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

 Try Our Automatic tool to find proximity measure  

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

 

Fazal Rehman Shamil
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