neurons in the input layer are connected to all neurons in 
the output layer. For some input data, only one neuron 
reacts in the output layer. The neuron that reacts is the 
one which has the features nearest the features of the 
input data. This is called the victory neuron. 
Self-organizing maps are learned by a competition method 
that has no teaching data. The characteristic feature of 
this method is that the positions of neurons in the output 
layer are related. The victory neuron and its neighborhood 
neurons are learned in a group. Self-organizing maps 
are unnecessary for obtaining information about 
categories of input data. Resemblance of input data is 
formed by itself in the output layer. The neurons placed 
in a neighborhood in the output layer have features 
nearest each other and the neurons placed away from 
each other in the output layer have different features. 
Since the category of the input data is not given while the 
self-organizing map is being learned, it is possible to 
design the self-organizing map so that it will reflect 
distribution conditions of input data. In other words, the 
character of a self-organizing map depends on its set of 
input data. The set of input data should therefore be 
examined closely. 
3. METHODS 
3.1 Outline 
Figure 1 shows the outline of this method. Image 
sequences of changing facial expressions are prepared. 
Positions of facial segments such as eyebrows, eyes and 
mouth, are already known and rectangular segments 
which include each facial segment are selected. For 
example, an image of the rectangular segment of an 
eyebrow is input into a self-organizing map which is 
learned to classify features of the eyebrow. Then, a 
feature of the image is represented by locating in the 
output layer the self-organizing map of the victory neuron 
that we refer to as its number. These procedures are 
applied to other facial segments as well. By applying 
these procedures on all Image sequences, the changes in 
the feature corresponding to the changes in the facial 
Input image 
sequences 
      
   
  
Self-organizing map 
expressions is considered to be the changes in the victory 
neuron number. 
Figure 1 summarizes this method. First, the eyebrows, 
the eyes and the mouth of the facial images are input into 
the self-organizing map. Facial expressions are 
classified by analyzing the change of victory neuron 
number. 
3.2 Learning Self-organizing Maps 
Important facial segments for recognition are the eyebrows, 
the eyes and the mouth. The self-organizing map for 
each segment is learned. 
In this study, input images for learning are image 
sequences that change from expressionless to one of the 
six types of facial expressions, and there are 30 such 
images per second. |t is necessary to prepare various 
kinds of input image to give self-organizing maps an ability 
to classify many kinds of facial expressions, including 
those which express transitional periods. 
Figure 2 shows the learning process of self-organizing 
maps. Initial conditions of self-organizing maps are given 
at random. A rectangular segment that includes an 
eyebrow is selected from the input image and is converted 
into a gray image consisting of 256 levels. Then intensity 
of each picture element of the selected segment is input 
into the self-organizing map of the eyebrow. The neuron 
in the output layer with the feature nearest the feature of 
the input image becomes the victory neuron. The 
features of the neurons in the output layer are defined by 
the interconnection weights of the input and output layers. 
The interconnection weights of the victory neuron and the 
neighborhood neurons are changed in order to make the 
features of these neurons approximate those of the input 
image by using Equation 1. w, is an th interconnection 
weight in the output layer. N, is a set of numbers of which 
interconnection weights are changed. In the beginning of 
learning, size of the N, is large and it becomes small as its 
learning makes progress. «a is a coefficient of learning. 
Thea becomes big as learning makes progress. A self- 
organizing map is formed by repeating this process 
changing input image. 
The self-organizing maps which correspond to the eyes 
Victory neuron number change | 
with the movement in the input | 
image sequences. j 
3 
idt 
Victory ^ Victory neurons 
  
Figure 1 Feature Extraction Method 
444 
  
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