifulness is greater than 1, which means that the proposed methodology recommends more products than those included in the initial user-product input matrix. This is a very important result as far as the sparsity problem is concerned. Note that the density of the initial user-product matrix is 6.3%, which is increased to about 14% by the proposed methodology (plentifulness rate \(\approx 8\%\)), while only a small fraction of initially non-empty cells turned into empty cells by the proposed methodology (plentifulness predictive value \(\approx 0.73\)). At the same time, the results in Figure 2 show that the value of positive predictive value is close to 1, which means that the proposed methodology does not recommend products that were negatively rated by the user (FP), although some of the products that were initially positively rated by the user are not recommended (sensitivity \(\approx 0.5\)). Therefore, the proposed methodology tackles the sparsity problem by recommending more new products than the known ones while, although it cannot detect all the known ones, it does not recommend products that the users do not like, based on the initial user-product input matrix. The above results hold also for the _in-matrix prediction_ setup, where 50% of the non-empty cells of each row (user) included in the test set were cleared and then they were updated by the proposed methodology. Therefore, only the sensitivity and positive predictive value measures are considered. In Figure 4, the cross-validation results (average over the \(k=10\) runs) for these evaluation measures are shown with respect to different values of \(\theta\) parameter while the minimum support is set to 15% and \(\varphi\) parameter to 0.001. In Figure 5, the cross-validation results for the evaluation measures are shown with respect to different values of minimum support while the \(\theta\) parameter is set to 1 and \(\varphi\) parameter to 0.001. Note that the fraction of cells of a row that is cleared does not affect the performance of the proposed methodology. In Figure 6, the cross-validation results (average over the \(k=10\) runs) for these evaluation measures are shown with respect to different fractions of cleared cells, while \(\theta\) parameter is set to 1, minimum support to 15%, and \(\varphi\) parameter to 0.001. Therefore, based on the experimental results, the proposed methodology can efficiently handle both the _in-matrix_ and _out-of-matrix prediction_, i.e., both matrices that are sparse and matrices that contain users even with no rating history at all. #### Comparison to Similar Methods

To further evaluate the accuracy of the proposed methodology, it is compared to similar methods presented in the literature, with respect to precision (positive predictive value), recall (sensitivity), and F1 measures. Table 3 shows the experimental results for these three measures concerning the MovieLens dataset ([PERSON] et al., 2016).