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Potentially,
SMOTE can also be extended for nominal features  SMOTEN  with the nearest neighbors computed using the modified version of Value Difference Metric [36]
proposed by Cost and Salzberg (1993). The Value Difference Metric (VDM) looks at the overlap of feature values over all feature vectors. A matrix defining the distance between corresponding feature values
for all feature vectors is created. The distance between two corresponding feature values
is defined as follows.
 
(1) 
In the above equation, V_{1} and V_{2} are the two corresponding feature values. C_{1} is the total
number of occurrences of feature value V_{1}, and C_{1i} is the number of occurrences of feature
value V_{1} for class i. A similar convention can also be applied to C_{2i} and C_{2}.
k is a constant, usually set to 1. This equation is used to compute the matrix of value differences
for each nominal feature in the given set of feature vectors. Equation 1 gives a geometric
distance on
a fixed, finite set of values [37]. Cost and Salzberg's modified VDM omits the weight term w_{f}^{a}
included
in the computation by Stanfill and Waltz, which has an effect of making symmetric.
The distance between two feature vectors is given by:
 
(2) 
r = 1 yields the Manhattan distance, and r = 2 yields the Euclidean distance [37]. w_{x} and w_{y} are the exemplar weights in the modified VDM. w_{y} = 1 for a new example (feature vector),
and w_{x} is the bias towards more reliable examples (feature vectors) and is computed as the ratio of the
number of uses of a feature vector to the number of correct uses of the feature vector; thus, more accurate
feature vectors will have w_{x} 1. For SMOTEN we can ignore these weights in equation 2, as SMOTEN is not used for classification purposes directly. However, we can redefine these
weights to give more weight to the minority class feature vectors falling closer to the majority class
feature vectors; thus, making those minority class features appear further away from the feature vector under
consideration. Since,
we are more interested in forming broader but accurate regions of the minority class, the weights
might be used to
avoid populating along neighbors which fall closer to the majority class.
To generate new minority class feature vectors, we can create new set feature values by taking the
majority vote of the feature vector in consideration and its k nearest neighbors. Table 6.2
shows an example of creating a synthetic feature vector.
Table 7:
Example of SMOTEN
Let F1 = A B C D E be the feature vector under consideration 
and let its 2 nearest neighbors be 
F2 = A F C G N 
F3 = H B C D N 
The application of SMOTEN would create the following feature vector: 
FS = A B C D N 

Next: Application of SMOTE to
Up: Future Work
Previous: SMOTENC
Nitesh Chawla (CS)
6/2/2002