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.
BinaryDistances(x, y = NULL, coefficient= "Simple_Matching", transformation="sqrt(1-S)")An object of class proximities.This has components:
Description of 'comp1'
Main binary data matrix. Distances among rows are calculated if y=NULL.
Second binary data matrix. If not NULL the distances among the rows of x and y are calculated
Similarity coefficient. Use the name (see details)
Transformation of the similarities. Use the name (see details)
Jose Luis Vicente-Villardon
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
Gower, J. C. (2006) Similarity dissimilarity and Distance, measures of. Encyclopedia of Statistical Sciences. 2nd. ed. Volume 12. Wiley
PrincipalCoordinates