Jaccard similarity in NLP - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of this Jaccard similarity calculation?

Given two sets A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, what is the Jaccard similarity computed by the code below?

NLP

A = {1, 2, 3, 4}
B = {3, 4, 5, 6}
intersection = A.intersection(B)
union = A.union(B)
jaccard_similarity = len(intersection) / len(union)
print(round(jaccard_similarity, 2))

A 0.50

B 0.33

C 0.25

D 0.40

💡 Hint

Recall that Jaccard similarity is the size of the intersection divided by the size of the union of two sets.

The intersection of A and B is {3, 4} with size 2. The union is {1, 2, 3, 4, 5, 6} with size 6. So, similarity = 2/6 = 0.3333, rounded to 0.33. But the code rounds to 2 decimals, so output is 0.33.

🧠 Conceptual

intermediate

Which statement best describes Jaccard similarity?

Choose the best description of what Jaccard similarity measures between two sets.

A The ratio of the size of the intersection to the size of the union of two sets.

B The difference in sizes between two sets.

C The sum of the sizes of two sets.

D The ratio of the size of the union to the size of the intersection of two sets.

💡 Hint

Think about how much two sets overlap compared to their total combined size.

Jaccard similarity is defined as the size of the intersection divided by the size of the union of two sets, measuring their overlap.

❓ Metrics

advanced

What is the Jaccard similarity between these two token sets?

Given two token sets from text documents: doc1 = {'apple', 'banana', 'cherry'} and doc2 = {'banana', 'cherry', 'date', 'fig'}, what is their Jaccard similarity?

A 0.4

B 0.5

C 0.6

D 0.75

💡 Hint

Count the common tokens and total unique tokens.

Intersection is {'banana', 'cherry'} size 2. Union is {'apple', 'banana', 'cherry', 'date', 'fig'} size 5. Similarity = 2/5 = 0.4.

🔧 Debug

advanced

Why does this Jaccard similarity code raise an error?

Consider this code snippet:

def jaccard_similarity(list1, list2):
    intersection = list1 & list2
    union = list1 | list2
    return len(intersection) / len(union)

print(jaccard_similarity(['a', 'b'], ['b', 'c']))

Why does it raise an error?

A The function returns a float but print expects a string.

B The function is missing a return statement.

C Lists do not support the '&' and '|' operators; sets are needed.

D The lists are empty, causing division by zero.

💡 Hint

Check the data types and operators used for intersection and union.

The '&' and '|' operators work only on sets, not lists. Using lists causes a TypeError.

❓ Model Choice

expert

Which model output best matches Jaccard similarity for text similarity?

You have two text documents and want to measure their similarity using Jaccard similarity on token sets. Which model output below correctly computes this similarity?

A

def jaccard(doc1, doc2):
    return len(set(doc1).intersection(set(doc2))) / len(set(doc1).union(set(doc2)))

B

def jaccard(doc1, doc2):
    tokens1, tokens2 = doc1.split(), doc2.split()
    return len(tokens1 & tokens2) / len(tokens1 | tokens2)

C

def jaccard(doc1, doc2):
    set1, set2 = set(doc1), set(doc2)
    return len(set1 & set2) / len(set1 | set2)

D

def jaccard(doc1, doc2):
    set1, set2 = set(doc1.split()), set(doc2.split())
    return len(set1.intersection(set2)) / len(set1.union(set2))

💡 Hint

Consider how to tokenize text properly before computing sets.

Option D splits the documents into words (tokens), converts to sets, then computes intersection and union correctly. Option D treats each character as a token, which is incorrect for word-level similarity. Option D uses list operators '&' and '|' which are invalid. Option D also treats characters as tokens.

Practice

1. What does the Jaccard similarity measure between two sets?

easy

A. The difference between the sizes of the two sets

B. The size of the union divided by the size of the intersection

C. The sum of the sizes of the two sets

D. The size of the intersection divided by the size of the union

Solution

1. Step 1: Understand the definition of Jaccard similarity

   Jaccard similarity is defined as the size of the intersection of two sets divided by the size of their union.

2. Step 2: Compare options with the definition

   The size of the intersection divided by the size of the union matches the definition exactly, while others describe different calculations.

