Proximity Measure for Nominal Attributes formula and example in data mining

How to calculate Proximity Measure for Nominal Attributes?

RollNo

Marks

Grade

1

90

A

2

80

B

3

82

B

4

90

A

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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