## 3 Methods
### Statistical Models  
We used word-grams and char-grams as statistical models (see Section 2.2). In addition, we applied the term-frequency-inverse document frequency (TF-IDF) to measure the relevance of each feature. Specifically, the normalized term frequency of TF was applied. This version of the algorithm divides the number of times that an specific feature appears in the text by the number of features extracted (see Equation (2)). This normalization over the term-frequency (TF) helps to prevent bias in longer or shorter documents.  
\[TF\text{-}IDF=TF*IDF \tag{1}\]  
\[TF=number\_of\_occurrences/number\_of\_grams \tag{2}\]  
\[IDF=\log_{2}corpus\_size/documents\_with\_terms. \tag{3}\]  
For the comparison between the statistical models, we have selected two machine-learning classifiers: (1) RF and (2) SMO. On the one hand, RF is a classification algorithm based on a decision tree [26]. It is an ensemble method, so this technique combines the predictions from multiple machine-learning algorithms together to make more accurate predictions than any individual model. Specifically, Random-Forest is an improvement over bagged decision-trees because the sub-trees are learned to produce less correlation and the results are not over-fitted. On the other hand, SMO is a SVM method, that is a classification algorithm which finds the optimum hyper-plane that distinctly separates the classes in a data-set [27]. SMO can be used to model non-linear relationships used in conjunction, such as specific kernels. However, to find which kernel is most suitable for specific data is a trial-error experiment. To solve this issue we chose a universal kernel based on the Pearson VII function (PUK) [28]. RF and SMO were selected because (1) SMO is an algorithm that can handle non-linearly separable data what it may the case of high-dimensionality problems; (2) RF, although it is not straightforward, allows the use of interpretation techniques that involves to understand what are the features which mostly contributes to its outputs. In this sense, [PERSON] et al., proposed in [29] a method capable of determining the influence of each feature variable for specific instances; (3) both algorithms were applied in the past to perform NLP [30]; and (4) decision-trees and SVM were included among the 25 best classifiers identified in a deep analysis performed in [31].  
The experiments described in this paper were executed in the WEKA platform [32]. Both machine-learning classifiers were trained with a 10-fold cross validation approach. The comparison between the machine learning classifiers was performed by comparing its accuracy (see Equation (4)),  
\begin{table}
\begin{tabular}{l r r r r} \hline \hline
**Fold** & **Size** & **Positive** & **Negative** & **Cut-Off Filter** \\ \hline corpus-1 & 100 & 50 & 50 & 0 \\ corpus-2 & 200 & 100 & 100 & 0 \\ corpus-3 & 400 & 200 & 200 & 0 \\ corpus-4 & 800 & 400 & 400 & 0 \\ corpus-5 & 1600 & 800 & 800 & 0 \\ corpus-6 & 3200 & 1600 & 1600 & 1 \\ corpus-7 & 6164 & 3082 & 3082 & 2 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Details of the corpora splits.  
because it was simple to measure, and because the corpus was balanced, so there was not a dominant class which can lead to high accuracy rates only predicting the dominant class. In addition, the measures of precision (see Equation (5)), recall (see Equation (6)) and F-measure (see Equation (7)) were used in the experiment.  
\[Accuracy=TP+TN/(TP+TN+FP+FN), \tag{4}\]  
\[Precision=TP/(TP+FP) \tag{5}\]  
\[Recall=TP/(TP+FN) \tag{6}\]  
\[F-Measure=2*(Precision*Recall)/(Precision+Recall) \tag{7}\]  
where TP (true positives) is the number of tweets classified as positive and, indeed, they are positive; TN (true negatives) is the number of tweets classified as negative and they are negative; FP (false positives) is the number of tweets classified as positive but they were negative; and, finally, FN (false negatives) stands for the the number of tweets classified as negative but they were labelled as positive.