Jaccard similarity in NLP - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to calculate the Jaccard similarity between two sets.

NLP

def jaccard_similarity(set1, set2):
    intersection = set1.intersection(set2)
    union = set1.[1](set2)
    return len(intersection) / len(union)

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

Aunion

Bdifference

Csymmetric_difference

Dadd

Attempts:

3 left

💡 Hint

Common Mistakes

Using difference instead of union causes incorrect denominator.

Using symmetric_difference excludes common elements, which is wrong.

The Jaccard similarity is the size of the intersection divided by the size of the union of two sets. Here, union method returns the union of two sets.

2fill in blank

medium

Complete the code to convert two sentences into sets of words for Jaccard similarity calculation.

NLP

def sentence_to_set(sentence):
    words = sentence.lower().split()
    return set([1])

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

Awords

Bsentence

Csentence.split()

Dsentence.lower()

Attempts:

3 left

💡 Hint

Common Mistakes

Passing the whole sentence string instead of the list of words to set().

Not converting to lowercase before splitting causes case mismatches.

We first split the sentence into words and then convert the list words into a set to remove duplicates.

3fill in blank

hard

Fix the error in the Jaccard similarity function to avoid division by zero.

NLP

def jaccard_similarity(set1, set2):
    intersection = set1.intersection(set2)
    union = set1.union(set2)
    if len(union) == 0:
        return [1]
    return len(intersection) / len(union)

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

Alen(intersection)

BNone

C1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Returning None causes errors when using the result.

Returning 1 incorrectly suggests full similarity for empty sets.

If both sets are empty, their union length is zero. Returning 0 avoids division by zero and logically means no similarity.

4fill in blank

hard

Fill both blanks to create a function that computes Jaccard similarity from two sentences.

NLP

def jaccard_from_sentences(s1, s2):
    set1 = set(s1.lower().[1]())
    set2 = set(s2.lower().[2]())
    intersection = set1.intersection(set2)
    union = set1.union(set2)
    if len(union) == 0:
        return 0
    return len(intersection) / len(union)

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

Asplit

Bstrip

Creplace

Djoin

Attempts:

3 left

💡 Hint

Common Mistakes

Using strip() removes whitespace but does not split words.

Using replace() or join() does not create word lists.

We use split() to break sentences into words before converting to sets.

5fill in blank

hard

Fill all three blanks to create a dictionary of Jaccard similarities for a list of sentence pairs.

NLP

def batch_jaccard(pairs):
    results = {}
    for i, (s1, s2) in enumerate(pairs):
        set1 = set(s1.lower().[1]())
        set2 = set(s2.lower().[2]())
        intersection = set1.[3](set2)
        union = set1.union(set2)
        if len(union) == 0:
            results[i] = 0
        else:
            results[i] = len(intersection) / len(union)
    return results

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

Asplit

Bstrip

Cintersection

Dreplace

Attempts:

3 left

💡 Hint

Common Mistakes

Using strip() instead of split() results in wrong sets.

Using replace() or other methods that do not create word lists.

Using union instead of intersection for common elements.

We split sentences into words, then use intersection to find common words for Jaccard similarity.

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