Jaccard similarity in NLP - ML Experiment: Train & Evaluate

Experiment - Jaccard similarity

Problem:Calculate the similarity between two text documents using Jaccard similarity. The current method uses simple token sets but does not handle stopwords or case sensitivity, leading to lower similarity scores than expected.

Current Metrics:Jaccard similarity score between two example texts: 0.35

Issue:The similarity score is low because common words and case differences reduce the overlap of tokens.

Your Task

Improve the Jaccard similarity score by preprocessing the text to remove stopwords and normalize case, aiming to increase the similarity score by at least 0.15.

Do not change the basic Jaccard similarity formula.

Only modify text preprocessing steps.

Hint 1

Hint 2

Hint 3

Solution

NLP

from sklearn.feature_extraction.text import ENGLISH_STOP_WORDS

def jaccard_similarity(text1: str, text2: str) -> float:
    # Convert to lowercase
    text1 = text1.lower()
    text2 = text2.lower()

    # Tokenize by splitting on whitespace
    tokens1 = set(text1.split())
    tokens2 = set(text2.split())

    # Remove stopwords
    tokens1 = tokens1 - ENGLISH_STOP_WORDS
    tokens2 = tokens2 - ENGLISH_STOP_WORDS

    # Calculate intersection and union
    intersection = tokens1.intersection(tokens2)
    union = tokens1.union(tokens2)

    # Avoid division by zero
    if not union:
        return 0.0

    return len(intersection) / len(union)

# Example texts
text_a = "The quick brown fox jumps over the lazy dog"
text_b = "A quick brown dog outpaces a lazy fox"

score = jaccard_similarity(text_a, text_b)
print(f"Improved Jaccard similarity score: {score:.2f}")

Converted all text to lowercase to normalize case differences.

Removed common English stopwords from token sets to focus on meaningful words.

Kept the original Jaccard similarity formula unchanged.

Results Interpretation

Before preprocessing, the Jaccard similarity score was 0.35.

After converting text to lowercase and removing stopwords, the score improved to 0.71.

Preprocessing text by normalizing case and removing common stopwords helps the Jaccard similarity better capture meaningful overlap between documents.

Bonus Experiment

Try using n-grams (like pairs of words) instead of single words for the Jaccard similarity calculation.

💡 Hint

Create sets of word pairs (bigrams) from the texts before computing intersection and union.

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