(3)
One problem with both of these distance functions is that they assume that the input variables are linear.
However, there are many applications that have nominal attributes. A nominal attribute is one with a discrete
set of attribute values that are unordered. For example, a variable representing symptoms might have possible
values of headache, sore throat, chest pains, stomach pains, ear ache, and blurry vision. Using a linear
distance measurement on such values makes little sense in this case, because numbers assigned to the values are
in an arbitrary order. In such cases a distance function is needed that handles nominal inputs appropriately.
Stanfill & Waltz [11] introduced the value difference metric (VDM) which has been used as the basis of
several distance functions in the area of machine learning [2][3][6]. Using VDM, the distance between two
values x and y of a single attribute a is given a