The **Hamming distance** between two vectors is simply the sum of corresponding elements that differ between the vectors.

For example, suppose we have the following two vectors:

x = [1, 2, 3, 4] y = [1, 2, 5, 7]

The Hamming distance between the two vectors would be **2**, since this is the total number of corresponding elements that have different values.

To calculate the Hamming distance between two vectors in R, we can use the following syntax:

sum(x != y)

This tutorial provides several examples of how to use this function in practice.

**Example 1: Hamming Distance Between Binary Vectors**

The following code shows how to calculate the Hamming distance between two vectors that each contain only two possible values:

#create vectors x <- c(0, 0, 1, 1, 1) y <- c(0, 1, 1, 1, 0) #find Hamming distance between vectors sum(x != y) [1] 2

The Hamming distance between the two vectors is **2**.

**Example 2: Hamming Distance Between Numerical Vectors**

The following code shows how to calculate the Hamming distance between two vectors that each contain several numerical values:

#create vectors x <- c(7, 12, 14, 19, 22) y <- c(7, 12, 16, 26, 27) #find Hamming distance between vectors sum(x != y) [1] 3

The Hamming distance between the two vectors is **3**.

**Example 3: Hamming Distance Between String Vectors**

The following code shows how to calculate the Hamming distance between two vectors that each contain several character values:

#create vectors x <- c('a', 'b', 'c', 'd') y <- c('a', 'b', 'c', 'r') #find Hamming distance between vectors sum(x != y) [1] 3

The Hamming distance between the two vectors is **1**.

**Additional Resources**

How to Calculate Euclidean Distance in R

How to Calculate Manhattan Distance in R

How to Calculate Minkowski Distance in R

How to Calculate Mahalanobis Distance in R