computes for binary data some distance matrice.
dist.binary(df, method = NULL, diag = FALSE, upper = FALSE)returns a distance matrix of class dist between the rows of the data frame
a matrix or a data frame with positive or null numeric values. Used with as.matrix(1 * (df > 0))
an integer between 1 and 10 . If NULL the choice is made with a console message. See details
a logical value indicating whether the diagonal of the distance matrix should be printed by `print.dist'
a logical value indicating whether the upper triangle of the distance matrix should be printed by `print.dist'
Daniel Chessel
Stéphane Dray stephane.dray@univ-lyon1.fr
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.
S3 coefficient of Gower & Legendre \(s_1 = \frac{a}{a+b+c}\)
S4 coefficient of Gower & Legendre \(s_2 =\frac{a+d}{a+b+c+d}\)
S5 coefficient of Gower & Legendre \(s_3 =\frac{a}{a+2(b+c)}\)
S6 coefficient of Gower & Legendre \(s_4 =\frac{a+d}{(a+2(b+c)+d)}\)
S7 coefficient of Gower & Legendre \(s_5 =\frac{2a}{2a+b+c}\)
S9 index of Gower & Legendre (1986) \(s_6 =\frac{a-(b+c)+d}{a+b+c+d}\)
S12 coefficient of Gower & Legendre \(s_7 =\frac{a}{\sqrt{(a+b)(a+c)}}\)
S13 coefficient of Gower & Legendre \(s_8 =\frac{ad}{\sqrt{(a+b)(a+c)(d+b)(d+c)}}\)
S14 coefficient of Gower & Legendre \(s_9 =\frac{ad-bc}{\sqrt{(a+b)(a+c)(b+d)(d+c)}}\)
\(s_1 = \frac{a}{a+b+c+d}\)
Gower, J.C. and Legendre, P. (1986) Metric and Euclidean properties of dissimilarity coefficients. Journal of Classification, 3, 5--48.
data(aviurba)
for (i in 1:10) {
d <- dist.binary(aviurba$fau, method = i)
cat(attr(d, "method"), is.euclid(d), "\n")}
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