In noeliarico/dists: Calculate Distances Between Objects Using a Common Interface

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
library(dists)
library(dplyr)
library(ggplot2)
library(tidyr)
data("toy_data1")

Available distance functions:

• can - Canberra distance
• che - Chebyshev distance
• cos - Cosine distance
• euc - Euclidean distance
• jac - Jaccard distance
• man - Manhattan distance
• mat - Matusita distance
• ney - Neyman distance
• pea - Pearson distance
• trd - Triangular discrimination distance

Distance functions

Minkowski distances

Euclidean distance {#euc}

$$ d_{\text{euc}}({\bf v}, {\bf w}) = \sqrt{\sum_{i=1}^n (v_i-w_i)^2}$$

Manhattan distance {#man}

$$d_{\text{man}}({\bf v}, {\bf w}) = \sum_{i=1}^n |v_i-w_i|$$

Chebyshev distance {#che}

$$d_{\text{che}}({\bf v}, {\bf w}) = \max_i\left|v_i-w_i\right|$$

Other distances

Canberra distance {#can}

$$ d_{\text{can}}({\bf v}, {\bf w}) = \sum_{i=1}^n \frac{\left|v_i-w_i\right|}{\left|v_i\right|+\left|w_i\right|} $$

Cosine distance {#cos}

$$d_{\text{cos}}({\bf v}, {\bf w}) = 1 - \frac{\sum_{i=1}^{n}{v_i w_i}}{\sqrt{\sum_{i=1}^{n}v_i^2} \sqrt{\sum_{i=1}^{n}w_i^2}}$$

Jaccard distance {#jac}

$$d_{\text{jac}}({\bf v}, {\bf w}) = \frac{\sum_{i=1}^{n}{(v_i - w_i)^2}}{\sum_{i=1}^{n}v_i^2 + \sum_{i=1}^{n}w_i^2 - \sum_{i=1}^{n}v_i w_i}$$

Matusita distance {#mat}

$$d_{\text{mat}}({\bf v}, {\bf w}) = \sqrt{\sum_{i=1}^{n}(\sqrt{v_i} - \sqrt{w_i})^2}$$

Max symmetric distance

$$ d_{\text{msc}}({\bf v}, {\bf w}) = \max\left(\sum_{i=1}^{n}\frac{\left(v_i - w_i\right)^2}{v_i},\sum_{i=1}^{n}\frac{\left(v_i - w_i\right)^2}{w_i}\right)$$

Neyman distance {#ney}

$$ d_{\text{ney}}({\bf v}, {\bf w}) = \sum_{i=1}^{n} \frac{(v_i - w_i)^2}{v_i}$$

Pearson distance {#pea}

$$ d_{\text{pea}}({\bf v}, {\bf w}) = \sum_{i=1}^{n}\frac{(v_i - w_i)^2}{w_i}$$

Triangular discrimination distance {#trd}

$$d_{tri}({\bf v}, {\bf w}) = \sum_{i=1}^{n} \frac{(v_i - w_i)^2}{v_i + w_i}$$

Vicissitude distance {#vic}

$$d_{\text{vsd}}({\bf v}, {\bf w}) = \sum_{i=1}^{n}\frac{\left(v_i - w_i\right)^2}{\max\left(v_i,w_i\right)}$$

noeliarico/dists documentation built on May 27, 2020, 9:45 a.m.