FANDOM


Definition Edit

Given a numeric set $ \textstyle \mathcal{N} $, the diference distance is a distance function $ \textstyle DiffDis: \mathcal{N}\times \mathcal{N}\longrightarrow \mathbb{R}^+ $ such that $ \textstyle \forall x,y\in \mathcal{N} $

$ DiffDis(x,y)=|x-y|. $

Examples Edit

  • $ DiffDis(-2,4) = 6 $
  • $ DiffDis(2.5, -1.2) = 3.7 $

Normalization Edit

It is not possible when the range of $ \textstyle \mathcal{N} $ is not bounded, otherwise

$ DiffSim(x,y)=1-\frac{|x-y|}{\max(\mathcal{N})-\min(\mathcal{N})}. $

Examples Edit

  • If $ \textstyle \mathcal{N}=\{0,1,2,\ldots,100\} \quad DiffSim(4,14) = 1-\frac{|4-14|}{100-0} = 0.9 $
  • If $ \textstyle \mathcal{N}=[-10,10] \quad DiffSim(2.5,-1.2) = \frac{|-1.2-2.5|}{10-(-10)} = 0.815 $