# BinaryDistances: Binary Distances In MultBiplotR: Multivariate Analysis Using Biplots in R

## Description

Calculates distances among rows of a binary data matrix or among the rows of two binary matrices. The end user will use BinaryProximities rather than this function. Input must be a matrix with 0 or 1 values.

## Usage

 `1` ```BinaryDistances(x, y = NULL, coefficient= "Simple_Matching", transformation="sqrt(1-S)") ```

## Arguments

 `x` Main binary data matrix. Distances among rows are calculated if y=NULL. `y` Second binary data matrix. If not NULL the distances among the rows of x and y are calculated `coefficient` Similarity coefficient. Use the name (see details) `transformation` Transformation of the similarities. Use the name (see details)

## Details

The following coefficients are calculated

1.- Kulezynski = a/(b + c)

2.- Russell_and_Rao = a/(a + b + c+d)

3.- Jaccard = a/(a + b + c)

4.- Simple_Matching = (a + d)/(a + b + c + d)

5.- Anderberg = a/(a + 2 * (b + c))

6.- Rogers_and_Tanimoto = (a + d)/(a + 2 * (b + c) + d)

7.- Sorensen_Dice_and_Czekanowski = a/(a + 0.5 * (b + c))

8.- Sneath_and_Sokal = (a + d)/(a + 0.5 * (b + c) + d)

9.- Hamman = (a - (b + c) + d)/(a + b + c + d)

10.- Kulezynski = 0.5 * ((a/(a + b)) + (a/(a + c)))

11.- Anderberg2 = 0.25 * (a/(a + b) + a/(a + c) + d/(c + d) + d/(b + d))

12.- Ochiai = a/sqrt((a + b) * (a + c))

13.- S13 = (a * d)/sqrt((a + b) * (a + c) * (d + b) * (d + c))

14.- Pearson_phi = (a * d - b * c)/sqrt((a + b) * (a + c) * (d + b) * (d + c))

15.- Yule = (a * d - b * c)/(a * d + b * c)

The following transformations of the similarity3 are calculated

1.- 'Identity' dis=sim

2.- '1-S' dis=1-sim

3.- 'sqrt(1-S)' dis = sqrt(1 - sim)

4.- '-log(s)' dis=-1*log(sim)

5.- '1/S-1' dis=1/sim -1

6.- 'sqrt(2(1-S))' dis== sqrt(2*(1 - sim))

7.- '1-(S+1)/2' dis=1-(sim+1)/2

8.- '1-abs(S)' dis=1-abs(sim)

9.- '1/(S+1)' dis=1/(sim)+1

## Value

An object of class `proximities`.This has components:

 `comp1 ` Description of 'comp1'

## Author(s)

Jose Luis Vicente-Villardon

## References

Gower, J. C. (2006) Similarity dissimilarity and Distance, measures of. Encyclopedia of Statistical Sciences. 2nd. ed. Volume 12. Wiley

`PrincipalCoordinates`
 `1` ```data(spiders) ```