Question at position 28 Which of the following numeric distance metrics is used most commonly for text mining?JaccardEuclideanManhattanCosine单项选择题
A
Jaccard
B
Euclidean
C
Manhattan
D
Cosine

Question

Question at position 28 Which of the following numeric distance metrics is used most commonly for text mining?JaccardEuclideanManhattanCosine

BlackTom AI · Accepted Answer

Cosine similarity measures the angle between document vectors, making it scale-invariant and ideal for comparing text represented as high-dimensional term vectors.

1. Relevant knowledge points and concepts
- Text is commonly represented as vectors (bag-of-words, TF, TF-IDF), producing high-dimensional, sparse representations.
- Cosine similarity = (A · B) / (||A|| ||B||) measures orientation (angle) between vectors, not magnitude.
- Euclidean distance = sqrt(sum (Ai - Bi)^2) measures absolute distance and is sensitive to document length.
- Manhattan distance = sum |Ai - Bi| also sensitive to magnitude/length.
- Jaccard index = |intersection| / |union| applies to sets (or binary vectors), useful for overlap of unique terms or shingles.

2. Step-by-step reasoning
- Represent two documents A and B as TF-IDF vectors. The key question: should similarity depend on total word counts (length) or on distribution of terms?
- Cosine normalizes by vector length via ||A|| and ||B||, so two documents with the same term proportions but different lengths have cosine = 1.
- Euclidean/Manhattan measure absolute differences; longer documents with proportionally similar term distributions produce larger distances, reducing their usefulness without additional normalization.
- Jaccard treats presence/absence; it ignores term frequency and is less informative when term frequency (TF or TF-IDF) matters.

3. Formula and example intermediate steps
- Cosine(A,B) = (Σ AiBi) / (sqrt(Σ Ai^2) sqrt(Σ Bi^2)).
- Example: A=(1,2,0), B=(2,1,0) → dot=1*2+2*1=4; ||A||=√5; ||B||=√5; cosine=4/5=0.8.

4. Why the correct answer is correct
- Text mining commonly uses TF-IDF vectors where relative term distributions matter more than raw length. Cosine similarity directly captures this by comparing orientation, making it the standard metric in document similarity, clustering, and information retrieval.

5. Why other options are incorrect
- Jaccard: good for binary/set overlap or shingles, but ignores term frequency and is less common for TF-IDF based tasks.
- Euclidean: sensitive to document length and scale; not ideal unless vectors are normalized.
- Manhattan: similar sensitivity to magnitude; less used than cosine for text.

6. Conclusion
Cosine is the most commonly used distance/similarity measure in text mining; this matches the provided answer "Cosine."

Question at position 28 Which of the following numeric distance metrics is used most commonly for text mining?JaccardEuclideanManhattanCosine单项选择题

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