Dissimilarity Matrix

- Dissimilarity Matrix (n objects x p attributes)

: Store a collection of proximities that are available for all pairs of n objects

 

A triangular matix, i.e., d(i,j) = d(j,i)

d(i,j) is the measured dissimilarity or "differce" between objects i and j

 

similarity measure sim(i,j) = 1 - d(i,j) 

d(i,j) is a non-negative number that is close to 0 when objects i and j are highly similar or "near" each other, and becomes larger the more they differ

 

 

 

- Proximity measure for Nominal attributes

 

M : # of states of a nominal attribute

m : # of matches for which objects i and j are in the same state

p : total # of nominal attributes describing the objects​

 

ex)  Find the dissimilarity matrix for test-1

 

 p=1 ; nominal attributes

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- Proximity Measure for Binary Attributes

 

 

 

 

 

1) dissimilarity matrix : 

 ​2) Asymmetric binary attributes :