NLP - Text Similarity and Search
Given two sentence embeddings `emb1 = [0.5, 0.5]` and `emb2 = [0.5, -0.5]`, what is their cosine similarity?
Given two sentence embeddings `emb1 = [0.5, 0.5]` and `emb2 = [0.5, -0.5]`, what is their cosine similarity?
medium📝 Predict Output Q5 of 15
Step-by-Step Solution
Solution:
Step 1: Calculate dot product of emb1 and emb2
Dot product = 0.5*0.5 + 0.5*(-0.5) = 0.25 - 0.25 = 0Step 2: Calculate magnitudes and cosine similarity
Magnitudes are both sqrt(0.5^2 + 0.5^2) = sqrt(0.5) ≈ 0.707; cosine similarity = 0 / (0.707*0.707) = 0Final Answer:
0.0 -> Option DQuick Check:
Dot product zero means cosine similarity zero [OK]
Quick Trick: Zero dot product means zero cosine similarity [OK]
Common Mistakes:
MISTAKES- Ignoring negative component in dot product
- Confusing cosine similarity with Euclidean distance
- Assuming similarity is always positive
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