Distance metrics (euclidean, cosine, manhattan) in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the euclidean distance function from scipy.

SciPy

from scipy.spatial.distance import [1]

Drag options to blanks, or click blank then click option'

Amanhattan

Bcosine

Ceuclidean

Dhamming

Attempts:

3 left

💡 Hint

Common Mistakes

Choosing cosine or manhattan which are different distance metrics.

Trying to import a function not available in scipy.spatial.distance.

The euclidean function calculates the straight-line distance between two points.

2fill in blank

medium

Complete the code to calculate the cosine distance between vectors a and b.

SciPy

distance = [1](a, b)

Drag options to blanks, or click blank then click option'

Acosine

Bmanhattan

Ceuclidean

Dhamming

Attempts:

3 left

💡 Hint

Common Mistakes

Using euclidean distance which measures straight-line distance, not angle.

Using manhattan distance which sums absolute differences.

The cosine function measures the cosine distance, which reflects the angle difference between vectors.

3fill in blank

hard

Fix the error in the code to correctly calculate Manhattan distance between x and y.

SciPy

dist = [1](x, y)

Drag options to blanks, or click blank then click option'

Acosine

Bmanhattan

Cminkowski

Deuclidean

Attempts:

3 left

💡 Hint

Common Mistakes

Using euclidean distance which calculates straight-line distance.

Using minkowski without specifying the order parameter.

The manhattan function calculates the sum of absolute differences between coordinates.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps each vector to its Euclidean distance from a reference vector ref_vec.

SciPy

distances = {vec: [1](vec, ref_vec) for vec in vectors if [2](vec, ref_vec) < 5}

Drag options to blanks, or click blank then click option'

Aeuclidean

Bcosine

Cmanhattan

Dlen

Attempts:

3 left

💡 Hint

Common Mistakes

Using different distance functions in the two blanks.

Using len() which returns length, not distance.

We use euclidean to calculate distances and to filter vectors closer than 5 units.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps each vector to its Manhattan distance from ref_vec, but only include vectors with cosine distance less than 0.5.

SciPy

distances = {vec: [1](vec, ref_vec) for vec in vectors if [2](vec, ref_vec) [3] 0.5}

Drag options to blanks, or click blank then click option'

Aeuclidean

Bmanhattan

Ccosine

D<

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up distance functions in the blanks.

Using wrong comparison operator like > instead of <.

We calculate Manhattan distance for values, but filter vectors where cosine distance is less than 0.5.

Practice

1. Which distance metric measures the straight-line distance between two points in space?

easy

A. Jaccard distance

B. Cosine distance

C. Manhattan distance

D. Euclidean distance

Solution

1. Step 1: Understand distance types

   Euclidean distance is the direct straight-line distance between two points.

2. Step 2: Compare with other distances

   Cosine measures angle difference, Manhattan sums absolute differences, Jaccard measures set similarity.

3. Final Answer:

   Euclidean distance -> Option D

4. Quick Check:

   Straight-line distance = Euclidean distance [OK]

Hint: Straight line means Euclidean distance [OK]

Common Mistakes:

• Confusing cosine with Euclidean
• Thinking Manhattan is straight-line
• Mixing Jaccard with numeric distances

2. Which of the following is the correct way to import the Euclidean distance function from scipy?

easy

A. from scipy.spatial.distance import euclidean

B. import scipy.distance.euclidean

C. from scipy.distance import euclidean

D. import euclidean from scipy.spatial

Solution

1. Step 1: Recall scipy import syntax

   The correct import path for distance functions is scipy.spatial.distance.

2. Step 2: Check each option

   from scipy.spatial.distance import euclidean uses correct syntax: from scipy.spatial.distance import euclidean. Others are invalid or incorrect syntax.

3. Final Answer:

   from scipy.spatial.distance import euclidean -> Option A

4. Quick Check:

   Correct import path = from scipy.spatial.distance import euclidean [OK]

Hint: Use 'from scipy.spatial.distance import' for distance functions [OK]

Common Mistakes:

• Using wrong module path
• Incorrect import syntax
• Trying to import from scipy.distance

3. What is the output of this code?

from scipy.spatial.distance import cosine
v1 = [1, 0, 1]
v2 = [0, 1, 0]
result = cosine(v1, v2)
print(round(result, 2))

medium

A. 1.0

B. 0.5

C. 0.0

D. 0.71

Solution

1. Step 1: Calculate cosine similarity basics

   Vectors v1 and v2 are orthogonal (no overlap), so cosine similarity is 0.

2. Step 2: Calculate cosine distance

   Cosine distance = 1 - cosine similarity = 1 - 0 = 1.0.

3. Final Answer:

   1.0 -> Option A

4. Quick Check:

   Orthogonal vectors cosine distance = 1.0 [OK]

Hint: Cosine distance = 1 - cosine similarity [OK]

Common Mistakes:

• Confusing cosine similarity with distance
• Rounding errors
• Assuming zero distance for orthogonal vectors

4. Find the error in this code snippet calculating Manhattan distance:

from scipy.spatial.distance import manhattan
a = [1, 2, 3]
b = [4, 5]
print(manhattan(a, b))

medium

A. Function name should be cityblock, not manhattan

B. Import statement is incorrect

C. Lists a and b must be the same length

D. Manhattan distance requires numpy arrays, not lists

Solution

1. Step 1: Check input vector lengths

   Vectors a and b have different lengths (3 and 2), which is invalid for distance calculation.

2. Step 2: Validate function and import

   Import and function name are correct; scipy.spatial.distance.manhattan is valid and accepts lists.

3. Final Answer:

   Lists a and b must be the same length -> Option C

4. Quick Check:

   Equal length vectors needed for distance [OK]

Hint: Vectors must be same length for distance functions [OK]

Common Mistakes:

• Assuming different length lists work
• Confusing function name with cityblock
• Thinking lists are invalid inputs

5. You have two points: p1 = [3, 4, 5] and p2 = [1, 1, 1]. Which distance metric will give the largest value?
Options:
A) Euclidean
B) Cosine
C) Manhattan
D) All equal

hard

A. Euclidean

B. Manhattan

C. Cosine

D. All equal

Solution

1. Step 1: Calculate Euclidean distance

   Euclidean = sqrt((3-1)^2 + (4-1)^2 + (5-1)^2) = sqrt(4 + 9 + 16) = sqrt(29) ≈ 5.39.

2. Step 2: Calculate Manhattan distance

   Manhattan = |3-1| + |4-1| + |5-1| = 2 + 3 + 4 = 9.

3. Step 3: Calculate Cosine distance

   Cosine similarity = (3*1 + 4*1 + 5*1) / (sqrt(3^2+4^2+5^2)*sqrt(1^2+1^2+1^2)) = 12 / (7.07*1.73) ≈ 0.98; Cosine distance = 1 - 0.98 = 0.02.

4. Final Answer:

   Manhattan -> Option B

5. Quick Check:

   Manhattan distance > Euclidean > Cosine distance [OK]

Hint: Manhattan sums absolute differences, usually largest [OK]

Common Mistakes:

• Assuming Euclidean is always largest
• Confusing cosine distance scale
• Ignoring absolute values in Manhattan