# How To Use the Dist Function in R to Calculate a Distance Matrix

The dist function in R can be utilized to calculate a distance matrix, which shows the distances between different kinds of data frame or rows of a matrix(grid).

This function utilizes the following basic syntax:

dist(x, method=”euclidean”)

where:

x: The name of the grid or data frame.
method: The distance matrices measure to utilize. Standard is “euclidean” but options involve “minkowski”, “binary”, “canberra”, “manhattan”, or “maximum”.
The following examples display how to use this distance function in conjunction with the following data frame:

#define four vectors
a : c(2, 4, 4, 6)
b : c(5, 5, 7, 8)
c : c(9, 9, 9, 8)
d : c(1, 2, 3, 3)

#row bind four vectors into grid
mat : rbind(a, b, c, d)

#view matrix
mat

[,1] [,2] [,3] [,4]
a 2 4 4 6
b 5 5 7 8
c 9 9 9 8
d 1 2 3 3

Example 1: Use dist() to Calculate Euclidean Distance in R Programming
The Euclidean length between two pair of vectors, A and B, is calculated as:

Euclidean distance = √Σ(Ai-Bi)2

The following code shows how to calculate a distance grid that shows the Euclidean length between each row of a grid in R:

#calculate Euclidean length between each row in grid
dist(mat)

a b c
b 4.795832
c 10.148892 6.000000
d 3.872983 8.124038 13.190906
Euclidean distance = √Σ(Ai-Bi)2

The following code displays how to compute a distance grid that shows the Euclidean length between each row of a grid in R:

#calculate Euclidean length between each row in grid
dist(mat)

a b c
b 4.795832
c 10.148892 6.000000
d 3.872983 8.124038 13.19090

Here’s how to determine the output:

The Euclidean distance among row a and row b is 4.795832.
The Euclidean distance among row a and row c is 10.148892.
The Euclidean distance among row a and row d is 3.872983.
The Euclidean distance among row b and row c is 6.000000.
The Euclidean distance among row b and row d is 8.124038.
The Euclidean length between row c and row d is 13.190906.

Example 2: Use dist() to Compute Maximum Distance
The Maximum distance among two vectors, A and B, is computed as the maximum difference between every pairwise elements.

The following code displays how to compute a distance grid that displays the Maximum distance among each row of a grid in R:

#calculate Maximum distance among each row in grid
dist(mat, method=”maximum”)

a b c
b 3
c 7 4
d 3 5 8

Example 3: Use dist() to Calculate Canberra Distance
The Canberra distance among two vectors, A and B, is computed as:

Canberra distance = Σ |Ai-Bi| / |Ai| + |Bi|

The following code displays how to calculate a distance matrix that shows the Canberra distance among each row of a grid in R:

#calculate Canberra distance among each row in grid
dist(mat, method=”canberra”)

a b c
b 0.9552670
c 1.5484515 0.6964286
d 1.1428571 1.9497835 2.3909091

Example 4: Use dist() to Calculate Binary Distance
The Binary distance among two vectors, A and B, is computed as the proportion of elements that the two vectors have.

The following code displays how to calculate a distance matrix that shows the Binary distance among each row of a grid in R:

#calculate Binary distance among each row in grid
dist(mat, method=”binary”)

a b c
b 0
c 0 0
d 0 0 0

Example 5: Use dist() to Calculate Minkowski Distance
The Minkowski distance among two vectors, A and B, is calculated as:

Minkowski distance = (Σ|ai – bi|p)1/p

where i is the ith element in every vector and p is an integer.

The following code displays how to calculate a distance matrix that shows the Minkowski distance (using p=3) among each row of a grid in R:

#compute Minkowski distance among each row in grid
dist(mat, method=”minkowski”, p=3)

a b c
b 3.979057
c 8.439010 5.142563
d 3.332222 6.542133 10.614765

Manhattan distance

Definition: The length among two points measured through axes by right angles. In a plane with p1 at (x1, y1) and p2 at (x2, y2), it is |x1 – x2| + |y1 – y2|.

Distance Matrix Computation
Description
This data science computes and reveals the length matrix computed by utilizing the specified distance measure to compute the distances among the rows of a data matrix.

Usage
dist(x, method = “euclidean”, diag = FALSE, upper = FALSE, p = 2)

as.dist(m, diag = FALSE, upper = FALSE)
## Default S3 method:
as.dist(m, diag = FALSE, upper = FALSE)

## S3 method for class ‘dist’
print(x, diag = NULL, upper = NULL,
digits = getOption(“digits”), justify = “none”,
right = TRUE, …)

## S3 method for class ‘dist’
as.matrix(x, …)
Arguments
x
a numeric matrix, data frame or “dist” object.

method
the length measure to be utilized. This must be one of “euclidean”, “maximum”, “manhattan”, “canberra”, “binary” or “minkowski”. Every unambiguous substring can be provided.

diag
logical value identifying whether the diagonal of the distance matrix could be printed by print.dist.

upper
logical value identifying whether the higher triangle of the length grid should be printed by print.dist.

p
The strength of the Minkowski distance.

m
An object with distance information to be converted to a “dist” object. For the standard method, a “dist” object, or a grid (of distances) or an object that can be coerced to such a matrix utilizing as.matrix(). (Only the bottom triangle of the matrix is utilized, the rest is forgotten).

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