ML Similarity Measurement

12 Jul 2018

Distance

Euclidean Distance

$d_{12} = \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2}$

$d_{12} = \sqrt{(x_1-x_2)^2 + (y_1-y_2)^2 + (z_1-z_2)^2}$

$d_{12} = \sqrt{\sum_{k=1}^n(x_{1k} - x_{2k})^2}$

Standardized Euclidean distance

$X^* = \frac{X - m}{s}$

also Weighted Euclidean distance

Manhattan Distance

also called City Block distance $d_{12} = |x_1 - x_2| + |y_1 - y_2|$

$d_{12} = \sum_{k=1}^n|x_{1k}-x_{2k}|$

Chebyshev Distance

$d_{12} = \max(|x_1 - x_2| , |y_1 - y_2|)$

$d_{12} = \max_i(|x_{1i} - x_{2i}|)$

$d_{12} = \lim_{k \rightarrow \infty}\bigg( \sum_{i=1}^n|x_{1i} - x_{2i}|^k \bigg)^{\frac{1}{k}}$

Minkowski Distance

Minkowski Distance is not a distance, but a set definition of distance.

$d_{12} = \sqrt[p]{\sum_{k=1}^n{|x_{1k} - x_{2k}}|^p}$

let’s say p is var

• p=1 city block distance
• p=2 Euclidean Distance
• $k \rightarrow \infty$ Chebyshev Distance

Mahalanobis Distance

Hamming distance

Cosine

Jaccard similarity coefficient

Correlation coefficient and Correlation distance

Information Entropy

Ref

• https://www.cnblogs.com/xbinworld/archive/2012/09/24/2700572.html