Manhattan {comparator}

Manhattan Numeric Comparator

Description

The Manhattan distance (a.k.a. L-1 distance) between two vectors x and y is the sum of the absolute differences of their Cartesian coordinates:

\mathrm{Manhattan}(x,y) = \sum_{i = 1}^{n} |x_i - y_i|.

Usage

Manhattan()

Value

A Manhattan instance is returned, which is an S4 class inheriting from Minkowski.

Note

The Manhattan distance is a special case of the Minkowski distance with p = 1.

See Also

Other numeric comparators include Euclidean, Minkowski and Chebyshev.

Examples

## Distance between two vectors
x <- c(0, 1, 0, 1, 0)
y <- seq_len(5)
Manhattan()(x, y)

## Distance between rows (elementwise) of two matrices
comparator <- Manhattan()
x <- matrix(rnorm(25), nrow = 5)
y <- matrix(rnorm(5), nrow = 1)
elementwise(comparator, x, y)

## Distance between rows (pairwise) of two matrices
pairwise(comparator, x, y)