Current Slide

Small screen detected. You are viewing the mobile version of SlideWiki. If you wish to edit slides you will need to use a larger device.

Special Cases of Minkowski Distance

  • h = 1: Manhattan (city block, L1 norm) distance
    • E.g., the Hamming distance: the number of bits that are different between two binary vectors
\[ d(i,j)=|x_{i1}-x_{j1}|+|x_{i2}-x_{j2}|+...+|x_{ip}-x_{jp}| \]

  • h = 2: (L2 norm) Euclidean distance

\[ d(i,j)=\sqrt{(|x_{i1}-x_{j1}|^2+|x_{i2}-x_{j2}|^2+...+|x_{ip}-x_{jp}|^2)} \]

  • h →≈ . “supremum” (Lmax norm, L norm) distance.
    • This is the maximum difference between any component (attribute) of the vectors
\[ d(i,j)=\lim_{h\rightarrow \infty }(\sum_{f=1}^{p}|x_{if}-x_{jf}|^{h})^\frac{1}{h} =max_{f}^{p}|x_{if}-x_{jf}| \]

Speaker notes:

Content Tools

Sources

There are currently no sources for this slide.