Minkowski Distance in Python

The Minkowski distance is a generalization of various distance metrics like Euclidean and Manhattan distances.

import numpy as np

def minkowski_distance(x, y, p):
    return np.sum(np.abs(x - y) ** p) ** (1 / p)

# Example usage
x = np.array([1, 2, 3])
y = np.array([4, 5, 6])

# Calculate Minkowski distance with p=3
distance = minkowski_distance(x, y, p=3)
print("Minkowski Distance:", distance)

Minkowski Distance: 4.3267487109222245

Explanation:

• x and y: The points in an n-dimensional space, represented as NumPy arrays.
• p: The parameter p in the Minkowski distance formula. For p=1, it becomes the Manhattan distance; for p=2, it becomes the Euclidean distance.
• np.abs(x - y) ** p: Calculates the absolute differences raised to the power of p for each dimension.
• np.sum(... ** (1 / p)): Sums these values and then takes the pth root.