3. Final Answer:

   The size of the intersection divided by the size of the union -> Option D

4. Quick Check:

   Jaccard similarity = intersection / union [OK]

Hint: Remember: overlap divided by total unique items [OK]

Common Mistakes:

• Confusing union with intersection
• Using subtraction instead of division
• Mixing up numerator and denominator

2. Which of the following Python code snippets correctly calculates the Jaccard similarity between two sets A and B?

easy

A. len(A | B) / len(A & B)

B. len(A & B) / len(A | B)

C. len(A - B) / len(B - A)

D. len(A) + len(B)

Solution

1. Step 1: Identify set operations for intersection and union

   In Python, & is intersection and | is union for sets.

2. Step 2: Check the formula for Jaccard similarity

   Jaccard similarity = size of intersection / size of union, which matches len(A & B) / len(A | B).

3. Final Answer:

   len(A & B) / len(A | B) -> Option B

4. Quick Check:

   Intersection & union operators used correctly [OK]

Hint: Use & for intersection, | for union in Python sets [OK]

Common Mistakes:

• Swapping intersection and union operators
• Using subtraction instead of intersection
• Adding lengths instead of dividing

3. Given two sets A = {'apple', 'banana', 'cherry'} and B = {'banana', 'cherry', 'date', 'fig'}, what is the Jaccard similarity computed by this code?

len(A & B) / len(A | B)

medium

A. 0.4

B. 0.5

C. 0.6

D. 0.75

Solution

1. Step 1: Calculate intersection and union of sets A and B

   Intersection: {'banana', 'cherry'} has 2 elements.
   Union: {'apple', 'banana', 'cherry', 'date', 'fig'} has 5 elements.

2. Step 2: Compute Jaccard similarity

   Similarity = 2 / 5 = 0.4.

3. Final Answer:

   0.4 -> Option A

4. Quick Check:

   2 / 5 = 0.4 [OK]

Hint: Count common and total unique items, then divide [OK]

Common Mistakes:

• Counting union incorrectly
• Using addition instead of division
• Mixing up intersection and union counts

4. The following code is intended to compute the Jaccard similarity between two sets A and B. What is the error?

def jaccard(A, B):
    return len(A & B) / len(A & B | B)

medium

A. Function missing return statement

B. Division by zero error possible

C. Incorrect use of union and intersection operators in denominator

D. Sets A and B are not defined

Solution

1. Step 1: Analyze the denominator expression

   The denominator is len(A & B | B). The operator precedence causes A & B to be evaluated first, then union with B. This results in len(B), which is incorrect for union of A and B.

2. Step 2: Correct denominator for union

   The union should be len(A | B) only. The current expression is wrong and will not compute union correctly.

3. Final Answer:

   Incorrect use of union and intersection operators in denominator -> Option C

4. Quick Check:

   Union must be A | B, not combined with & [OK]

Hint: Use parentheses or correct operators for union [OK]

Common Mistakes:

• Confusing operator precedence
• Using intersection inside union calculation
• Not testing code before use

5. You want to compare two documents by their unique words using Jaccard similarity. Document 1 has 100 unique words, Document 2 has 80 unique words, and they share 30 unique words. What is the Jaccard similarity? Also, if you add 20 common words to both documents, how does the similarity change?

hard

A. Initial similarity 0.2; after adding common words similarity increases to 0.3

B. Initial similarity 0.15; after adding common words similarity decreases

C. Initial similarity 0.25; after adding common words similarity stays the same

D. Initial similarity 0.18; after adding common words similarity increases to 0.33

Solution

1. Step 1: Calculate initial Jaccard similarity

   Intersection = 30
   Union = 100 + 80 - 30 = 150
   Similarity = 30 / 150 = 0.2

2. Step 2: Calculate similarity after adding 20 common words

   New intersection = 30 + 20 = 50
   New union = (100 + 20) + (80 + 20) - 50 = 170
   Similarity = 50 / 170 ≈ 0.2941, approximately 0.3

3. Final Answer:

   Initial similarity 0.2; after adding common words similarity increases to 0.3 -> Option A

4. Quick Check:

   Adding common words increases intersection and similarity [OK]

Hint: Adding shared items increases similarity numerator and denominator [OK]

Common Mistakes:

• Forgetting to subtract intersection in union
• Not updating intersection after adding words
• Assuming similarity stays constant