Manhattan Distance
Manhattan distance is a distance metric between two points in an N-dimensional vector space. It is defined as the sum of absolute distance between coordinates in corresponding dimensions. For example, in a 2-dimensional space having two points Point1 (x1 , y1) and Point2 (x2 , y2), the Manhattan distance is given by |x1 – x2| + |y1 – y2|.
In R Manhattan distance is calculated with respect to vectors. The Manhattan distance between the two vectors is given by,
Σ|vect1i - vect2i|
where,
- vect1 is the first vector
- vect2 is the second vector
For example, we are given two vectors, vect1 as (3, 6, 8, 9) and vect2 as (1, 7, 8, 10). Their Manhattan distance is given by, |3 – 1| + |6 – 7| + |8 – 8| + |9 – 10| which is equal to 4.
Syntax:
dist(vect, method = “manhattan”, diag = TRUE or FALSE, upper = TRUE or FALSE)
Example: Manhattan distance
R
# R program to illustrate how to calculate # Manhattan distance# using dist() function# Initializing a vectorvect1 <- c(1, 4, 8, 9, 2, 3)# Initializing another vectorvect2 <- c(9, 4, 1, 2, 4, 7)# Initializing another vectorvect3 <- c(1, 7, 9, 3, 2, 8)# Initializing another vectorvect4 <- c(2, 1, 4, 7, 8, 9)# Initializing another vectorvect5 <- c(1, 4, 8, 3, 9, 2)# Initializing another vectorvect6 <- c(3, 7, 8, 6, 5, 9)#Row bind vectors into a single matrixtwoDimensionalVect <- rbind(vect1, vect2, vect3, vect4, vect5, vect6)print("Manhattan distance between each pair of vectors is: ")cat("\n\n")# Calculate Manhattan distance between vectors using # built in dist method By passing two-dimensional# vector as a parameter Since we want to calculate # Manhattan distance between each unique pair of vectors# That is why we are passing Manhattan as a methoddist(twoDimensionalVect, method = "manhattan", diag = TRUE, upper = TRUE) |
Output:
How to Use Dist Function in R?
In this article, we will see how to use dist() function in R programming language.
R provides an inbuilt dist() function using which we can calculate six different kinds of distances between each unique pair of vectors in a two-dimensional vector. dist() method accepts a numeric matrix as an argument and a method that represent the type of distance to be measured. The method must be one of these distances – Euclidean, Maximum, Manhattan, Canberra, Binary, and Minkowski. It accepts other arguments also but they are optional.
Syntax:
dist(vect, method = ” “, diag = TRUE or FALSE, upper = TRUE or FALSE)
Parameters:
- vect: A two-dimensional vector
- method: The distance to be measured. It must be equal to one of these, “euclidean”, “maximum”, “manhattan”, “canberra”, “binary” or “minkowski”
- diag: logical value (TRUE or FALSE) that conveys whether the diagonal of the distance matrix should be printed by print.dist or not.
- upper: logical value (TRUE or FALSE) that conveys whether the upper triangle of the distance matrix should be printed by print.dist or not.
Return type:
It return an object of class “dist”
Now let us see how to calculate these distances using dist() function.