## 4 Results  
To extract the user' opinion (positive or neutral/negative) for the different item characteristics, once the ALS factorization of the input matrix is completed, we proceed to categorize the output data (i.e., predicted \(\hat{s}_{uij}\) sentiment scores) into two classes depending on whether the opinion for a specific topic is positive (\(\hat{s}_{uij}>0\) class), or negative or neutral (\(\hat{s}_{uij}\leq 0\) class).  
The model performance is assessed by means of \(2\times 2\) confusion matrices and their associated metrics: accuracy, F1-Score, precision and Recall; that measures the percentage of the correctly predicted values. These metrics provide insights on result goodness but, due to the unbalanced number of positive/negative samples ratio and the equally importance of misleading a positive or negative prediction, the AUC as performance metric is recommended. Recall that AUC considers the relationship between the sensitivity (true positive rate) and fall-out (false positive rate) being a more robust metric for our case.  
The final results of the above described optimal model are shown in Table 5. It can be observed that there exists consistency among the metrics for the different datasets. Overall, smaller datasets perform slightly better than larger ones in terms of \(F_{1}\), accuracy, precision, and recall metrics. The reason for this behavior is two-fold: First, the input matrix sparsity increases with the dataset size, which hinders the learning process. Second, the positive score population is also patently larger in smaller datasets (with a maximum at 87.1%), dominating over the negative/neutral class. This does not undermine the model foundation, however: This positive-negative score ratio is observed to be shared by most Amazon datasets and, in any case, we are equally interested in both classes of opinions.  
It is in this sense, the AUC metric gives equal importance to positive and negative/neutral classes resulting in a more suitable metric to measure the model prediction capabilities from an application perspective. Its best results are now obtained for the larger datasets and it is also worth highlighting the relatively large AUC achieved for the combined dataset. These results follow from the existence of user complementary information in intersecting datasets.  
Figure 7: AUC versus the regularization parameter \(\lambda\) for \(K=20\) and \(n_{\text{iter}}=10\) for the different datasets.  
To be certain about the significance of the results using the AUC metric, it must be noticed that any random binary classifier is expected to yield an average AUC of 1/2. All our experiments were significantly better than 0.500 compared with the Monte Carlo simulated frequency distribution of the computed AUC over our datasets. The distribution peaks at 0.500, as expected, and is relatively narrow, with approximately 99% of all repeated measurements lower than 0.507. This demonstrates a negligible probability of generating the true experimental value of 0.551 by chance (see Table 5) and the significance of the improvement obtained with our method.  
Finally, it is worth discussing an actual review instance of the full experimental procedure to spot its strengths and aspects that call for improvement. Such an example is shown in Table 6. This particular review contains eight syntactic structures which are shown independently (notice that the NLP analysis for obtaining the opinion keywords and its sentiment is performed at sentence level). Our sentiment analysis service detects five topics/opinion keywords and assesses them with unprocessed sentiment strength scores (third column). The frequencies of occurrence of two of these opinion keywords, namely 'weld' (at row 6) and 'quality' (at row 8), are lower than the threshold frequency explained in Section 3.1, and are therefore discarded. The remaining three entries, normalized as explained in Section 2.2, were originally positive and therefore successfully predicted as such by our binary classifier.