## 3 Methodology
### Improved SVM Model  
The SVM theory can be found in the research of [PERSON] [35] and [PERSON] et al. [36]. Its advantage is that the SVM can search for support vectors with greater discrimination ability, perform the construction of classifiers, and maximize the interval between various types. The primary idea is to map non-linear separable sample data to a high-dimensional linear space, and then create an optimal classification hyperplane in the kernel space, transform the classification problem into a convex quadratic programming problem, and then introduce a kernel function. Furthermore, we synthesize empirical risk and confidence range in order to find the decision function to minimize the expected upper bound on risk [37]. The original SVM algorithm seeks a linear decision surface by using \(f(x)=W\cdot X+b\), where \(W\) denotes the vector of dimension coefficients and \(b\) the offset. The linear SVM achieves the best hyperplane by solving the following optimization problems:  
\[W\cdot X_{i}+b\geq 1\ Y_{i}=1,\ i=1,2,3,\ldots N\]  
\[W\cdot X_{i}+b\leq-1\ Y_{i}=-1\]  
Combining the above formulas gives the following formula:  
\[Y_{i^{\prime}}(W\cdot X_{i}+b)\geq 1\ i=1,2,3,\ldots N\]  
The optimization of the best hyperplane can be transformed into a Lagrangian dual problem as follows:  
\[L(W,b,a)=\frac{1}{2}\|W\|^{2}-\sum_{i=1}^{N}a_{i}[(W\cdot X_{i}+b)-1]\]  
where \(a_{i}\geq 0\) denotes the Lagrangian multiplier. The final classification discriminant function can be expressed as follows:  
\[f(X)=\sum_{i=1}^{N}a_{i}Y_{j}X_{i}^{T}X+b\]  
In most cases, the SVM maps non-linear training samples to a high-dimensional feature space and constructs a linear discriminant function. RBF is one of the most popular and generally used kernel functions. It offers satisfactory generalization ability. One has the following:  
\[f(X)=\sum_{i=1}^{N}a_{i}Y_{j}K(X_{i}\cdot X)+b\]  
where \(K\geq 0\) denotes the constant coefficient. RBF is a useful feature, which has been widely implemented to map multiple original features to infinite dimensions. The RBF kernel needs to set two important parameters, namely, C and \(\gamma\). C is the penalty parameter, which indicates a positive constant that determines the degree of penalized loss. \(\gamma\) is the kernel parameter, which controls the width of the RBF kernel and determines the distribution after datasets is mapped to a new feature space [38]. To explore the method for quickly finding the optimal parameters (C and \(\gamma\)) of the SVM classifier, this research employed an improved method. Aiming at the object-oriented high-resolution remote-sensing image classification, a large amount of sample data and a large number of dimensions led to the disadvantage of the time required by the grid search method in finding the best parameters. This study used PCA to achieve data-dimensionality reduction and eliminate the correlation between sample attributes, following which it set the initial value of the parameter search range on the basis of the dimensionality-reduction data [39]. On the basis of the optimal parameters of the SVM classifier based on PCA dimensionality reduction data [40; 41], we delimited the search range of the original data classifier parameters, and we also optimized the parameters of the grid search method to obtain the best combination of parameters based on the original data.