Distance metrics (euclidean, cosine, manhattan) in SciPy

Introduction

Distance metrics help us measure how far apart two points or objects are. They are useful to compare things in many areas like shopping, sports, or health.

To find the closest store to your home based on location coordinates.

To compare how similar two songs are by their features.

To measure the difference between two people's health data.

To group customers with similar buying habits.

To check how different two images are by their pixel values.

Syntax

SciPy

from scipy.spatial import distance

# Euclidean distance
distance.euclidean(point1, point2)

# Cosine distance
distance.cosine(point1, point2)

# Manhattan distance
distance.cityblock(point1, point2)

point1 and point2 are lists or arrays of numbers representing coordinates or features.

Euclidean is straight-line distance, Cosine measures angle difference, Manhattan sums absolute differences.

Examples

Calculates straight-line distance between points (1,2) and (4,6).

SciPy

distance.euclidean([1, 2], [4, 6])

Measures how different two vectors are in direction.

SciPy

distance.cosine([1, 0, 0], [0, 1, 0])

Calculates total absolute difference along each dimension.

SciPy

distance.cityblock([1, 2, 3], [4, 0, 6])

Sample Program

This program calculates three types of distances between two points and prints them with two decimals for clarity.

SciPy

from scipy.spatial import distance

pointA = [3, 4]
pointB = [7, 1]

# Calculate Euclidean distance
euclid = distance.euclidean(pointA, pointB)

# Calculate Cosine distance
cosine = distance.cosine(pointA, pointB)

# Calculate Manhattan distance
manhattan = distance.cityblock(pointA, pointB)

print(f"Euclidean distance: {euclid:.2f}")
print(f"Cosine distance: {cosine:.2f}")
print(f"Manhattan distance: {manhattan}")

Important Notes

Euclidean distance is like measuring with a ruler in straight line.

Cosine distance is good when you care about direction, not size.

Manhattan distance is like walking city blocks, adding up all steps.

Summary

Distance metrics measure how far or different two points are.

Euclidean is straight-line, Cosine is angle-based, Manhattan sums absolute differences.

Use scipy.spatial.distance functions to calculate these easily in Python.