## 3 The Proposed Scheme
### Feature Clustering and Weighting  
In order to efficiently analyze a large amount of features extracted from the training dataset, a feature clustering and weighting strategy is proposed. The clustering is performed to partition the features into representative groups generating a smaller classification model and allow a higher accuracy of sentiment prediction. In this paper two representative groups, \(G_{D}\) and \(G_{N}\), are constructed to accommodate the distinctive and non-distinctive terms of a category [48].  
distributions, the distribution of the target word over the whole feature space is examined. Then, the words of similar distribution are clustered [49]. The relative distance of similarity, \(D_{i,j}\), between word_w\({}_{i}\) and cluster_G\({}_{\theta}\) (\(\theta=D\lor N\)) is obtained as:  
\[D_{i,j}=||x||_{2}=\sqrt{\sum_{i}x_{i}^{2}}=\sqrt{\sum_{i}\left(\Phi(w_{i},c_{j} )-\exp(G\ _{\theta},c_{j})\right)^{2}} \tag{18}\]  
Here the distance is measured by the Euclidean norm of the \(\Phi\) value of word_w\({}_{i}\) for category_c\({}_{j}\) from the expectation. Recall that the \(\Phi\) value measures the discriminability of a word for the given category. Therefore, it is utilized in measuring the status of the word in that category. \(exp(G_{\theta}\)_c\({}_{j})\) is the expectation of word_w\({}_{i}\) for category_c\({}_{j}\), and it is computed as:  
\[exp(G_{\theta},c_{j})=\frac{1}{p}\sum_{i=1}^{p}\Phi(w_{i},c_{j}) \tag{19}\]  
Here \(p\) is the number of unique words in cluster_G\({}_{\theta}\). The average distance, \(D_{\theta}\) (\(\theta=D\lor N\)), of the words from cluster_G\({}_{\theta}\) is obtained as:  
\[D_{\theta}=\frac{1}{p}\sum_{i=1}^{p}D_{i,j} \tag{20}\]  
Then, all the words of cluster_G\({}_{D}\) are compared with the average distance, \(D_{D}\), to extract the relevant emotive words. If \(D_{D}\geq D_{i,j}\), word_w\({}_{i}\) is not regarded as relevant to \(G_{D}\). Otherwise, it is put to \(G_{N}\). Note that cluster_G\({}_{D}\) accommodates highly relevant words of large discriminative information. Then, the weight for word_w\({}_{i}\), W, is calculated, reflecting its significance in terms of inter-class and intra-class distribution, and it is expressed as:  
\[W(w_{i},G_{D},c_{k})= \frac{1}{p}\cdot\frac{\sum_{i=1}^{p}D_{i}}{\sum_{j=1}^{q}D_{j}} \cdot\sum_{i=1}^{p}IDM(w_{i},c_{k}) \tag{21}\]  
\[W(w_{i},G_{N},c_{k})= \frac{1}{q}\cdot\sum_{i=1}^{q}IDM(w_{i},c_{k}) \tag{22}\]  
Here, the weight assigned to word_w\({}_{i}\) of cluster_G\({}_{D}\) and cluster_G\({}_{N}\) of class_c\({}_{k}\) are represented as \(W(w_{i},G_{D},c_{k})\) and \(W(w_{i},G_{N},c_{k})\), respectively, and \(p\) and \(q\) are the number of unique words of \(G_{D}\) and \(G_{N}\), respectively. Note that cluster_G\({}_{D}\) retains emotive words obtained with fine-grained selection, and \(\sum_{i=1}^{p}D_{i}/\sum_{i=1}^{q}D_{i}\) reflects the ratio of inter-distribution measures between \(G_{D}\) and \(G_{N}\), capturing the intuition that the emotive words greatly represent the orientation of sentiment of the document. \(IDM(w_{i},c_{k})\) is employed as an intra-category distribution metric to accurately reflect the degree of the significance of word_w\({}_{i}\) in class_c\({}_{k}\).