## 3 The Proposed Scheme
### Category Discriminative Strength  
In order to characterize the inter-category distribution, a specific VSM is constructed to represent the feature weight of the words among the whole categories. Here, every single category, \(c_{i}\) (\(\in\)C, \(C\) = {\(c_{1}\),..., \(c_{n}\)}, \(n\) \(\geq\) 1) is viewed as a vector on the feature space, and it is represented as \(v_{c_{i}}(\in V,V=\{v_{c_{1}},\ldots,v_{c_{n}}\})\). \(n\) is the number of the categories, and \(v_{c_{i}}\) denotes the feature value of word_w_ based on target category_c\({}_{i}\). In TF the number of occurrences of a word for a certain document is counted to represent the feature weight of the document. Typically, the greatest feature value among the whole categories is utilized as the global feature weight of the word for that category, which is denoted as:  
\[V_{t}=(v_{c_{1}},\ldots,v_{c_{n}})=\big{(}\underset{1\leq i\leq d_{c_{1}}}{max} (tf_{c_{1},i}),\ldots,\underset{1\leq i\leq d_{c_{n}}}{max}(tf_{c_{n},i})) \tag{6}\]  
This approach effectively analyzes the relative weight of the words based on the frequency. However, the discriminative strength of the words is not properly considered. Note that appropriately reflecting the discriminative strength of the word is crucial for the measure of inter-category distribution. Therefore, the frequency with which a word appears in all of the whole documents of a category, _cf_, is employed instead of TF, and then the VSM is expressed as:  
\[V_{t}=(v_{c_{1}},\ldots,v_{c_{n}})=(cf_{c_{1}},\ldots,cf_{c_{n}})=(\sum_{i=1} ^{d_{c_{1}}}{(tf_{c_{1},i})},\ldots,\underset{i=1}{\overset{d_{c_{n}}}{max}}( tf_{c_{n},i})) \tag{7}\]  
Assume that word_w occurs only in category_c\({}_{1}\). Then, the VSM becomes one element vector, which indicates that word_w is solely relevant to class_c\({}_{1}\). Note that the more categories a word belongs to, the less discriminative information the word retains to distinguish a certain category. Especially, when \(cf_{c_{1}}=cf_{c_{2}}=\ldots=cf_{c_{n}}\), word_w is distributed uniformly in the class space, which indicates that word_w is meaningless in representing any category. In order to effectively measure the inter-class distribution, a novel model called _CDS_ is introduced to measure how much discriminative information a word contains in representing a category, which is expressed as:  
\[CDS(w_{\mu},c_{\
u})=cf_{w_{\mu},c_{\
u}}-cf_{w_{\mu},c_{n}}-\ldots-cf_{w_{\mu },c_{1}}=2 cf_{w_{\mu},c_{\
u}}-\sum_{j=1}^{n}cf_{w_{\mu},c_{j}} \tag{8}\]  
Here, \(n\) is the number of categories containing word_w\({}_{\mu}\) in the training dataset, and \(cf_{w\mu,cv}\) is the frequency of word_w\({}_{\mu}\) appearing in category_c\({}_{\
u}\), which is obtained by summing up the total number of occurrences of word_w\({}_{\mu}\)_ appearing within all the documents of that category. \(CDS(w_{\mu},c_{\
u})\) denotes the total frequency distance of word_w\({}_{\mu}\)_ on the pre-measured category_c\({}_{\
u}\) in the feature space. If \(CDS(w_{\mu},c_{\
u})>0\), word_w\({}_{\mu}\) is viewed as having positive relevance to category_c\({}_{\
u}\), and owns discriminative information with respect to that category. Otherwise, it is regarded as meaningless. Assume that word_w\({}_{\mu}\)_ appears in \(n\) categories. Then, a queue \(Q_{p}\) is built with the sorted values of _CDS_ with respect to \(n\) individual categories in descending order, which is expressed as \(Q_{p}=CDS(w_{\mu},c_{\alpha})\)\(\geq\ldots\)\(\geq CDS(w_{\mu},c_{\beta})\) (\(1\leq\alpha\leq m\), \(1\leq j\leq n\)). Here, \(CDS(w_{\mu},c_{\alpha})\) represents the highest _CDS_ value of the \(n\) elements, which indicates that category_c\({}_{\alpha}\) is the choice for word_w\({}_{\mu}\).