maximum likelihood method. On the other hand, it is easy to 
handle two-dimensional data in neural networks. Therefore, 
classification using co-occurrence matrices can be carried out 
simply by using a neural network (Inoue et al., 1993). 
  
  
  
  
  
  
  
  
  
Figure 1: Landscape pattern of three regions 
2.2 Neural Network Methods for Pattern Recognition 
A neural network is a directed graph consisting of neurons or 
nodes arranged in layers with interconnecting links (Haykin, 
1994). These structures represent systems composed of many 
simple processing elements operating in parallel, whose func- 
tion is determined by network structure, connection weights, 
and node function (Hara et al., 1994). 
Recently, neural networks have been applied to a number of 
image classification problems due to the following characteris- 
tics of neural networks (e. g., Chen et al., 1993): (1) they have 
an intrinsic ability to generalize; (2) they make weaker a priori 
assumptions about the statistical distribution of the classes in 
the dataset than a parametric Bayes classifier; and (3) they are 
capable of forming highly non-linear decision boundaries in the 
feature space. Therefore, a neural network has the potential of 
outperforming a parametric Bayes classifier when a feature 
statistics deviate significantly from the assumed Gaussian nor- 
mal distribution. Indeed, the results of Benediktsson et al. 
(1990), Bischof et al. (1992), and Heermann and Khazenie 
(1992) indicate that a neural network can classify imagery 
better than a conventional supervised classification procedure 
using identical training sites. 
Several neural network models have been proposed since Ro- 
senblatt (1958) introduced the perceptron. The most common 
network type is the multilayer feed-forward neural network 
with connections only between nodes in neighbouring layers. 
The connection weights are iteratively adjusted in order to 
minimize an error criterion function. One of the most popular 
and widely investigated supervised learning paradigms is back- 
propagation (Rumelhart et al., 1986). It uses a gradient descent 
technique to minimize a cost function equal to the mean square 
difference between the desired and actual net outputs. The 
backpropagation method is an efficient algorithm and can solve 
problems of non-linear decision. However, it suffers from the 
weakness of very slow convergence during training. Very often 
the learning dynamics stop at a local minima rather than the 
global minima. Another procedure is introduced for this reason 
here which stands out due to its extremely fast learning ability. 
2.3 The ATL Network Model 
ATL (Adaptive Threshold Learning) is a supervised feedfor- 
ward network, but one that differs significantly in concept from 
backpropagation. ATL is a proprietary paradigm belonging to 
Neurotec, Inc. The ATL algorithm is similar to RCE (Restricted 
Coulomb Energy) which is patented by Nestor. Inc. RCE got its 
name from the way it models attractor basins, analogous to the 
Coulomb law of attraction between particles of opposite electri- 
cal charge. ATL is based on a similar concept. 
Figure 2 shows the architecture of an ATL network. Input 
nodes are fully connected to the internal nodes, and the internal 
nodes are selectively connected to the output nodes. An output 
node operates as an OR gate. If any of its inputs are active it 
produces an output - otherwise it does not (Chester, 1993). 
Output Layer 
Hidden Layer 
Input Layer 
  
Figure 2: Three-layer topology of an ATL network 
The ATL training algorithm attempts to create basins of attrac- 
tion which cover each decision region. Figure 3 shows a simple 
two-dimensional case. The circles in the diagram are the at- 
tractor basins, whose center are located by the synaptic weight 
vector, w, of the internal node. The radius 6j of the ith basin 
corresponds to the node's threshold. If an input vector, i. falls 
within an attractor basin, then the internal node associated with 
that attractor basin is activated. 
Class A 
P. 
    
Class B 
Internal neuron 
is not active 
Figure 3: Two-dimensional decision regions with training 
vectors and basins of attraction. 
. The training process starts with no basins of attraction; the 
72 
system creates them as a result of actions taken when training 
vectors are presented sequentially. The following two rules, 
applied to each training vector in turn, suffice to produce these 
basins (Wasserman, 1994): 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B7. Vienna 1996 
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