where J is a set of neurons from previous layer and 
S is usually a sigmoid function. The weights of 
connections are changed using the back propagation 
algorithm until all node values in the input and 
output layer are approximately the same. Then the 
corresponding values in the middle layer can be 
considered as the effective comprimation of the 
original information. Finally the new features are 
computed for all pixels when the original feature 
values are introduced to the input layer of 
"instructed" network. The synthetic images computed 
may be used as R, G, B components of additive color 
composite. The technical details and description of 
adaptation process are beyond the scope of this 
paper and has been discussed by several authors 
(Fahlman, 1988). 
2.2 Interpretation of clustering results 
  
The ISODATA method produces clusters that can be 
bounded by a hypersphere or by a hyperellipsoid. 
Therefore it is necessary to group the data into 
more clusters than is the number of spectral 
classes. Some of the classes are broken into 
a several clusters. Higher number of clusters 
brings problems in subsequent interpretation of 
classification results. The theory of information 
gives us an efficient tool for solution of this 
problem (Charvat, 1990). 
If P(x) denotes probability distribution of random 
variable X in some discrete space, the Shannons 
entropy H(Px) is defined as follows: 
H(Px) = - XI P(x) . log P(x). (2) 
When P(x,y) is a probability distribution of 
a composed variable (X,Y) and P(x), P(y) are the 
marginal distributions, then mutual information 
between variables X and Y is defined as follows: 
P(x,y) 
I(X,)z X "P(x.y). 109 
Xy P(X) . Py) 
  
(3) 
The mutual information I(X,Y) can be considered as 
a general dependency measure between the variables 
X and Y. 
The result of unsupervised classification may be 
interpereted easily when using the mutual 
information. Number of resulting clusters even 
after removing of nonsignificant ones is usually 
high. It is necessary to join several classes in 
the resulting image. Let P( wi, wj) is 
a probability that the classes wi and Wj occur in 
the neighbouring pixels and P(wi), P(wj) are 
aposteriori probabilities of classes (areal 
extents). Then the spatial dependency between 
individual classes may be described using the 
mutual information by the expression: 
P(wi, wi) 
  
IP(wWi, Wi) . log 
1,3 P( C2 1).P( 923) 
(4) 
It is the mutual information computed in the image 
Space. For every two classes the value of loss of 
this mutual information is computed if they are 
joined. The system recommends to join such two 
classes for which this loss of ‘information is 
874 
minimized. The procedure is repeated until a 
satisfactory result is reached. 
A preliminary unsupervised classification and 
interpretation yields the approximate areal extents 
of the cover classes. They can be used as estimates 
of apriori class probabilities when supervised 
classification is applied. The resulting cluster 
domains and color composite map are used to route 
the terrestrial investigations when main landcover 
classes are delineated. 
3. SUPERVISED CLASSIFICATION 
3.1 Verification of training samples 
When the supervised classification is used for 
satellite image data interpretation, the gathering 
of suitable training samples creates the main 
problem. It is necessary to test the separability 
of classes and verify labeling of training 
polygons. Some methods solving these problems for 
normally distributed data have been already 
investigated (Charvat, 1987b). They are based on 
the statistical comparisons of mean vectors and 
covariance matrices. 
The mutual information can characterize the 
separability between classes. Let the training sets 
are collected for every <class W; ef, for 
j = 1,...,M (M is a number of classes), x will be a 
random vector of feature space X which represents 
the multispectral image. The probability 
distributions P(wi), P(x) and P(x, wi) can be 
estimated on the ground of training samples. In the 
case of absolutely separable classes the mutual 
information I(X,f) and entropy H(Po ) of probability 
distribution of classes are equal: It follows: 
  
I(X,4&)/ H(Pa ) 21, (5) 
where 
P(x, wi) 
I(X,4h) = X P(x, wi) . 109g (6) 
x,i P(x) . P( 41) 
and 
HP) = - : P(wi) . log P( Wi). (7) 
The algorithm for verification of training samples 
is based on this idea: 
1) Class identifiers are assigned to every 
training polygon - every polygon is considered 
as a temporary spectral class. 
2) The mutual information I(X,.fA) and entropy 
H(Pg,) are computed using the estimates of 
P(x), P(wi), P(x, wi). The method of Parzen 
windows which will be described is used for 
this purpose. 
3) If 1 = IX, J/NP ) "« €^ tnen the 
algorithm stops. 
4) For every two temporary classes the loss of 
I(X,£) is computed if they are joined. 
5) Such two classes for which is the loss 
minimal are found and joined. The current set 
of features cannot be probably used for 
discrimination of these classes. The algorithm 
goes back to the step 2). 
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