## Definition Edit

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.