The Euclidean distance is a measure of the distance between two points in a multidimensional space. In Python, the Euclidean distance can be calculated using the NumPy library.
To calculate the Euclidean distance between two points, we first need to import the NumPy library. We can do this by using the following code:
import numpy as np
Once we have imported the NumPy library, we can use the np.linalg.norm()
function to calculate the Euclidean distance between two points. The np.linalg.norm()
function takes a single argument, which is the difference between the two points.
Here is an example of how to use the np.linalg.norm()
function to calculate the Euclidean distance between two points:
point1 = [1, 2, 3]
point2 = [4, 5, 6]
distance = np.linalg.norm(np.array(point1)  np.array(point2))
print(distance)
In this example, we have defined two points, point1
and point2
, and calculated the Euclidean distance between them using the np.linalg.norm()
function. The output of this code will be 5.196152422706632
, which is the Euclidean distance between the two points.
We can also create a function to calculate the euclidean distance between two points
def euclidean_distance(point1, point2):
return np.linalg.norm(np.array(point1)  np.array(point2))
point1 = [1, 2, 3]
point2 = [4, 5, 6]
print(euclidean_distance(point1, point2))
We can also calculate euclidean distance between two vectors of different lengths or different number of features by using scipy library
from scipy.spatial import distance
point1 = [1, 2, 3]
point2 = [4, 5, 6]
print(distance.euclidean(point1, point2))
In addition to the above methods, we can also calculate the euclidean distance using the square root of the sum of the squares of the differences between the coordinates of the two points.
def euclidean_distance_2(point1, point2):
distance = 0
for i in range(len(point1)):
distance += (point1[i]  point2[i]) ** 2
return distance ** 0.5
point1 = [1, 2, 3]
point2 = [4, 5, 6]
print(euclidean_distance_2(point1, point2))
In this article, we have learned how to calculate the Euclidean distance between two points in Python using the NumPy library, Scipy library, and by using the square root of the sum of the squares of the differences between the coordinates of the two points.
The Euclidean distance is a widely used measure of distance in many fields, including machine learning, computer vision, and pattern recognition. It is particularly useful in cases where the data points have a Euclidean structure, such as images or 3D point clouds.
In addition to the basic Euclidean distance, there are several variants of the Euclidean distance that are used in different applications. For example, the squared Euclidean distance is often used in optimization problems, as it can lead to faster convergence and is computationally more efficient.
Another variant of the Euclidean distance is the Mahalanobis distance, which takes into account the covariance of the data. This distance measure is particularly useful when the data points have a nonuniform distribution and can help to improve the performance of classifiers and clustering algorithms.
In some cases, the Euclidean distance is not the most appropriate measure of distance. For example, in data with categorical variables, it may be more appropriate to use a measure such as the Hamming distance. Similarly, in data with a temporal structure, it may be more appropriate to use a measure such as the Dynamic Time Warping distance.
In addition to the above examples, it's also worth noting that the euclidean distance can be used with other types of data such as text data and sequence data. For example, the Levenshtein distance which is a string metric used for measuring the difference between two sequences and it is also known as Edit Distance. And also it's possible to calculate the euclidean distance between two images, such as measuring the difference between two images in a dataset.
In conclusion, the Euclidean distance is a widely used measure of distance in many fields and it's a powerful tool for measuring similarity or difference between data points. However, it's important to remember that in some cases, other measures of distance may be more appropriate. It's also important to keep in mind that there are many variants of the Euclidean distance, each with its own set of properties and use cases.
Popular questions

What is the Euclidean distance?
The Euclidean distance is a measure of the distance between two points in a multidimensional space. It is calculated as the square root of the sum of the squares of the differences between the coordinates of the two points. 
How can we calculate the Euclidean distance in Python?
The Euclidean distance can be calculated in Python using the NumPy library. Thenp.linalg.norm()
function can be used to calculate the Euclidean distance between two points by passing the difference between the two points as an argument. 
What are some variants of the Euclidean distance?
Some variants of the Euclidean distance include the squared Euclidean distance, which is often used in optimization problems, and the Mahalanobis distance, which takes into account the covariance of the data. 
When is the Euclidean distance not the most appropriate measure of distance?
The Euclidean distance may not be the most appropriate measure of distance in cases where the data points have a categorical structure or a temporal structure. In such cases, it may be more appropriate to use a measure such as the Hamming distance or the Dynamic Time Warping distance. 
Can we use the Euclidean distance with other types of data?
Yes, the Euclidean distance can be used with other types of data such as text data, sequence data and images. For example, the Levenshtein distance can be used to measure the difference between two sequences and it's possible to calculate the Euclidean distance between two images.
Tag
Distance