Distance matrix computation in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Euclidean distance matrix computation

What is the output of this code that computes the Euclidean distance matrix between points?

SciPy

import numpy as np
from scipy.spatial import distance_matrix
points = np.array([[0, 0], [3, 4], [6, 8]])
dist_mat = distance_matrix(points, points)
print(dist_mat)

A

[[ 0.  7. 14.]
 [ 7.  0.  7.]
 [14.  7.  0.]]

B

[[0 5 10]
 [5 0 5]
 [10 5 0]]

C

[[ 0.  5. 10.]
 [ 5.  0.  5.]
 [10.  5.  0.]]

D

[[ 0.  3.  6.]
 [ 3.  0.  4.]
 [ 6.  4.  0.]]

💡 Hint

Recall that Euclidean distance between (x1,y1) and (x2,y2) is sqrt((x2-x1)^2 + (y2-y1)^2).

The distances between points (0,0), (3,4), and (6,8) are 5, 10, and 5 respectively, forming the symmetric matrix shown in option C.

❓ data_output

intermediate

Number of elements in Euclidean distance matrix

Given 4 points in 2D space, how many elements are in the Euclidean distance matrix computed by scipy.spatial.distance_matrix?

SciPy

import numpy as np
from scipy.spatial import distance_matrix
points = np.array([[1,2], [3,4], [5,6], [7,8]])
dist_mat = distance_matrix(points, points)
print(dist_mat.size)

A 16

B 8

C 4

D 12

💡 Hint

Distance matrix between n points is an n x n matrix.

With 4 points, the distance matrix is 4 rows by 4 columns, so total elements = 4*4 = 16.

🔧 Debug

advanced

Identify the error in distance matrix computation code

What error does this code raise when computing a distance matrix?

SciPy

import numpy as np
from scipy.spatial import distance_matrix
points = [[0, 0], [1, 1], [2, 2]]
dist_mat = distance_matrix(points, points)
print(dist_mat)

A No error, prints the correct distance matrix

B TypeError: unsupported operand type(s) for -: 'list' and 'list'

C ValueError: setting an array element with a sequence

D NameError: name 'distance_matrix' is not defined

💡 Hint

Check if input is accepted as list of lists or needs to be numpy array.

scipy.spatial.distance_matrix accepts list of lists as input and converts internally, so no error occurs.

🧠 Conceptual

advanced

Which distance metric is NOT supported by scipy.spatial.distance_matrix?

Which of these distance metrics cannot be directly computed using scipy.spatial.distance_matrix function?

A Euclidean distance

B Manhattan (cityblock) distance

C Hamming distance

D Cosine distance

💡 Hint

Check scipy.spatial.distance_matrix documentation for supported metrics.

scipy.spatial.distance_matrix only computes Euclidean distance. Other metrics like Manhattan, Cosine, or Hamming require scipy.spatial.distance.pdist or cdist with metric parameter.

🚀 Application

expert

Find the closest pair of points using distance matrix

Given this code, which option correctly identifies the indices of the closest pair of points?

SciPy

import numpy as np
from scipy.spatial import distance_matrix
points = np.array([[1, 2], [4, 6], [1, 3], [7, 8]])
dist_mat = distance_matrix(points, points)
np.fill_diagonal(dist_mat, np.inf)
min_index = np.unravel_index(np.argmin(dist_mat), dist_mat.shape)
print(min_index)

A (2, 3)

B (0, 2)

C (0, 1)

D (1, 3)

💡 Hint

Look for the smallest non-zero distance after ignoring diagonal.

Points at indices 0 and 2 are closest with distance 1, so min_index is (0, 2).