# RPC-EAU: Radar Plot Classification Algorithm Based on Evidence Adaptive Updating
## 3 Proposed Method
### Correction and Combination of Evidences
Here, \(S_{l,T}\) is used to represent the confidence similarity between \(m_{I}\) and \(m_{T}\), and \(S_{l,C}\) is used to represent the confidence similarity between \(m_{I}\) and \(m_{C}\), defined as:  
\[S_{l,T}=\sqrt{\sum_{\omega_{P}\in\{\omega_{T},\Theta\}}(m_{I}(\omega_{p})-m_{ T}(\omega_{p}))^{2}} \tag{25}\]  
\[S_{l,C}=\sqrt{\sum_{\omega_{q}\in\{\omega_{c},\Theta\}}(m_{I}(\omega_{q})-m_{ C}(\omega_{q}))^{2}} \tag{26}\]  
Then, we also use the number of evidences as a discount factor, and the updated mass functions for each class from \(m_{I}\) can be obtained as:  
\[\left\{ \begin{array}{l}dm_{I}(\omega_{T})=\frac{(K_{1}+K_{3})m_{T}(\omega_{ T})}{(K_{1}+K_{2}+K_{3})S_{l,T}}\\ dm_{I}(\omega_{C})=\frac{(K_{2}+K_{3})m_{C}(\omega_{C})}{(K_{1}+K_{2}+K_{3})S_{ l,C}}\\ dm_{I}(\Theta)=1-\frac{(K_{1}+K_{3})m_{T}(\omega_{T})S_{l,C}+(K_{2}+K_{3})m_{C}( \omega_{C})S_{l,T}}{(K_{1}+K_{2}+K_{3})S_{l,T}S_{l,C}}\end{array} \right. \tag{27}\]  
Step 5: The Yager rule is still used to combine \(m_{T,C}\) and \(dm_{I}\), so that the global mass function \(m_{G}^{\Phi_{K}}\) can be obtained by:  
\[\left\{ \begin{array}{l}m_{G}^{\Phi_{K}}(\omega_{T})=(m_{T,C}(\omega_{T})+m_ {T,C}(\Theta))dm_{I}(\omega_{T})+m_{T,C}(\omega_{T})dm_{I}(\Theta)\\ m_{G}^{\Phi_{K}}(\omega_{C})=(m_{T,C}(\omega_{C})+m_{T,C}(\Theta))dm_{I}( \omega_{C})+m_{T,C}(\omega_{C})dm_{I}(\Theta)\\ m_{G}^{\Phi_{K}}(\Theta)=m_{T,C}(\omega_{T})dm_{I}(\omega_{C})+m_{T,C}(\omega_{ C})dm_{I}(\omega_{T})+m_{T,C}(\Theta)dm_{I}(\Theta)\end{array} \right. \tag{28}\]  
Each radar plot can form its own global mass function through the above steps. In a sense, these mass functions reflect the confidence distribution in the feature space between different radar plots. This is very helpful for the design and updating of classifiers in the following section of this paper. The correction and combination of evidences discussed above is summarized as a flowchart in Figure 3.  
Figure 3: Flowchart of the correction and combination of evidences in the proposed method. To better illustrate the combination of \(K\) nearest neighbor evidences, an example is given below. **Example 2**. : _Assume there are six pieces of nearest neighbor evidence. We need to combine them to give a decision on the class to which the object belongs. For simplicity, we use #1, #2, #3, #4, #5, and #6 to represent them sequentially. Evidences #1 and #3 suggest that the object may belong to class \(\omega_{T}\); therefore, they provide confidence levels of 0.8 and 0.9 for class \(\omega_{T}\), respectively. On the contrary, evidences #2, #4, and #5 suggest that the object may belong to class \(\omega_{c}\), therefore giving the confidence levels of 0.5, 0.4, and 0.2 for class \(\omega_{c}\), respectively. Evidence #6 does not provide any information about the target class; therefore, all confidence is given to the unknown. The specific mass function representations of these six pieces of nearest neighbor evidence are shown in Table 3. According to the combination process in the proposed method, evidences belonging to the same class are first combined based on the D-S rule--that is, combining #1 and #3 to obtain \(m_{T}\), as well as #2, #4 and #5 to obtain \(m_{C}\); then, combining \(m_{T}\) and \(m_{C}\) to obtain \(m_{T,C}\) by using the Yager rule, while also correcting #6 based on them. Finally, the global mass function is obtained by fusing \(m_{T,C}\) with the modified evidence \(dm_{I}\). The results obtained from these steps are shown in Table 4._