Distance matrix computation in SciPy

Introduction

We use distance matrix computation to find how far apart items are from each other. This helps us understand relationships or groupings in data.

Comparing distances between cities on a map.

Finding similar customers based on their shopping habits.

Grouping animals by their features in biology.

Measuring how close different documents are in text analysis.

Syntax

SciPy

from scipy.spatial import distance_matrix

distance_matrix(X, Y=None, p=2, threshold=1000.0)

X and Y are arrays of points (rows are points, columns are features).

p sets the distance type: 2 means Euclidean (straight line).

Examples

Compute distances between points in X itself.

SciPy

from scipy.spatial import distance_matrix
import numpy as np

X = np.array([[0, 0], [1, 1]])
D = distance_matrix(X, X)
print(D)

Compute distances from points in X to points in Y.

SciPy

from scipy.spatial import distance_matrix
import numpy as np

X = np.array([[0, 0], [1, 1]])
Y = np.array([[2, 2]])
D = distance_matrix(X, Y)
print(D)

Sample Program

This program calculates the distances between each point in X and each point in Y. The result is a matrix where each row corresponds to a point in X and each column to a point in Y.

SciPy

from scipy.spatial import distance_matrix
import numpy as np

# Define two sets of points
X = np.array([[0, 0], [3, 4], [6, 8]])
Y = np.array([[0, 0], [1, 1]])

# Compute the distance matrix
D = distance_matrix(X, Y)

print(D)

Important Notes

The distance matrix is always a 2D array with shape (len(X), len(Y)).

Euclidean distance (p=2) is the most common, but you can use other distances by changing p.

If Y is not given, distances are computed between points in X itself.

Summary

Distance matrix shows how far points are from each other.

Use scipy.spatial.distance_matrix to compute it easily.

It helps in clustering, similarity, and spatial analysis tasks.