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