The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
3.1.2 DFNN input variables: Vegetation spectral 
reflectance is associated with the biochemical composition in 
leaves, such as structure of mesophyll cells, chlorophyll 
content and water content. In different wavelengths, vegetation 
spectrum reflectance curves show different patterns and 
characteristics (Yunzhao Wu et al., 2005). A number of studies 
have demonstrated that shifts in vegetation spectra due to 
heavy metal contamination occurred both the visible and the 
near-infrared part of the spectrum. These studies used spectral 
vegetation indices to investigate changes in plant stress, for 
they can combine two or more spectral bands to enhance the 
vegetative signal while minimizing background effects 
(Lehmann, F. et al., 1991; Sommer, S. et al., 1998; Mohammed 
et al., 2000; L. Kooistr et al., 2004).Heavy metal contamination 
will affect the status of plants, such as pigment contents, 
photosynthetic efficiency, nitrogen contents in canopy, and 
carbon contents of leaf. Values of NDVI, EVI and NDVIg can 
indicate the changes of these factors listed above. Therefore, 
they were chosen as the input variables in this model. 
3.2 DFNN Training Algorithm 
The aim of the training procedure is to minimize the error, i.e. 
the difference between the calculated output values and the 
target output values, and to generate fuzzy rules. The 
adaptation of the weights during the training process can lead 
to a so called over training problem. This means that the neural 
network can reproduce the training data quite well but has lost 
its ability to generalize. The phenomenon is especially severe 
when only a few training patterns are available. 
Therefore, this model starts with a simple network structure 
which contains no fuzzy rules and goes over stepwise to more 
complicated structure. During training process, fuzzy rules will 
be generated according to the system performance. And in the 
meantime, insignificant rules will be deleted. 
3.2.1 DFNN structure determination: In fuzzifier layer, 
input data are fuzzified and membership grades are calculated 
according to Gaussian membership function. The membership 
grade of each input value X i (i=l, 2...r) is given by: 
p..(x ) = exp[ ' 2 V ] (i=l ...r; j=l, 2... u) (2) 
a v 
Where p.. = the membership grade of x. according to the j th 
V t 
membership function 
= the centre of the j th membership function 
<Tj = the importance of the j th membership function. 
The output results obtained from this layer are then used as 
input values to the inference engine where T-norm product 
operator is applied to calculate the trigger weight of each rule. 
The output value of the j th rule is computed according to the 
following function: 
r (Xi-ca) 
<f> fx v x 2 ,...,x r ) = exp[-X -J-—] (3) 
/=1 a ÿ 
The single node in defuzzifier layer is a fixed node labeled X , 
which computes the overall output as the summation of all 
incoming signals: 
u 
y(Xj, x 2 ,..., x r ) = jL^ (û. ■ (f). (4) 
Where y = the output results of this system 
cùj = the weight of the j th rule 
3.2.2 Rule extraction standards: Two standards, output 
error and the width of a Gaussian membership function, are 
introduced to determine whether a new rule should be added 
into current system. 
To the i th training data (X., ) , the output error can be 
computed as follows: 
Ikll = Ik-T/ll (5) 
Where X. = the input vector 
t. = the target output value 
y. = the calculated output value resulted from current 
system 
In comparison with the predefined precision k £ , if 
Then a new rule should be generated. 
In this model, the input variables are classified into several 
fuzzy sets according to Gaussian membership function. The 
amount of overlap between data sets is controlled by the widths 
of Gaussian membership functions. An input training data can 
be present by a Gaussian membership function, if its 
membership grade is within the accommodation range. 
To the i^ training data (X., t.), the distance between input 
value X. and the center of Gaussian membership function can 
be computed as follows: 
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