ROOT-LEVEL 
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1. le ly. 1a 
Figure 1: The three-level tree structure of SX- 
WEB. 
  
representing SHALLOW WATER (SW). The largest 
mean value for BLUE is 149 and is found in the 
concept class BARREN 2 (B2). To determine 
whether BLUE is an attribute predictive of 
class membership, the standard deviation of the 
attribute BLUE in the root node (sd-20.63) is 
used to normalize the mean scores of all 
concept-level children. That is, each pair of 
mean values for the chosen attribute are 
subtracted from one another. The absolute value 
of each subtraction is then divided by the 
standard deviation of the attribute found 
within the root node. These standardized 
difference values are summed and divided by the 
number of paired attribute computations that 
have been made. This gives an average 
standardized mean difference value for the 
attribute relative to the root node. If this 
average difference is larger than a user 
specified threshold value, the attribute is 
considered to be predictive. Making this 
computation for the attribute BLUE results in 
a value of approximately 1.075. If the 
predictiveness threshold is set at 1.0, BLUE is 
then determined to be a predictive attribute. 
Figure 3 shows the predictiveness scores for 
the attributes found within the 155 instance 
training set. 
Finally, family resemblance scores are stored 
within the root node and each concept-level 
node. Family resemblance scores computed from 
the 155 instance training set are shown in 
Figure 2 in the final column, labeled FR. 
Family resemblance scores form the basis of 
SX-WEB's evaluation function by giving a 
measure of the overall similarity of the 
exemplars making up individual concept classes. 
The concept class with the lowest family 
resemblance score is Shrub Swamp (SS). As we 
will see in Section 2.3, those concept classes 
containing highly similar instances will have 
lower family resemblance scores. 
2.2 Computing the similarity of two exemplars 
SX-WEB uses two formulas to compute similarity. 
One formula is used when attributes are nominal 
or mixed and a second similarity measure is 
used when attributes are strictly real-valued. 
Once again, we will limit our discussion to 
real-valued exemplar similarity. 
To compute the similarity between exemplars E, 
and E,, the absolute value of the difference 
between each attribute value in E, and its 
corresponding attribute value in E, is divided 
by the standard deviation of the attribute 
found in the concept-level node being 
considered for instance classification. These 
standardized differences are summed over all 
attributes. Finally, the sum of the standar- 
dized differences are divided by the number of 
attributes giving an average standardized 
difference value among the attributes of E, and 
E,. Notice that similarity scores closer to 
zero mean greater similarity between two 
exemplars. 
Figure 2: Standard deviations, means, and family 
resemblance scores for the 155-instance training 
  
set. 
  
652 
2.3 Classification and the family resemblance 
principle 
When presented with a set of training 
instances, SX-WEB builds a three level tree 
structure. SX-WEB uses this tree structure 
together with its evaluation function to 
classify newly presented instances into one of 
the concept-level classes. When learning is not 
incremental, once an unknown instance is 
classified, it is discarded. In an incremental 
learning mode, the new instance becomes part of 
the classification tree. We now examine 
SX-WEB's evaluation function. 
SX-WEB's evaluation function is based on the 
family resemblance principle (Cantor, 1979) 
which states that: 
Most  prototypical members of a 
concept class share many features in 
common with members of their own 
class and few features in common with 
members of other closely related 
categories; 
From a classification point of view, this 
principle implies that new instances to be 
classified should be placed in the category 
class that will result in a best overall family 
resemblance value as a result of instance 
inclusion. Based on this, we used a method 
proposed in (Tversky, 1977) for computing class 
family resemblance. Specifically: 
FR(C) = 2/(N*(N-1)) * X Sim(a,b) 
where C is the concept class whose family 
resemblance score is being computed, N is the 
total number of exemplars contained in concept 
class C, and Y Sim(a,b) represents the sum 
total of all computed similarity scores between 
the class exemplars. In other words, to find 
the family resemblance score for concept class 
C, the similarity of each exemplar to all other 
exemplars in the class is summed. This sum is 
then divided by the total number of similarity 
computations made, giving an average similarity 
value for the class. Along these same lines, 
typicality is defined as the average similarity 
of one class exemplar to all other members of 
the class, or: 
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