Jaccard similarity in NLP - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is Jaccard similarity?

Jaccard similarity is a way to measure how similar two sets are. It is the size of the overlap divided by the size of the union of the sets.

beginner

How do you calculate Jaccard similarity between two sets A and B?

Jaccard similarity = (Number of elements in both A and B) / (Number of elements in A or B). In formula: |A ∩ B| / |A ∪ B|.

beginner

Why is Jaccard similarity useful in NLP?

It helps compare texts by looking at shared words or features, showing how much two texts overlap in content.

beginner

What is the Jaccard similarity between the sets {apple, banana} and {banana, cherry}?

The intersection is {banana} (1 element), the union is {apple, banana, cherry} (3 elements). So similarity = 1/3 ≈ 0.33.

beginner

Can Jaccard similarity be used for comparing sentences? How?

Yes. Convert sentences into sets of words, then calculate Jaccard similarity to see how many words they share compared to total unique words.

What does Jaccard similarity measure?

A Overlap between two sets divided by their union

B Difference between two sets

C Sum of elements in two sets

D Number of elements in the first set

Jaccard similarity measures how much two sets overlap compared to their combined size.

If two sets have no elements in common, what is their Jaccard similarity?

A 0

B 0.5

C 1

D Undefined

No overlap means intersection size is zero, so similarity is 0.

Which of these is the correct formula for Jaccard similarity?

A |A| - |B|

B |A ∪ B| / |A ∩ B|

C |A| + |B|

D |A ∩ B| / |A ∪ B|

Jaccard similarity is intersection size divided by union size.

In NLP, what do we usually compare using Jaccard similarity?

A Number of sentences

B Sets of words from texts

C Length of paragraphs

D Number of characters

We compare sets of words to see how much two texts share.

If set A = {1, 2, 3} and set B = {2, 3, 4, 5}, what is their Jaccard similarity?

A 0.6

B 0.5

C 0.4

D 0.75

Intersection is {2,3} (2 elements), union is {1,2,3,4,5} (5 elements), so 2/5 = 0.4.

Explain in your own words what Jaccard similarity is and how it can be used to compare two texts.

Think about how much two groups share compared to all items they have.

Describe how to calculate Jaccard similarity step-by-step for two example sets.

Use a simple example with fruits or numbers.

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