Distance metrics (euclidean, cosine, manhattan) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Calculate Euclidean distance between two points

What is the output of this code that calculates the Euclidean distance between points (1, 2) and (4, 6)?

SciPy

from scipy.spatial import distance
point1 = [1, 2]
point2 = [4, 6]
result = distance.euclidean(point1, point2)
print(round(result, 2))

A 5.0

B 7.0

C 4.24

D 3.61

💡 Hint

Euclidean distance is the straight line distance between two points in space.

Euclidean distance between (1,2) and (4,6) is sqrt((4-1)^2 + (6-2)^2) = sqrt(9 + 16) = sqrt(25) = 5.0.

❓ data_output

intermediate

Cosine distance between two vectors

What is the cosine distance between vectors [1, 0, -1] and [-1, 0, 1] using scipy?

SciPy

from scipy.spatial import distance
vec1 = [1, 0, -1]
vec2 = [-1, 0, 1]
result = distance.cosine(vec1, vec2)
print(round(result, 2))

A 0.0

B 1.0

C 2.0

D 0.5

💡 Hint

Cosine distance is 1 minus the cosine similarity.

The vectors are exact opposites, so cosine similarity is -1, thus cosine distance = 1 - (-1) = 2. Scipy cosine distance returns 2 for opposite vectors.

❓ Predict Output

advanced

Manhattan distance calculation

What is the Manhattan distance between points (3, 5) and (1, 1)?

SciPy

from scipy.spatial import distance
p1 = [3, 5]
p2 = [1, 1]
result = distance.cityblock(p1, p2)
print(result)

A 6

B 8

C 4

D 10

💡 Hint

Manhattan distance sums the absolute differences of coordinates.

Manhattan distance = |3-1| + |5-1| = 2 + 4 = 6.

❓ visualization

advanced

Visualize Euclidean vs Manhattan distance

Which option correctly plots the Euclidean and Manhattan distances between points (0,0) and (3,4) on a 2D grid?

SciPy

import matplotlib.pyplot as plt
import numpy as np

fig, ax = plt.subplots()
ax.plot([0,3], [0,4], label='Euclidean')
ax.plot([0,3,3], [0,0,4], label='Manhattan')
ax.scatter([0,3], [0,4], color='red')
ax.legend()
plt.show()

A A circle centered at (0,0) with radius 5

B A straight line from (0,0) to (3,0) and a diagonal from (3,0) to (3,4)

C Two diagonal lines crossing at (3,4)

D A line from (0,0) to (3,4) and an L-shaped path from (0,0) to (3,0) to (3,4)

💡 Hint

Manhattan distance looks like walking along grid streets, Euclidean is straight line.

Euclidean distance is the straight line connecting points. Manhattan distance is the sum of horizontal and vertical moves, forming an L shape.

🧠 Conceptual

expert

Understanding cosine distance range

Which statement about cosine distance computed by scipy.spatial.distance.cosine is correct?

A Cosine distance ranges from -1 to 1, where -1 means opposite and 1 means identical vectors

B Cosine distance ranges from 0 to 2, where 0 means identical and 2 means opposite vectors

C Cosine distance is always between 0 and 1, with 1 meaning identical vectors

D Cosine distance is the same as Euclidean distance normalized between 0 and 1

💡 Hint

Recall cosine distance = 1 - cosine similarity.

Cosine similarity ranges from -1 (opposite) to 1 (identical). Cosine distance = 1 - cosine similarity, so it ranges from 0 (identical) to 2 (opposite).