## 2 Related Work
### Feature Weighting  
Feature weighting is a process of assigning appropriate weight to individual features in accordance with their relevance to the given domains. It is generally thought of as the generalization of feature selection, where the presence of a feature serves as the criterion for its extraction [44]. Each feature is represented as a binary vector, wherein \"0\" denotes the absence of the feature (evict the feature), and \"1\" denotes the presence (keep the feature) [19]. A variety of feature weighting methods have been introduced, and DF is the simplest one, where the \"single appearance\" of a word is equivalent with \"multiple appearances\" [45]. It counts the number of documents in which a word occurs, and uses the value to represent the corresponding document. TF is another criterion that explores feature weighting in a different direction. It is based on the intuition that the term of multiple appearances is more important than that of a single appearance [46]. Here, the frequency of a word occurring in a document is counted, which is used to represent the document, and is expressed as:  
\[tf_{i,max}=max_{j=1}^{N}\{tf_{i,j}\} \tag{1}\]  
Here, \(tf_{i,j}\) represents the frequency of word_i in document_j, and \(N\) is the number of documents in category_c\({}_{k}\). TF has been proved to be effective, but its performance is degraded with the multi-domain dataset because of the simple measure of words. Term Frequency and Inverse Document Frequency (TF-IDF) is a \"state-of-the-art\" method of feature weighting [47], which comprehensively measures the appearance frequency and distribution of words in assigning the weights, and it is obtained as:  
\[TF-IDF(i,j,D)=tf_{i,j}\cdot idf(i,D) \tag{2}\]  
where \(idf(i,D)\) measures how much information word_i provides to represent document_j in document set_D, which is formulated as:  
\[idf(i,D)\ =\ \log\frac{N}{|\{i\in D\,:\,i\in j\}|} \tag{3}\]  
Here, \(|\{i\in D\text{:}i\in j\}|\) represents the number of documents containing word_i in \(D\). The TF-IDF is effective in selecting important words in a document while eliminating common words, yielding good performance in terms of classification accuracy. Part of Speech-based Weighting (PSW) is another novel feature weighting approach improving the accuracy of Twitter sentiment analysis. It clusters unique words of the categories into different subsets based on the word's Part Of Speech (POS) feature, which is shown in Table 1.  
The words in the subsets are weighted considering the intra-category relevance of the words, which is measured as:  
\[wf_{i,j}=\left\{\begin{array}{c}x\cdot tf_{i},\ tf_{i}\geq E\big{[}F_{j} \big{]}\\ tf_{i},\ otherwise\end{array}\right. \tag{4}\]  
Here, \(wf_{i,j}\) represents the assigned weight for word_i in subset_j, and \(x\) is the weight of the value of 2, 1.5, or 1 for each of the three subsets, which is given to leverage the role of the words in different  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Subset** & **Property** & **POS Tag** \\ \hline Emotion & Adverb, Adjective, Verb & JJ, JJR,..., RB, RBR,..., VB, VBD,... \\ Normal & Norm & NN, NNS, NNP, NNPS... \\ Remain & Remaining & Remaining \\ \hline \hline \end{tabular}
\end{table}
Table 1: The subsets with Part Of Speech (POS) tag.  
subsets in affecting the orientation of the sentiment. \(E[F_{j}]\) refers to the expected frequency of the words in subset_j_ which is computed as:  
\[E[F_{j}]=\sum_{i=1}^{n}tf_{i}\cdot p_{i},\ p_{i}=\frac{tf_{i}}{\sum_{i=1}^{n}tf_ {i}}\ (j=1,2,3) \tag{5}\]  
Note from Equation (4) that only when the TF value of a word is larger than the expected frequency of the subset, the weight is adjusted. This indicates that the word is more informative than the average level of the subset. The PSW method incorporates a clustering technique to classify the words and assign weights based on the semantical meaning and hierarchical relevance of the words, allowing effective feature weighting.