How to calculate Proximity Measure for Nominal Attributes?

RollNo	Marks	Grade
1	90	A
2	80	B
3	82	B
4	90	A

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Pairs for distance Measurement:

d(RollNo1,RollNo1)	d(RollNo1,RollNo2)	d(RollNo1,RollNo3)	d(RollNo1,RollNo4)
d(RollNo2,RollNo1)	d(RollNo2,RollNo2)	d(RollNo2,RollNo3)	d(RollNo2,RollNo4)
d(RollNo3,RollNo1)	d(RollNo3,RollNo2)	d(RollNo3,RollNo3)	d(RollNo3,RollNo4)
d(RollNo4,RollNo1)	d(RollNo4,RollNo2)	d(RollNo4,RollNo4)	d(RollNo3,RollNo4)

Formulae to calculate Proximity Measure for Nominal Attribute:

distance(object1, Object2) = P – M / P

P is total number of attributes

M is total number of matches

So in our case we have four objects RollNo1, RollNo2, RollNo3, RollNo4

d(1,1) = P – M / P = 2 – 2 / 2 = 0	d(RollNo1,RollNo2)	d(RollNo1,RollNo3)	d(RollNo1,RollNo4)
(2,1) = P – M / P = (2 – 0) / 2 = 1	(2,2) = P – M / P = (2 – 2) / 2 = 0	d(RollNo2,RollNo3)	d(RollNo2,RollNo4)
(3,1) = P – M / P = (2 – 0) / 2 = 1	(3,2) = P – M / P = (2 – 1 )/ 2 = 0.5	(3,3) = P – M / P = (2 – 2 )/ 2 = 0	d(RollNo3,RollNo4)
(4,1) = P – M / P = (2 – 2) / 2 = 0	(4,2) = P – M / P = (2 – 0) / 2 = 1	(4,3) = P – M / P =( 2 – 0 )/ 2 = 1	(4,4) = P – M / P =( 2 – 2) / 2 = 0

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