Distance computation (distance.cdist) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Euclidean distance matrix

What is the output of the following code that computes Euclidean distances between two sets of points?

SciPy

import numpy as np
from scipy.spatial import distance

A = np.array([[0, 0], [1, 1]])
B = np.array([[1, 0], [2, 2]])
result = distance.cdist(A, B, 'euclidean')
print(result)

A

[[1.41421356 2.23606798]
 [1.         1.41421356]]

B

[[1.         2.23606798]
 [1.41421356 1.        ]]

C

[[1.         2.23606798]
 [1.         1.41421356]]

D

[[1.         2.82842712]
 [1.         1.41421356]]

💡 Hint

Remember Euclidean distance is the straight line distance between points.

The Euclidean distance between points in A and B is calculated pairwise. For example, distance between [0,0] and [1,0] is 1, and between [0,0] and [2,2] is sqrt(2^2 + 2^2) = 2.828. Option A matches the correct matrix values.

❓ data_output

intermediate

Number of distances computed with cityblock metric

Given two arrays A and B, how many distances are computed by distance.cdist(A, B, 'cityblock')?

SciPy

import numpy as np
from scipy.spatial import distance

A = np.array([[1, 2], [3, 4], [5, 6]])
B = np.array([[7, 8], [9, 10]])
result = distance.cdist(A, B, 'cityblock')
print(result.shape[0] * result.shape[1])

A 3

B 5

C 2

D 6

💡 Hint

The output shape is (number of rows in A, number of rows in B).

distance.cdist computes distances between every pair of points from A and B. A has 3 points, B has 2 points, so total distances = 3 * 2 = 6.

🔧 Debug

advanced

Identify the error in distance.cdist usage

What error will this code raise and why?

SciPy

import numpy as np
from scipy.spatial import distance

A = np.array([[1, 2, 3], [4, 5, 6]])
B = np.array([[7, 8]])
result = distance.cdist(A, B, 'euclidean')

A No error, runs successfully

B ValueError: A and B must have the same number of columns

C IndexError: index out of bounds

D TypeError: Unsupported metric 'euclidean'

💡 Hint

Check the shape of A and B carefully.

distance.cdist requires both input arrays to have the same number of features (columns). Here, A has 3 columns but B has only 2, causing a ValueError.

❓ visualization

advanced

Visualizing cosine distances between points

Which option correctly plots the cosine distance matrix heatmap between points in A and B?

SciPy

import numpy as np
from scipy.spatial import distance
import matplotlib.pyplot as plt

A = np.array([[1, 0], [0, 1]])
B = np.array([[1, 1], [-1, 0]])
dist_matrix = distance.cdist(A, B, 'cosine')
plt.imshow(dist_matrix, cmap='viridis')
plt.colorbar()
plt.show()

A A heatmap with values close to 0 and 1, showing cosine distances between points.

B A bar chart of distances between points.

C A line plot of distances over index.

D A scatter plot of points A and B.

💡 Hint

Cosine distance values range between 0 and 1 and are best shown as a heatmap.

The code computes cosine distances and visualizes them as a heatmap using imshow. This shows the pairwise cosine distances clearly.

🧠 Conceptual

expert

Understanding distance.cdist with custom metric

Which statement about using a custom metric function with distance.cdist is TRUE?

A distance.cdist does not support custom metric functions.

B The custom metric function can accept arrays of any shape and return an array of distances.

C The custom metric function must accept two 1-D arrays and return a scalar distance.

D The custom metric function must return a boolean indicating if points are equal.

💡 Hint

Think about how distance.cdist computes pairwise distances.

distance.cdist allows a custom metric function that takes two 1-D arrays (points) and returns a single scalar distance value.