Table 5. Percentages of correctly classified pixels by using 
  
  
  
  
  
  
  
  
  
  
back-propagation neural networks.. 
f of nodes in Training set Testing set 
a hidden layer of data of data 
Average Overall Average Overall 
accuracy | accuracy | accuracy | accuracy 
2 80.18% 80.02% 64.83% | 60.64% 
3 92.51% 92.56% 90.33% | 90.23% 
7 97.97% 97.91% 93.90% 93.80% 
11 98.17% 98.08% 95.59% | 95.47% 
15 98.55% 98.41% 96.02% 96.05% 
19 98.45% 98.41% 96.21% | 96.13% 
23 98.44% 98.33% 96.36% 96.32% 
27 98.40% 98.33% 96.30% | 96.27% 
31 98.13% 98.08% 96.15% 96.13% 
  
  
  
  
  
  
  
  
  
  
  
iterations. The training time for the network trained by 500 
iterations was 1 hour and 35 minutes, while the classification 
time was 3 minutes. The training time for the network trained by 
10000 iterations was 31 hours and 30 minutes, while the 
classification time was 1 hour and 45 minutes. The resulting 
classification map for the maximum likelihood classifier is 
shown in the Figure 4. The resulting classification map for the 
back-propagation classifier is shown in the Figure 5. Comparing 
the maximum likelihood classification map with the back- 
propagation neural network classification map, it is obvious that 
the network output is more accurate than the statistical output. 
Figure 4. contains about 8% pixels (marked black), which are 
not classified at all. Mathematically, the difference in the overall 
test data accuracy between the classifiers mentioned above is 
5%. The areas not classified in Figure 4. where checked on the 
ground and compared with the Figure 5$. These unclassified 
pixels are classified with very high accuracy by the neural 
network.. This proved our state that neural network is more 
robust and stable classification tool than the maximum likelihood 
classifier. From the Table 5. it can be seen that neural networks 
with three processing elements in a hidden layer produce map 
with train side accuracies higher than those achived by 
maximum likelihood classifier, but at the same time they 
produce map with test side accuracies slightly less than those 
achieved by maximum likelihood classifer. 
5$. CONCLUSION 
Our objective in this work was twofold. Firstly, we examined the 
various back-propagation neural network architectures (by 
changing a number of the processing elements in a hidden layer) 
to find out, which one gives the biggest accuracy. The increase 
of network classifier performance is evident when we use a large 
number of processing elements Secondly, we compared the 
380 
Îter. 0.0 0.102 03 04 0.55 06 07 0.8 09 10 
EE 
Figure 3. Normalized total error for neural network 
classifier. 
These networks required fifth the time that we need to train the 
network with 19 processing elements in a hidden layer. By this 
way, we can significantly reduce the network classification time. 
classification accuraciy of neural network with the statistical 
maximum likelihood classifier. Neural network is superior to the 
statistical classifier. It has also the advantage that it is 
distribution free. The biggest drawback to the network classifier 
is the large learning time when the sample size is large. This 
problem could be overcome in the future, when the new more 
sofisticated computers will be designed. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998