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.

Similar Questions

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?

Suppose you have trained an SVM classifier with a RBF kernel, and You suspect that the SVM is underfitting your dataset. What should you do to C?

The effectiveness of an SVM depends upon:

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler