最大间隔分类器发现了以下规范超平面。支持向量的个数是多少个？

A maximal margin classifier found the following canonical hyperplanes. How many support vector are there？

Question

最大间隔分类器发现了以下规范超平面。支持向量的个数是多少个？

A maximal margin classifier found the following canonical hyperplanes. How many support vector are there？

BlackTom AI · Accepted Answer

Support vectors are exactly the training points that lie on the two margin lines (the canonical hyperplanes w·x + b = +1 or w·x + b = −1). These are the points that touch the yellow parallel lines in the figure; interior points or points strictly beyond the margins are not support vectors.

1) Relevant concepts
- In a maximal margin (canonical) SVM the margin is determined by two parallel hyperplanes w·x + b = +1 and w·x + b = −1.
- Support vectors are the data points for which equality holds (they lie exactly on one of those two hyperplanes).
- All other points (strictly inside a margin region or further away) are not support vectors.

2) Step–by–step visual reasoning
- Inspect the plot and locate which red (negative class) and blue (positive class) markers lie exactly on a yellow margin line.
- On the lower/left yellow line there are three red circles that lie exactly on the line (they touch the line rather than being strictly inside the negative region).
- On the upper/right yellow line there are three blue squares that lie exactly on that line.
- Every other red or blue marker is either strictly inside its class region (away from the yellow line) or further from the margin, so those are not support vectors.

3) Intermediate steps / counting
- Count red markers on margins: 3
- Count blue markers on margins: 3
- Total support vectors = 3 + 3 = 6

4) Why this is correct
- By definition, only points on the hyperplanes w·x + b = ±1 are support vectors in the canonical SVM formulation. The diagram clearly shows three points touching the upper margin and three touching the lower margin; therefore exactly six points satisfy the equality condition and determine the margin.

5) Why the other choices are wrong
- 5 or 4 undercount: they would imply some margin-touching points were ignored, but the picture shows three on each margin.
- 7 overcounts: there is no seventh point lying exactly on either yellow line—adding any interior point would violate the definition of a support vector.

Conclusion: counting the three red and three blue margin-touching points gives 6 support vectors, so the correct answer is 6.

最大间隔分类器发现了以下规范超平面。支持向量的个数是多少个？ A maximal margin classifier found the following canonical hyperplanes. How many support vector are there？单项选择题

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最大间隔分类器发现了以下规范超平面。支持向量的个数是多少个？ A maximal margin classifier found the following canonical hyperplanes. How many support vector are there？ 单项选择题