FANDOM


DefinitionEdit

Given the sets $ E_1,\ldots,E_n $, let $ E_1\times \cdots\times E_n=\bigotimes_{i=1}^nE_i $ the set of $ n $-tuples with $ (u_1,\ldots,u_n) $ with $ u_i\in E_i,\ \forall i=1,ldots,n $. The Hamming similarity for tuples is a function $ HammingSim:\bigotimes_{i=1}^nE_i\times \bigotimes_{i=1}^nE_i\longrightarrow [0,1] $ that measures the number of equals components, divided by the length of tuples:

$ HammingSim(u,v)=\frac{\sum_{i=1}^{n}IdSim(u[i],v[i])}{n}, $

where $ IdSim $ is the Identity similarity.

Examples Edit

  • HammingSim((1,a,0,b),(0,a,1,b)) = 2/4 = 0.25.
  • HammingSim((1,a,0,b),(0,b,1,a))= 0/4 = 0.
  • HammingSim(('A.Sanchez','asanchez@gmail.com','913724710'),('A.Sanchez','sanchez@yahoo.com',' ') = 1/3 = 0.33.

Normalization Edit

It is normalized.

Variations Edit

When the components of tuples are of the same types, we have the Hamming similarity for vectors.

Applications Edit

Useful for comparing entities described by a fixed set of attributes of different types.

References Edit