The **dist()** function in R can be used to calculate a distance matrix, which displays the distances between the rows of a matrix or data frame.

This function uses the following basic syntax:

**dist(x, method=”euclidean”)**

where:

**x:**The name of the matrix or data frame.**method:**The distance measure to use. Default is “euclidean” but options include “maximum”, “manhattan”, “canberra”, “binary” or “minkowski”.

The following examples show how to use this function in practice 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 matrix 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**

The **Euclidean distance** between two vectors, A and B, is calculated as:

**Euclidean distance = √Σ(A _{i}-B_{i})^{2}**

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

#calculate Euclidean distance between each row in matrix dist(mat) a b c b 4.795832 c 10.148892 6.000000 d 3.872983 8.124038 13.190906

Here’s how to interpret the output:

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

**Example 2: Use dist() to Calculate Maximum Distance**

The **Maximum distance** between two vectors, A and B, is calculated as the maximum difference between any pairwise elements.

The following code shows how to compute a distance matrix that shows the Maximum distance between each row of a matrix in R:

#calculate Maximum distance between each row in matrix 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** between two vectors, A and B, is calculated as:

**Canberra distance = Σ |A _{i}-B_{i}| / |A_{i}| + |B_{i}|**

The following code shows how to compute a distance matrix that shows the Canberra distance between each row of a matrix in R:

#calculate Canberra distance between each row in matrix 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** between two vectors, A and B, is calculated as the proportion of elements that the two vectors share.

The following code shows how to compute a distance matrix that shows the Binary distance between each row of a matrix in R:

#calculate Binary distance between each row in matrix 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** between two vectors, A and B, is calculated as:

**Minkowski distance = (Σ|a _{i} – b_{i}|^{p})^{1/p}**

where *i* is the i^{th} element in each vector and *p* is an integer.

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

#calculate Minkowski distance between each row in matrix dist(mat, method="minkowski", p=3) a b c b 3.979057 c 8.439010 5.142563 d 3.332222 6.542133 10.614765

**Additional Resources**

How to Calculate Jaccard Similarity in R

How to Calculate Cosine Similarity in R

How to Calculate the Dot Product in R