The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
288 
(2) Calculate the kernel matrix K , and calculate K b and 
K t according to the Equation (15) and (17). 
(3) Resolve the Equation K h a = A,K w a in order to get the 
eigenvector a, corresponding to the maximum eigenvalue. 
(4) Get other discriminant vectors a 2 ,a 3 ,L ,a d by Equation 
(22), and standardize them by dividing yjaf Ka j . 
(5) Extract the feature using Equation (25) for any input 
sample x . 
3. EXPERIMENT 
In order to know whether the feature extraction based on GDA 
could improve the classification precision of hyperspectral 
image, we did two experiments. The experiments data are 
obtained by different remote sensors (AVIRIS and PHI). We 
also compared the GDA with other feature extraction methods, 
including Principal Component Analysis (PCA), Kernel PCA 
(KPA), and Linear Discriminant Analysis (LDA). 
3.1 Experiment Flow 
The steps of the experiments we have done are given below: 
(1) Collect the samples of different ground types according the 
spectral library or the known ground cover information. 
And then, divide the samples into training samples and test 
samples. 
(2) Using the training samples, calculate the transform 
matrixes of different feature extraction methods separately, 
including PCA, KPCA, LDA and GDA. 
(3) From the transform matrixes which we got in Step 2 we 
extracted the feature of the hyperspectral images. 
(4) Train the Minimum Distance Classifier (MDC) through 
training samples with feature extracted by Step 3. And 
then, evaluate the classification result of the testing 
samples. 
3.2 Experiment 1 
Experiment Data: The NASA AVIRIS (Airborne Visible/ 
Infrared Imaging Spectrometer) instrument acquired data over 
the Cuprites mine field, Nevada, USA. AVIRIS acquired data in 
224 bands of 10 nm width with centre wavelengths from 400 - 
2500 nm. The image of this data is shown in Figure 1. There are 
eight kinds of ores in this area; the samples of them are 
described in Table 1. 
Figure 1. Hyperspectral image from AVIRIS 
(R:178,G:111,B:33) 
Class Name 
Samples Number 
Alunite 
604 
Buddingtonite 
89 
Dickite 
395 
Kaolinite 
290 
Lite 
762 
Quartz 
285 
Sait 
381 
Tuff 
1033 
Table 1. Samples of this hyperspectral image 
Atmospheric radiation correction based on ATREM has been 
applied to the AVIRIS image. After eliminating the bands 
which have too much noise and which are absorbed by the 
vapour, we used 190 bands in the experiment. 
We selected 50 samples each class randomly as the training 
samples, and talked the others as testing samples. In the test, we 
selected the Poly kernel and RBF kernel for KPCA and GDA. 
The feature images extracted based on RBF-GDA is shown in 
Figure 2. 
(1) Image of the first feature 
(2) Image of the second feature 
(3) Image of the third feature