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HYPERSPECTRAL IMAGE FEATURE EXTRACTION BASED ON 
GENERALIZED DISCRIMINANT ANALYSIS 
Guopeng Yang 3, *, Xuchu Yu b , Xin Zhou c ’ 
a Zhengzhou Institute of Surveying and Mapping,450052, Henan, China - yangguopeng@hotmail.com 
b Zhengzhou Institute of Surveying and Mapping,450052, Henan, China - xc_yu@yahoo.com 
c Institute of Information Engineering,450052, Zhengzhou, Henan, China - zx007_0_0@126.com 
Commission VII, WG VII/3 
KEY WORDS: Hyperspectral Image, Feature Extraction, Generalized Discriminant Analysis, Kernel Function 
ABSTRACT: 
The hyperspectral image enriches spectmm 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. 
1. INTRODUCTION 
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 
* Corresponding author. Tel.:+86-13733179927; E-mail address:.yangguopeng@hotmail.com.