In this post, we will learn how to compute Manhattan distance, one. of the commonly used distance meeasures, in Python using Numpy. Manhattan distance is also known as the “taxi cab” distance as it is a measure of distance between two points in a grid-based system like layout of the streets in Manhattan, New York City. It is calculated by determining the vertical and horizontal distance between two points and then adding them together.
We can define Manhattan distance as the sum of the absolute differences of the coordinates between two points in a grid. For example, if we have two points (x1, y1) and (x2, y2), the Manhattan distance would be:
|x1 - x2| + |y1 - y2|
First, let’s start importing Numpy.
import numpy as np
. Computing Manhattan distance between 2D points in Python
Let us compute Manhattan distance between two points shown in the aabove figure illustrating the Manhattan distance.
point1 = np.array([0, 0]) point2 = np.array([4, 4]) print(point1) print(point2)
We first compute the differences between two points.
diff = point1 - point2 diff array([-4, -4])
Then we compute the absolute values of the differences.
abs_diff = np.abs(diff) abs_diff array([4, 4])
Then we add them up to get the Manhattan distance. For the example we have the Manhattan distance is 8.
manhattan_dist = np.sum(abs_diff) manhattan_dist 8
We can use the above steps in a single statement and compute Manhattan distance. For our toy example in the figure, the Manhattan distance is 8 and we can visually verify that as well.
# Calculate the Manhattan distance in 2D manhattan_distance = np.sum(np.abs(point1-point2)) print(manhattan_distance) 8
Here is another example of computing Manhattan distance between two 2D points.
point1 = np.array([1, 2]) point2 = np.array([4, 6])
# Calculate the Manhattan distance in 2D manhattan_distance = np.sum(np.abs(point1-point2)) print(manhattan_distance) 7
<h3. Computing Manhattan distance between two points in 3D
We can use the same approach to compute distance between two points in 2-dimension. For example, the Manhattan distance between two points (x1,y1,z1) and (x2,y2,z2) in 3D is
abs(x1-x2) + abs(y1-y2) + abs(z1-z2)
Let us create some data for points in 3D.
point1 = np.array([1, 2, 3]) point2 = np.array([4, 6, 8])
We can compute Manhattan distance by summing the absolute values of differences between points.
manhattan_distance = np.sum(np.abs(point1-point2)) manhattan_distance 12
