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The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008
d i U) = \\xi- c jI 0=1» 2...u)
of this process. This result indicated that the best network
architecture had been formed.
Where u = the number of total fuzzy rules
c .
J
=the centre of Gaussian membership function.
In comparison with the accommodation criterion value , if
arg min(J. (j)) > k d
(8)
Then a new rule should be generated.
3.3 Performance Evaluation
The performance of a FNN model should be evaluated based
on following requirements (Ralf Wieland et al., 2008):
1. Accuracy: The error resulting between the calculated
and target output values should be minimal;
2. Generalization: The model should reduce the
complexity of the real world using an approximation of
the data based on fundamental knowledge;
3. Portability: The model should be usable in different
sites with slightly changed inputs compared to the training
data.
Herein, the root mean square error (RMSE) and the output
error were considered as statistical performance evaluation
factors. To check the utility of this DFNN model, 250 samples
containing hyperspectral vegetation indices values and heavy
metal stress level information were applied to neural-network
training process. And fuzzy rules were generated as is shown in
Figure 2. During this process, a total number of eight fuzzy
rules were generated. Considering the significance of each rule,
one of them was deleted. At last, this training process
generated seven fuzzy rules.
Fuzzy Riie Generation
Root mean square error
Figure 3. Root mean square error during training process based
on 250 training samples obtained from MODIS data
Another dataset was prepared to evaluate the accuracy and
generalization ability of this model. It was composed of 60
samples which were quite different from training data samples
on crop heavy metal stress. The comparison of calculated and
target outputs was shown in Figure 4. Three samples within
these 60 testing samples were misclassified because their stress
levels were distributed near the edge of two levels. According
to the experimental result, this system achieve to an accuracy
of 95% by a total number of seven fuzzy rules. It was
confirmed that for crop heavy metal stress level assessment,
this DFNN model can produce a satisfying recognition rates
with minimal number of hidden neurons.
Companion of calculated and target outputs
—er
Calculated outputs
* Target outputs
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Figure 4. Comparison of calculated and target outputs based
on 60 testing samples obtained from MODIS data
Figure 2. Generation of fuzzy rules based on 250 training
samples obtained from MODIS data
4. CONCLUSIONS
This paper presents a dynamic fuzzy neural-network (DFNN)
model and its application to the assessment of crop heavy metal
stress levels based on MODIS data. The proposed model uses
hyperspectral vegetation indices as input variables in order to
Figure 3 presents the change of RMSE value during training
procedure. The RMSE can be achieved less than 0.5 at the end