Hyperspectral Image Feature Extraction Based on Generalized Discriminant Analysis

The hyperspectral image enriches spectrum information, so compared with panchromatic image and multispectral image; it can classify the ground target better. The feature extraction of hyperspectral image is the necessary step of the ground target classification, and the kernel method is a new way to extract the nonlinear feature. In this paper, First the mathematical model of the generalized discriminant analysis was described, and then the processing method of this model was given, finally, we did two experiments. Through the tests, we can see that, in the feature space extracted by generalized discriminant analysis, the samples of the same class are near with each other; the samples of the different classes are far away. It can be concluded that the method described in this paper is suitable to hyperspectral image classification, and it can do better job than the method of linear discriminant analysis. * Corresponding author. Tel.:+86-13733179927; E-mail address:[email protected]. 1. INTRODUNCTION Hyperspectral remote sensing technology, which firstly comes out in the early 1980s, organically hangs the radiation information which relates to the targets’ attribute, and the space information which relates to the targets’ position and shape together. The spectrum information, which the hyperspectral image enriches, compared with panchromatic remote sensing image and multi-spectral remote sensing image, can be used to classify the ground target classification better. Hyperspectral remote sensing has very wide electromagnetic wave range, from visible light to shortwave red, even to medium infrared and thermal infrared. It has high spectral resolution, and has lots of bands, so can get the ground target’s spectral feature curve, and recognize the targets by selecting and extracting the bands. We can get the target’s spectral radiant parameters, and the quantitative analysis of the earth's surface target and extraction become possible. Because of the advantages of hyperspectral remote sensing, at present, lots of countries in the world have respect for this type of remote sensing. Hyperspectral remote sensing craft is form aerial to space aerospace. It’ will become an important path of map cartography, vegetation investigation, ocean remote sensing, agriculture remote sensing, atmosphere research, environment monitoring, military information acquiring (Tong et al., 2006). The hyperspectral images have so high dimension and the ground targets are so complicated, that it’s difficult to obtain enough training samples (Hoffbeck et al., 1996). However, the traditional image classification method, such as the statistical pattern recognition and neural networks methods, which are based on large number samples hypothesis, need to get enough training samples to evaluate the prior classes’ information which often cause the “Hughes” phenomenon. So, the feature extraction is one of the most important steps when we analyze the hyperspectral images (Zhang, 2003). In the mid 1990s, with the kernel method applied to support vector machine successfully, people try to extend the ordinary linear methods of feature extraction and classification to nonlinear situation by using kernel function. Kernel methods for pattern analysis are developing so fast that there are so many achievements in the applied fields. It is named as the third revolution of pattern analysis algorithms following the linear analysis algorithms, neural networks and decision trees learning algorithms. Kernel methods have become focus of machine learning, application statistic, pattern recognition, and data mining, successfully applied in face recognition, speech recognition, character recognition, machine malfunction classification and so on (John et al., 2005). We don’t need to know the concrete form and parameters of the nonlinear mapping, the changes of form and parameters of kernel function can change the mapping from the input space to feature space, and change the performance of kernel methods. We can avoid dimension disasters phenomenon which exits in traditional mode analysis methods by using the kernel function, and it also can simplify computation, therefore, Kernel methods can precede the input with high dimensions. The kernel methods can combine with the different analysis algorithms, design the different kernel algorithms, and the two parts can be designed separately, so we can select different kernel function and analysis algorithm in different application fields. In order to improve classification accuracy of hyperspectral remote sensing image, we can use the special classifier, such as SVM and KFDA. If we extract suitable feature of the hyperspectral image, the common classifier also can be used. One of the research trends in hyperspectral image is the