## 3 A Novel Method Combining Information and Separability: LBI-BPSO  
From the above introduction, it can be found that both IOIF and GA-BPSO are based on a single wavelength selection criterion to reduce the dimension of HSIs. For objects with similar colors and close spectra, this DR method cannot take into account the high amount of information and the separability between objects, and there are problems such as large redundancy and a large number of selected wavelength information, which leads to a decrease in the accuracy of classification results. Aiming at the shortcomings of the above two methods, this section proposes a new DR method combining wavelengths information and inter-class separability: LBI-BPSO. It focuses the search direction of the particle swarm in the wavelength region with a large amount of information and can obtain a wavelength combination that takes into account the two DR criteria of greater information amount and better sample separability. Finally, the goal of improving the classification accuracy of objects with similar colors is achieved. In this paper, the performance of the above three DR methods is tested by the established HSI dataset. The research ideas of LBI-BPSO can be summarized by the process shown in Figure 2. The object of DR and classification research is the hyperspectral simulation image dataset established in this paper. Some bands of its samples have close characteristics, and the SNR of the data is controlled by controlling the input noise. In the information calculation stage, the local band index LBI of Equation (3) applied in the IOIF algorithm is used to obtain the information content of all wavelengths, and the wavelength with a larger value is selected according to a certain proportion \(\varepsilon\) to complete the preliminary screening of the spectral wavelength. In the search stage, according to the distance between classes, the binary particle swarm optimization algorithm GA-BPSO with the introduction of a genetic mechanism, is applied to realize the search for the optimal solution of the fitness function \(F\) of Equation (11). The wavelength combination with the largest inter-class distance obtained in the data subset with a large amount of information can determine the DR result that contains both high information content and the largest class distance. The data sample \(\mathbf{X}_{i}\) of a certain point in the HSI can be expressed as \(\mathbf{X}_{i}=[x_{1},x_{2},\ldots,x_{n}]\), and \(n\) is the characteristic dimension of the sample, that is, the number of selected wavelengths. Object points of the same class are represented as \(\mathbf{X}_{\omega i}=[X_{1},X_{2},\ldots,X_{N_{i}}]\), and \(N_{i}\) is the number of samples in class \(\omega_{i}\), that is, the number of pixels corresponding to a certain class of ground objects in the image. The pattern average vector of class \(\mathbf{m}_{i}\) is defined as in Equation (8), where \(N_{C}\) is the number of object categories to be classified. As shown in Equation (9), \(d_{ij}\) represents the Euclidean distance from the center of class \(i\) to the center of class \(j\):  
\[\mathbf{m}_{i}=\frac{1}{N_{i}}\sum\limits_{X\in\omega_{j}}X \tag{8}\]  
\[d_{ij}=\left\|\mathbf{m}_{i},\mathbf{m}_{j}\right\|_{2}^{2}=(\mathbf{m}_{i}-\mathbf{m}_{j})( \mathbf{m}_{i}-\mathbf{m}_{j})^{T} \tag{9}\]  
The sample can be identified by judging the distance between the class center vector and the sample feature vector [36]. Based on the maximum distance between classes [36; 37], using the center distance Equations (8) and (9), the objective function \(f\) of the following Equation (10) can be obtained. When the distances between the classes of the samples are larger, the separability between the objects is better. Let the objective function \(f\) be the reciprocal of the sum of the center distances between the classes, and the minimum solution of the function is the best combination of wavelengths.