In data science and machine learning, measuring the similarity between two points is a foundational task. One of the most common ways to do this is by calculating the Euclidean Distance.
While many beginners learn the formula for 2D points (X and Y), the math stays remarkably similar even as you add more dimensions (features). In this guide, we’ll look at how to calculate distance for 4 features and how to write a generalized Python function for any number of dimensions.
The Formula
The Euclidean distance between two points $P$ and $Q$ in $n$-dimensional space is the square root of the sum of the squares of the differences between their coordinates.
$$Distance = \sqrt{\sum_{i=1}^{n} (Q_i - P_i)^2}$$
For 4 Features:
If we have Point A $(a_1, a_2, a_3, a_4)$ and Point B $(b_1, b_2, b_3, b_4)$: $$Dist = \sqrt{(b_1-a_1)^2 + (b_2-a_2)^2 + (b_3-a_3)^2 + (b_4-a_4)^2}$$
Manual Calculation in Python
If you have two specific points, you can calculate the distance using Python’s math.sqrt():
import math
# Point A: (Width, Height, Weight, ColorValue)
A = (1, 2, 5, 1)
# Point B: (Width, Height, Weight, ColorValue)
B = (7, 1, 3, 0)
dist = math.sqrt((7-1)**2 + (1-2)**2 + (3-5)**2 + (0-1)**2)
print(f"Distance: {dist:.4f}")
# Output: 6.4807
Creating a Generalized Function
In a real project, you don’t want to hardcode the subtraction for every feature. We can write a function that takes two lists of any length and returns the distance.
import math
def calculate_euclidean_distance(p1, p2):
if len(p1) != len(p2):
raise ValueError("Points must have the same number of dimensions")
squared_differences = []
for i in range(len(p1)):
diff = (p1[i] - p2[i]) ** 2
squared_differences.append(diff)
return math.sqrt(sum(squared_differences))
# Example usage with 4 features
point_x = [10, 20, 15, 5]
point_y = [12, 18, 14, 8]
result = calculate_euclidean_distance(point_x, point_y)
print(f"Result: {result}")
The “Professional” Way: Using NumPy
If you are working on a data science project with large datasets, calculating distances in a loop is slow. The NumPy library is optimized for these calculations and is much more concise.
import numpy as np
p1 = np.array([1, 2, 5, 1])
p2 = np.array([7, 1, 3, 0])
# NumPy can subtract entire arrays and calculate the norm in one step
dist = np.linalg.norm(p1 - p2)
print(f"NumPy Distance: {dist:.4f}")
Why does this matter?
Euclidean distance is the engine behind many popular machine learning algorithms, including: 1. K-Nearest Neighbours (K-NN): Finding the closest neighbors to a new data point. 2. K-Means Clustering: Assigning data points to the nearest cluster center. 3. Recommendation Systems: Finding users with similar tastes (coordinates).
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Written by
Abdur-Rahmaan Janhangeer
Chef
Python author of 7+ years having worked for Python companies around the world
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