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Proximity Measures for Binary and Ordinal Variables, Assignments of Data Mining

How to calculate proximity measures for binary and ordinal variables using different methods. Examples for binary variables and demonstrates how to find the proximity measure for ordinal attributes. It also includes the manhattan distance formula for calculating distances between ordinal variables.

Typology: Assignments

2019/2020

Uploaded on 08/18/2020

rahul-sharma-51
rahul-sharma-51 🇮🇳

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2. Proximity measure for Binary Variables
If M and N are two binary variables, then we can four different cases
a{M:1 , N:1}M:1 , N:1}
b{M:1 , N:1}M:1, N:0}}
C{M:1 , N:1}M:0},N:1}
d{M:1 , N:1}M:0},N:0}}
dist(M,N)=b+c/a+b+c--------Asymmetric Binary Variables
dist(M,N)=b+c/a+b+c+d---Symmetric Binary Variables
Example
Name T1 T2 T3 T4 T5 T6
X10}10}0}0}
Y10}10}10}
Z110}0}0}0}
Find dist(X,Y),Dist(X,Z) and Dist(Y,Z)
Dist(X,Y)
a2
b0}
c1
d3
pf3

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  1. Proximity measure for Binary Variables If M and N are two binary variables, then we can four different cases a{M:1 , N:1}M:1 , N:1} b{M:1 , N:1}M:1, N:0}} C{M:1 , N:1}M:0},N:1} d{M:1 , N:1}M:0},N:0}} dist(M,N)=b+c/a+b+c--------Asymmetric Binary Variables dist(M,N)=b+c/a+b+c+d---Symmetric Binary Variables Example Name T1 T2 T3 T4 T5 T X 1 0} 1 0} 0} 0} Y 1 0} 1 0} 1 0} Z 1 1 0} 0} 0} 0} Find dist(X,Y),Dist(X,Z) and Dist(Y,Z) Dist(X,Y) a 2 b0} c 1 d 3

dist(X,Y)=b+c/a+b+c=0}+1/2+0}+1=0}. a1,b1,c 1 dist(X,Z)=b+c/a+b+c=0}. dist(y,Z)=b+c/a+b+c b2,a1,C 1 =2+1/1+2+1=3/4=0}. 3.Finding Proximity measure Ordinal Attribute Objects T 1 High 2 Low 3 Me dium 4 High Step1: Find out total number for ordinal variables,Mf= 3 Step2:High1, Medium2, Low 3 Step3:Normalize the states into [0},1] Zif=rif-1/Mf- For high=1-1/3-1=0} For Medium=2-1/3-1=0}. For Low=3-1/3-1= High0},Medium0}.5 and Low 1