Computation of Distance Matrices for Binary Data

computes for binary data some distance matrice.

Usage

dist.binary(df, method = NULL, diag = FALSE, upper = FALSE)

Arguments

df: a matrix or a data frame with positive or null numeric values. Used with as.matrix(1 * (df > 0))
method: an integer between 1 and 10 . If NULL the choice is made with a console message. See details
diag: a logical value indicating whether the diagonal of the distance matrix should be printed by `print.dist'
upper: a logical value indicating whether the upper triangle of the distance matrix should be printed by `print.dist'

Details

Let be the contingency table of binary data such as \(n_{11} = a\), \(n_{10} = b\), \(n_{01} = c\) and \(n_{00} = d\). All these distances are of type \(d=\sqrt{1-s}\) with s a similarity coefficient.

1 = Jaccard index (1901): S3 coefficient of Gower & Legendre \(s_1 = \frac{a}{a+b+c}\)
2 = Simple matching coefficient of Sokal & Michener (1958): S4 coefficient of Gower & Legendre \(s_2 =\frac{a+d}{a+b+c+d}\)
3 = Sokal & Sneath(1963): S5 coefficient of Gower & Legendre \(s_3 =\frac{a}{a+2(b+c)}\)
4 = Rogers & Tanimoto (1960): S6 coefficient of Gower & Legendre \(s_4 =\frac{a+d}{(a+2(b+c)+d)}\)
5 = Dice (1945) or Sorensen (1948): S7 coefficient of Gower & Legendre \(s_5 =\frac{2a}{2a+b+c}\)
6 = Hamann coefficient: S9 index of Gower & Legendre (1986) \(s_6 =\frac{a-(b+c)+d}{a+b+c+d}\)
7 = Ochiai (1957): S12 coefficient of Gower & Legendre \(s_7 =\frac{a}{\sqrt{(a+b)(a+c)}}\)
8 = Sokal & Sneath (1963): S13 coefficient of Gower & Legendre \(s_8 =\frac{ad}{\sqrt{(a+b)(a+c)(d+b)(d+c)}}\)
9 = Phi of Pearson: S14 coefficient of Gower & Legendre \(s_9 =\frac{ad-bc}{\sqrt{(a+b)(a+c)(b+d)(d+c)}}\)
10 = S2 coefficient of Gower & Legendre: \(s_1 = \frac{a}{a+b+c+d}\)

Value

returns a distance matrix of class dist between the rows of the data frame

References

Gower, J.C. and Legendre, P. (1986) Metric and Euclidean properties of dissimilarity coefficients. Journal of Classification, 3, 5–48.

Author

Daniel Chessel
Stéphane Dray stephane.dray@univ-lyon1.fr

Examples

data(aviurba)
for (i in 1:10) {
    d <- dist.binary(aviurba$fau, method = i)
    cat(attr(d, "method"), is.euclid(d), "\n")}
#> JACCARD S3 TRUE 
#> SOKAL & MICHENER S4 TRUE 
#> SOKAL & SNEATH S5 TRUE 
#> ROGERS & TANIMOTO S6 TRUE 
#> CZEKANOWSKI S7 TRUE 
#> GOWER & LEGENDRE S9 TRUE 
#> OCHIAI S12 TRUE 
#> SOKAL & SNEATH S13 TRUE 
#> Phi of PEARSON S14 TRUE 
#> GOWER & LEGENDRE S2 TRUE