When comparing texts, a higher cosine similarity means:

Question

BlackTom AI · Accepted Answer

Cosine similarity measures the cosine of the angle between two vector representations of text, so a larger cosine means the angle is smaller and the vectors (texts) point more in the same direction.

1) Relevant concepts:
- Texts are commonly represented as vectors (e.g., TF, TF-IDF, or embedding vectors).
- Cosine similarity formula: cos(theta) = (A · B) / (||A|| ||B||), where A · B is the dot product and ||A|| is the vector norm.
- Values range from -1 to 1 for signed vectors, and typically 0 to 1 for nonnegative text vectors; larger values indicate greater similarity (smaller angle).

2) Step-by-step reasoning with examples:
- Represent two texts as vectors A and B.
- Compute dot product A · B = sum_i A_i * B_i.
- Compute norms: ||A|| = sqrt(sum_i A_i^2), ||B|| = sqrt(sum_i B_i^2).
- Compute cos(theta) = (A · B) / (||A|| ||B||).

Example 1 (identical texts): A = (1,1,0), B = (1,1,0).
- A · B = 1*1 + 1*1 + 0*0 = 2.
- ||A|| = sqrt(1+1+0) = sqrt(2); ||B|| = sqrt(2).
- cos = 2 / (sqrt(2)*sqrt(2)) = 2/2 = 1 → maximum similarity.

Example 2 (less similar): A = (1,1,0), C = (1,0,1).
- A · C = 1*1 + 1*0 + 0*1 = 1.
- ||C|| = sqrt(1+0+1) = sqrt(2).
- cos = 1 / (sqrt(2)*sqrt(2)) = 1/2 = 0.5 → lower similarity than 1.

3) Why the correct answer is correct:
A higher cosine similarity corresponds to a larger cos(theta), meaning the vectors are more aligned and therefore the texts are more similar in content or distribution of features.

4) Why other options are incorrect:
- A. More different texts: opposite of the truth—higher cosine means less difference.
- C. More words: cosine similarity is insensitive to absolute length once normalized; it measures orientation, not raw word count.
- D. Less variance: variance is a statistical property of a dataset, not what cosine similarity directly measures.

Conclusion: Therefore the correct choice is B. More similar texts, which matches the provided answer.

When comparing texts, a higher cosine similarity means:单项选择题

类似问题

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

The most common similarity measure in contrastive learning is ___________ similarity.

Is the following statement true or false? In the products of methylation-hydrolysis, every -OH group corresponds to the position of a glycosidic bond in the starting polysaccharide.

Which of the follwoing structures represents amylopectin?

Which of the following is true about an aldopentose?I. It is a monosaccharide.II. It contains a CHO groupIII. It is a disaccharide.IV. It is an oligosaccharide.

For stock A, we have 𝛽 𝑖 = 0.70. Suppose the expected market risk premium next year is 9% and the risk-free rate is 3%. What is the expected return of this stock based on the CAPM? (Please answer in % and round to 2 decimal places. If the answer is 8.057%, then in the box, write 8.06)

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单