从下列 2-D训练数据中哪个点可能会是支持向量？

（图：2 维空间，两个轴线都在 0-5 之间。数据点 a (0, 1)、b (1, 2)、c (1, 3)、d (2, 2)，（绿色三角形表示）属于一类，数据点 e (2, 4)、 f (3, 4)、g (4, 5)、h (4, 3)，（棕色六边形）属于另一类。）

Which of the following points from the below 2-D training data could be the support vectors by SVM?

(Image: 2-d space with both axes ranging from 0-5. Datapoints a (0, 1), b (1, 2), c (1, 3), d (2, 2), (represented by green triangles) belong to one class while datapoints e (2, 4), f (3, 4), g (4, 5), h (4, 3) (brown hexagons) belong to another class.)

Question

从下列 2-D训练数据中哪个点可能会是支持向量？

（图：2 维空间，两个轴线都在 0-5 之间。数据点 a (0, 1)、b (1, 2)、c (1, 3)、d (2, 2)，（绿色三角形表示）属于一类，数据点 e (2, 4)、 f (3, 4)、g (4, 5)、h (4, 3)，（棕色六边形）属于另一类。）

Which of the following points from the below 2-D training data could be the support vectors by SVM?

(Image: 2-d space with both axes ranging from 0-5. Datapoints a (0, 1), b (1, 2), c (1, 3), d (2, 2), (represented by green triangles) belong to one class while datapoints e (2, 4), f (3, 4), g (4, 5), h (4, 3) (brown hexagons) belong to another class.)

BlackTom AI · Accepted Answer

Support vectors are the training points that lie on (or closest to) the optimal separating hyperplane; equivalently they are the points from each class with the smallest perpendicular distance to that boundary.

1) Relevant concepts
- SVM chooses a linear separator that maximizes the margin, so support vectors are the points nearest the other class. 
- For a 2-class, linearly separable 2-D set, the closest inter-class pairs (smallest Euclidean distances) indicate which points will typically lie on the margin.

2) Step-by-step reasoning (use coordinates)
Green points: a(0,1), b(1,2), c(1,3), d(2,2).
Brown points: e(2,4), f(3,4), g(4,5), h(4,3).
Find nearest cross-class distances to see which points are closest to the opposite class.

3) Distance calculations (intermediate steps)
Distances from e(2,4) to greens:
- to a: sqrt((2-0)^2+(4-1)^2)=sqrt(4+9)=√13 ≈3.606
- to b: sqrt(1+4)=√5 ≈2.236
- to c: sqrt(1+1)=√2 ≈1.414
- to d: sqrt(0+4)=2
Nearest for e is c at 1.414.

Distances from f(3,4) to greens:
- nearest ≈2.236 (to c or d).

Distances from g(4,5) to greens:
- nearest ≈3.606.

Distances from h(4,3) to greens:
- nearest ≈2.236 (to d).

For greens: c’s nearest brown is e (1.414); d’s nearest brown is e (2.0); b and a are farther from browns.

4) Why c, d, e are the support vectors
- The smallest inter-class distance is between c and e (≈1.414), so the optimal margin will lie roughly midway between c and e and thus both are almost certainly support vectors.
- d is the next green point close to the brown cluster (distance 2 to e) and lies near the decision boundary region; depending on exact optimal orientation, d commonly ends up on the margin as an additional support vector from the green class.
- f, g, h are farther from the green cluster (distances ≥2.236), so they are less likely to constrain the margin and thus are not support vectors here. a and b are well inside the green region, so they are not support vectors.

5) Why other multiple-choice options are incorrect
- "c, e" omits d, which is plausibly on the margin and therefore incomplete.
- Options including f or h (c, d, e, f or c, e, d, h) add points that are farther from the opposing class and thus unlikely to be support vectors for the maximal margin.

6) Conclusion
Based on nearest cross-class distances and the definition of support vectors, the points c, d, and e are the ones that could (and most likely would) be the support vectors. This matches the provided correct answer: c, d, e.

类似问题

A marketing analytics team is using an RBF kernel SVM to classify consumers based on a complex dataset. The model in Panel B (Right) uses the following parameters: C = 1 Gamma = 5 Which of the following parameter sets is most likely used in Panel A (Left)?

Question at position 4 To construct a support vector machine, only the observations closest to the separating hyperplane are used. This avoids the curse of dimensionality.TrueFalse

Question at position 2 What are support vectors?The only data points that determine the location of the maximum-margin hyperplaneThe data points that are easiest to classifyThe data points that are farthest from the maximum-margin hyperplane

In a Support Vector Machine (SVM), what are ‘support vectors’?

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？

给定下列数字哪一个判定边界更好，为什么？ Given the following figure Which decision boundary is better and why?

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