FANDOM


DefinitionEdit

Given two squences (or strings) of symbols in an alphabet $ \mathcal{L} $, the Hamming distance is a function that measures the number of positions for which the corresponding symbols are different,

$ \sigma(s,t)=\frac{\sum_{i=1}^{\min\{|s|,|t|\}}\sigma_{id}(s[i],t[i])}{\max\{|s|,|t|\}}, $

where $ \sigma_{id} $ is the identity similarity

$ \sigma_{id}(s[i],t[i])\left\{% \begin{array}{ll} 1, & \hbox{si $s[i]=t[i]$;} \\ 0, & \hbox{si $s[i]\neq t[i]$.} \\\end{array}% \right. $

Examples Edit

  • HammingSim('house','horse') = 3/5 = 0.6.
  • HammingSim('abcd',' ') = 0/4 = 0.
  • HammingSim('abcd','a') = 1/4 = 0.25.
  • HammingSim('abcd','b') = 0/4 = 0.25.
  • HammingSim('id0345','id1352') = 3/6 = 0.5.

Normalization Edit

It is normalized.

Applications Edit

Useful for comparing codes.

References Edit