Simple matching coefficient

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Published on February 6, 2022 2:54:19 AM ● Video Link: https://www.youtube.com/watch?v=hUwMNvMTCZs

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The simple matching coefficient (SMC) or Rand similarity coefficient is a statistic used for comparing the similarity and diversity of sample sets.
Given two objects, A and B, each with n binary attributes, SMC is defined as:









SMC




=


number of matching attributes
number of attributes








=




M

00


+

M

11





M

00


+

M

11


+

M

01


+

M

10











{\displaystyle {\begin{aligned}{\text{SMC}}&={\frac {\text{number of matching attributes}}{\text{number of attributes}}}\\[8pt]&={\frac {M_{00}+M_{11}}{M_{00}+M_{11}+M_{01}+M_{10}}}\end{aligned}}}
where:





M

00




{\displaystyle M_{00}}
is the total number of attributes where A and B both have a value of 0.





M

11




{\displaystyle M_{11}}
is the total number of attributes where A and B both have a value of 1.





M

01




{\displaystyle M_{01}}
is the total number of attributes where the attribute of A is 0 and the attribute of B is 1.





M

10




{\displaystyle M_{10}}
is the total number of attributes where the attribute of A is 1 and the attribute of B is 0.
The simple matching distance (SMD), which measures dissimilarity between sample sets, is given by



1
−

SMC



{\displaystyle 1-{\text{SMC}}}
.SMC is linearly related to Hamann similarity:



S
M
C
=
(
H
a
m
a
n
n
+
1
)

/

2


{\displaystyle SMC=(Hamann+1)/2}
. Also,



S
M
C
=
1
−

D

2



/

n


{\displaystyle SMC=1-D^{2}/n}
, where




D

2




{\displaystyle D^{2}}
is the squared Euclidean distance between the two objects (binary vectors) and n is the number of attributes.

Source: https://en.wikipedia.org/wiki/Simple_matching_coefficient
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