kmed (version 0.3.0)

matching: A pair distance for binary/ categorical variables

Description

This function computes the simple matching distance from two data frames/ matrices.

Usage

matching(x, y)

Arguments

x

A first data frame or matrix (see Details).

y

A second data frame or matrix (see Details).

Value

Function returns a distance matrix with the number of rows equal to the number of objects in the x data frame/ matrix (\(n_x\)) and the number of columns equals to the number of objects in the y data frame/ matrix (\(n_y\)).

Details

The x and y arguments have to be data frames/ matrices with the same number of columns where the row indicates the object and the column is the variable. This function calculates all pairwise distance between rows in the x and y data frames/ matrices. If the x data frame/ matrix is equal to the y data frame/ matrix, it explicitly calculates all distances in the x data frame/ matrix.

The simple matching distance between objects i and j is calculated by $$d_{ij} = \frac{\sum_{s=1}^{P}(x_{is}-x_{js})}{P}$$ where \(P\) is the number of variables, and \( x_{is}-x_{js} \in\) {0, 1}. \( x_{is}-x_{js} = 0\), if \( x_{is}=x_{js}\) and \(x_{is}-x_{js} = 1\), when \(x_{is} \neq x_{js}\).

As an example, the distance between objects 1 and 2 is presented.

object	x	y	z
1	1	2	2

The distance between objects 1 and 2 is $$d_{12} = \frac{\sum_{s=1}^{3}(x_{is}-x_{js})}{3} = \frac{0 + 0 + 1}{3} = \frac{1}{3} = 0.33$$

Examples

# NOT RUN {
set.seed(1)
a <- matrix(sample(1:2, 7*3, replace = TRUE), 7, 3)
matching(a, a)

# }