Distance computation (distance.cdist) in SciPy - Step-by-Step Execution

Concept Flow - Distance computation (distance.cdist)

Input: Two sets of points A and B

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Select distance metric (e.g., Euclidean)

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Compute pairwise distances between each point in A and each point in B

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Output: Distance matrix with shape (len(A), len(B))

We start with two groups of points, pick a distance type, then calculate distances between every pair from the two groups, producing a matrix of distances.

Execution Sample

SciPy

import numpy as np
from scipy.spatial import distance

A = np.array([[0, 0], [1, 1]])
B = np.array([[1, 0], [2, 2]])

D = distance.cdist(A, B, 'euclidean')
print(D)

This code calculates Euclidean distances between points in A and B, outputting a matrix of distances.

Execution Table

Step	Action	Points from A	Points from B	Distance Computed	Distance Matrix State
1	Start with points A and B	[[0,0],[1,1]]	[[1,0],[2,2]]	-	Empty matrix (2x2)
2	Compute distance between A[0] and B[0]	[0,0]	[1,0]	sqrt((1-0)^2+(0-0)^2)=1.0	[[1.0, ?], [?, ?]]
3	Compute distance between A[0] and B[1]	[0,0]	[2,2]	sqrt((2-0)^2+(2-0)^2)=2.8284	[[1.0, 2.8284], [?, ?]]
4	Compute distance between A[1] and B[0]	[1,1]	[1,0]	sqrt((1-1)^2+(0-1)^2)=1.0	[[1.0, 2.8284], [1.0, ?]]
5	Compute distance between A[1] and B[1]	[1,1]	[2,2]	sqrt((2-1)^2+(2-1)^2)=1.4142	[[1.0, 2.8284], [1.0, 1.4142]]
6	All pairs computed	-	-	-	Final distance matrix completed

💡 All pairs of points from A and B have been processed, distance matrix fully computed.

Variable Tracker

Variable	Start	After Step 2	After Step 3	After Step 4	After Step 5	Final
D	empty 2x2 matrix	[[1.0, ?], [?, ?]]	[[1.0, 2.8284], [?, ?]]	[[1.0, 2.8284], [1.0, ?]]	[[1.0, 2.8284], [1.0, 1.4142]]	[[1.0, 2.8284], [1.0, 1.4142]]

Key Moments - 3 Insights

Why does the output matrix have shape (2, 2) instead of (4, 4)?

Because the distance matrix rows correspond to points in A (2 points) and columns to points in B (2 points), so shape is (len(A), len(B)) as shown in execution_table rows 2-5.

How is the Euclidean distance calculated between two points?

It uses the formula sqrt((x2 - x1)^2 + (y2 - y1)^2), as shown in the 'Distance Computed' column in execution_table rows 2-5.

What happens if we change the metric from 'euclidean' to 'cityblock'?

The distances would be computed as sum of absolute differences instead of Euclidean, changing the values in the distance matrix but keeping the same shape and process.

Visual Quiz - 3 Questions

Look at the execution table, what is the distance between A[1] and B[1] at step 5?

A 1.0

B 1.4142

C 2.8284

D 0.0

💡 Hint

Check the 'Distance Computed' column at step 5 in the execution_table.

At which step does the distance matrix become fully filled?

A Step 4

B Step 6

C Step 5

D Step 3

💡 Hint

Look at the 'Distance Matrix State' column; the matrix becomes fully filled (no ? left) at step 5.

If we add one more point to B, how would the distance matrix shape change?

A It would have one more column

B It would have one more row

C It would stay the same size

D It would become a 3D matrix

💡 Hint

Distance matrix shape is (len(A), len(B)) as explained in key_moments and concept_flow.

Concept Snapshot

distance.cdist(A, B, metric)
- Computes pairwise distances between points in A and B
- Returns matrix shape (len(A), len(B))
- metric='euclidean' is default for straight-line distance
- Supports many metrics like 'cityblock', 'cosine'
- Useful for comparing sets of points quickly

Full Transcript

This visual execution shows how scipy.spatial.distance.cdist computes distances between two sets of points. We start with two arrays A and B, each holding points in 2D space. The function calculates the distance between every point in A and every point in B using the chosen metric, here Euclidean distance. The output is a matrix where each row corresponds to a point in A and each column to a point in B. The matrix entries are the distances. Step by step, we see each pair's distance computed and placed in the matrix until all pairs are done. This helps understand how cdist works internally and what the output means.