Distance matrix computation in SciPy - Step-by-Step Execution

Concept Flow - Distance matrix computation

Start with data points

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Choose distance metric

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Compute pairwise distances

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Store results in matrix

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Use matrix for analysis

We start with data points, pick a distance type, compute distances between all pairs, and save them in a matrix for further use.

Execution Sample

SciPy

from scipy.spatial import distance_matrix
import numpy as np

points = np.array([[1, 2], [4, 6], [7, 8]])
dist_mat = distance_matrix(points, points)
print(dist_mat)

This code calculates the distance matrix for three 2D points using Euclidean distance.

Execution Table

Step	Action	Points involved	Distance computed	Matrix update
1	Start with points	[[1,2],[4,6],[7,8]]	-	Matrix empty
2	Compute distance between point 0 and 0	[1,2] & [1,2]	0.0	dist_mat[0,0] = 0.0
3	Compute distance between point 0 and 1	[1,2] & [4,6]	5.0	dist_mat[0,1] = 5.0
4	Compute distance between point 0 and 2	[1,2] & [7,8]	8.48528137423857	dist_mat[0,2] = 8.48528137423857
5	Compute distance between point 1 and 0	[4,6] & [1,2]	5.0	dist_mat[1,0] = 5.0
6	Compute distance between point 1 and 1	[4,6] & [4,6]	0.0	dist_mat[1,1] = 0.0
7	Compute distance between point 1 and 2	[4,6] & [7,8]	3.605551275463989	dist_mat[1,2] = 3.605551275463989
8	Compute distance between point 2 and 0	[7,8] & [1,2]	8.48528137423857	dist_mat[2,0] = 8.48528137423857
9	Compute distance between point 2 and 1	[7,8] & [4,6]	3.605551275463989	dist_mat[2,1] = 3.605551275463989
10	Compute distance between point 2 and 2	[7,8] & [7,8]	0.0	dist_mat[2,2] = 0.0
11	All pairs computed	-	-	Distance matrix complete

💡 All pairwise distances computed and stored in the matrix.

Variable Tracker

Variable	Start	After Step 2	After Step 4	After Step 7	After Step 10	Final
dist_mat	empty	[[0.0, 0, 0], [0, 0, 0], [0, 0, 0]]	[[0.0, 5.0, 8.485], [0, 0, 0], [0, 0, 0]]	[[0.0, 5.0, 8.485], [5.0, 0.0, 3.606], [0, 0, 0]]	[[0.0, 5.0, 8.485], [5.0, 0.0, 3.606], [8.485, 3.606, 0.0]]	[[0.0, 5.0, 8.48528137], [5.0, 0.0, 3.60555128], [8.48528137, 3.60555128, 0.0]]

Key Moments - 3 Insights

Why is the distance between a point and itself always zero?

Because the distance formula measures how far apart two points are, and a point is zero units away from itself. See execution_table rows 2, 6, and 10 where distances are 0.0.

Why is the distance matrix symmetric?

Distance from point A to B is the same as from B to A, so dist_mat[i,j] equals dist_mat[j,i]. This is shown in rows 3 and 5, 4 and 8, 7 and 9.

What happens if we use different sets of points for rows and columns?

The matrix will have distances between each point in the first set to each point in the second set, not necessarily square or symmetric. Here, both sets are the same, so matrix is square and symmetric.

Visual Quiz - 3 Questions

Look at the execution_table at step 4, what is the distance computed between points [1,2] and [7,8]?

A 8.48528137423857

B 5.0

C 3.605551275463989

D 0.0

💡 Hint

Check the 'Distance computed' column at step 4 in execution_table.

At which step does the distance between points [4,6] and [7,8] get computed?

A Step 9

B Step 6

C Step 7

D Step 3

💡 Hint

Look for the row where points involved are [4,6] & [7,8] in execution_table.

If we add a new point [0,0], how will the size of the distance matrix change?

A It will remain 3x3

B It will become 4x4

C It will become 3x4

D It will become 4x3

💡 Hint

Distance matrix size is number of points by number of points, see variable_tracker for matrix size.

Concept Snapshot

Distance matrix computation:
- Input: list/array of points
- Use scipy.spatial.distance_matrix(pointsA, pointsB)
- Computes pairwise distances (default Euclidean)
- Returns matrix with distances between each pair
- Matrix is square and symmetric if pointsA == pointsB

Full Transcript

Distance matrix computation starts with a set of points. We pick a distance metric, usually Euclidean. Then, for every pair of points, we calculate how far apart they are. These distances fill a matrix where each cell shows the distance between two points. The diagonal is zero because a point is zero distance from itself. The matrix is symmetric because distance from A to B equals distance from B to A. This matrix helps in many data science tasks like clustering or nearest neighbor search.