Cosine similarity in NLP - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding the range of cosine similarity values

What is the range of values that cosine similarity between two vectors can take?

A From -1 to 0, where -1 means identical vectors and 0 means orthogonal vectors

B From -1 to 1, where 1 means identical direction and -1 means opposite direction

C From 0 to 1, where 0 means orthogonal vectors and 1 means identical vectors

D From 0 to infinity, where higher values mean more similarity

💡 Hint

Think about the angle between two vectors and how cosine behaves.

Cosine similarity measures the cosine of the angle between two vectors. It ranges from -1 (vectors point in opposite directions) to 1 (vectors point in the same direction). Zero means vectors are orthogonal (at 90 degrees).

❓ Predict Output

intermediate

Output of cosine similarity calculation

What is the output of this Python code calculating cosine similarity between two vectors?

NLP

import numpy as np

def cosine_similarity(a, b):
    return np.dot(a, b) / (np.linalg.norm(a) * np.linalg.norm(b))

vec1 = np.array([1, 0, 0])
vec2 = np.array([0, 1, 0])
result = cosine_similarity(vec1, vec2)
print(round(result, 2))

A 0.71

B 1.00

C -1.00

D 0.00

💡 Hint

Consider the angle between the two vectors.

The vectors are orthogonal (at 90 degrees), so their cosine similarity is 0. The dot product is zero, and norms are 1, so the result is 0.

❓ Model Choice

advanced

Choosing cosine similarity for text similarity

You want to measure similarity between two text documents represented as TF-IDF vectors. Which similarity measure is most appropriate?

A Cosine similarity

B Euclidean distance

C Manhattan distance

D Jaccard index

💡 Hint

Think about how vector length affects similarity in text data.

Cosine similarity is preferred for text vectors because it measures the angle between vectors, ignoring their length, which is useful when document lengths vary.

❓ Metrics

advanced

Interpreting cosine similarity value in recommendation

A recommendation system uses cosine similarity between user preference vectors. If two users have a cosine similarity of 0.95, what does this imply?

A They have no preferences in common

B They have very different preferences

C They have very similar preferences

D They have opposite preferences

💡 Hint

Recall what a high cosine similarity value means.

A cosine similarity close to 1 means the vectors point in nearly the same direction, indicating very similar preferences.

🔧 Debug

expert

Debugging cosine similarity code with zero vector

What error will this code raise when computing cosine similarity if one input vector is all zeros?

NLP

import numpy as np

def cosine_similarity(a, b):
    return np.dot(a, b) / (np.linalg.norm(a) * np.linalg.norm(b))

vec1 = np.array([0, 0, 0])
vec2 = np.array([1, 2, 3])
result = cosine_similarity(vec1, vec2)
print(result)

A ZeroDivisionError

B ValueError

C TypeError

D No error, outputs 0

💡 Hint

Think about what happens when dividing by zero norm.

The norm of vec1 is zero, so the denominator is zero, causing a ZeroDivisionError.