Minkowski distance

* Minkowski distance

 

 

 i and j are p-dimentional data objects and h is order

 

              

 

 

* Proximity Measure for Ordinal Variable​

 

- ordinal data: order is important ; rank

- can be treated like numeric :  replace xif by its rank  

  :  map the range of each variable onto [0,1] by replacing i-th object in the f-th attribute by

- compute the dissimilarity using methods for numeric attributes -> use euclidean distance to construct a matrix

 

ex)

 

- test-2 의 ordinal data를 이용하여 dissimilarity matrix를 계산

 

- 먼저 데이터의 rank를 정한다  => { excellent = 3, good = 2, good = 1​ } , 따라서 r (i, test2) 의 M(f)는 3이 된다.

 

-  Z (1, test2) = (3-1)/(3-1) = 1

    Z (2, test2) = (1-1)/(3-1) = 0

    Z (3, test2) = (2-1)/(3-1) = 0.5

    Z (4, test2) = (3-1)/(3-1) = 1

 

- Euclidean Method 를 이용하여 각각의 거리를 계산한다.

 

 

* Proximity Measure for Numerical Variable​

 

 

 

 

 

 - 위의 표에서 계산하면 , use test 3

 - d(1,2) = |45-22| / (64-22) = 0.55 .. 이렇게 쭉쭉 계산해주면 된다 !