# Fusion Information Multi-View Classification Method for Remote Sensing Cloud Detection
## 3 Proposed Method
### Fusion Information Multi-View SVM Classification Method  
Fusion information multi-view SVM classification method (FIMV-SVM) is based on MCPK, using feature extraction network and three-channel statistical features as view A, and view B data, using privileged information view P to correct the separation hyperplane of view A and view B. The optimized structure constructed is as per Equation (4). \[\underset{w_{A},w_{B},w_{P},\xi_{A},\xi_{B},\xi_{P}}{min} \frac{1}{2}(\|w_{A}\|^{2}+\gamma\|w_{B}\|^{2}+\gamma_{P}\|w_{P}\|^{ 2})\] \[+C_{A}\sum_{i=1}^{l}\xi_{i}^{A}+C_{B}\sum_{i=1}^{l}\xi_{i}^{B}+C_{ P}\sum_{i=1}^{l}\xi_{i}^{P}+C\sum_{i=1}^{l}\xi_{i}^{A}\xi_{i}^{B},\] \[s.t. y_{i}(w_{A}\cdot\phi_{A}(x_{i}^{A}))\geq 1-\xi_{i}^{A},\] \[y_{i}(w_{B}\cdot\phi_{B}(x_{i}^{B}))\geq 1-\xi_{i}^{B},\] \[y_{i}(w_{P}\cdot\phi_{P}(x_{i}^{P}))\geq 1-\xi_{i}^{B},\] \[y_{i}(w_{P}\cdot\phi_{P}(x_{i}^{P}))\geq 1-\xi_{i}^{P},\] \[\xi_{i}^{A}\geq y_{i}(w_{B}\cdot\phi_{B}(x_{i}^{B})),\] \[\xi_{i}^{B}\geq y_{i}(w_{A}\cdot\phi_{A}(x_{i}^{A})),\] \[\xi_{i}^{A}\geq y_{i}(w_{P}\cdot\phi_{P}(x_{i}^{P})),\] \[\xi_{i}^{B}\geq y_{i}(w_{P}\cdot\phi_{P}(x_{i}^{P})),\] \[+C_{A}\sum_{i=1}^{l}\xi_{i}^{A}+C_{B}\sum_{i=1}^{l}\xi_{i}^{B}+C_{ P}\sum_{i=1}^{l}\xi_{i}^{P}+C\sum_{i=1}^{l}\xi_{i}^{A}\xi_{i}^{B},\]0  
In optimization problem (4), \(\|w_{A}\|^{2}\) and \(\|w_{A}\|^{2}\) are regularization terms of view A and view B, \(\|w_{p}\|^{2}\) is a regularization term for privileged information view P, respectively. \(C_{A}\), \(C_{B}\), and \(C_{P}\) are non-negative penalty parameters, \(\xi_{i}^{A}=[\xi_{1}^{A},\ldots,\xi_{l}^{A}]\), \(\xi_{i}^{B}=[\xi_{1}^{B},\ldots,\xi_{l}^{B}]\), and \(\xi_{i}^{P}=[\xi_{1}^{P},\ldots,\xi_{l}^{P}]\) are non-negative slack parameters. \(\gamma\) is the balance parameter to balance the weight of view A and view B. \(\gamma_{P}\) is used to weigh the influence of privileged information view P; \(\phi_{A}(x_{i}^{A})\), \(\phi_{B}(x_{i}^{B})\), and \(\phi_{P}(x_{i}^{P})\) represent the mapping of views data. In the constraint, \(y_{i}(w_{P}\cdot\phi_{P}(x_{i}^{P}))\geq 1-\xi_{i}^{P}\) denote that the slack variables are constrained by the view P. \(\xi_{i}^{A}\geq y_{i}(w_{P}\cdot\phi_{P}(x_{i}^{P}))\), and \(\xi_{i}^{B}\geq y_{i}(w_{P}\cdot\phi_{P}(x_{i}^{P}))\) correcting constraints on the classification hyperplane through the correction hyperplane formed by privileged information. For the solution of the above optimization problem, it can be transformed into a Lagrangian dual problem and solved by solving quadratic convex optimization. The Lagrangian function is Equation (5). \[+C_{A}\sum_{i=1}^{l}\xi_{i}^{A}+C_{B}\sum_{i=1}^{l}\xi_{i}^{B}+C_{ P}\sum_{i=1}^{l}\xi_{i}^{P}+C\sum_{i=1}^{l}\xi_{i}^{A}\xi_{i}^{B},\]1 \[+C_{A}\sum_{i=1}^{l}\xi_{i}^{A}+C_{B}\sum_{i=1}^{l}\xi_{i}^{B}+C_{ P}\sum_{i=1}^{l}\xi_{i}^{P}+C\sum_{i=1}^{l}\xi_{i}^{A}\xi_{i}^{B},\]2 \[+C_{A}\sum_{i=1}^{l}\xi_{i}^{A}+C_{B}\sum_{i=1}^{l}\xi_{i}^{B}+C_{ P}\sum_{i=1}^{l}\xi_{i}^{P}+C\sum_{i=1}^{l}\xi_{i}^{A}\xi_{i}^{B},\]3 \[+C_{A}\sum_{i=1}^{l}\xi_{i}^{A}+C_{B}\sum_{i=1}^{l}\xi_{i}^{B}+C_{ P}\sum_{i=1}^{l}\xi_{i}^{P}+C\sum_{i=1}^{l}\xi_{i}^{A}\xi_{i}^{B},\]4 \[+C_{A}\sum_{i=1}^{l}\xi_{i}^{A}+C_{B}\sum_{i=1}^{l}\xi_{i}^{B}+C_{ P}\sum_{i=1}^{l}\xi_{i}^{P}+C\sum_{i=1}^{l}\xi_{i}^{A}\xi_{i}^{B},\]5  
where \(K_{A}(x_{i}^{A},x_{j}^{A}),K_{B}(x_{i}^{B},x_{j}^{B}),K_{P}(x_{i}^{P},x_{j}^{ P})\) represents the kernel mapping mode of view A, view B, and view P feature data, respectively. The optimization problem Equation (6) is a quadratic convex programming problem, which can be solved by the quadratic convex programming method. Solving the optimal parameters \(\alpha_{i}^{A*},\alpha_{i}^{B*},\beta_{i}^{A*},\beta_{i}^{B*},\lambda_{i}^{A* },\lambda_{i}^{B*},\mu_{i}^{A*},\mu_{i}^{B*},\)\(\mu_{i}^{B*}\), we use the Karush-Kuhn-Tucker(KKT) [29] condition to obtain the optimal result \(w_{A}^{*}\) and \(w_{B}^{*}\). The calculation results are shown in Equations (7) and (8).