最近邻分类器 k-NN 是基于什么来指定标签？

Nearest Neighbor Classifier k-NN assigns a label to a node based on

Question

最近邻分类器 k-NN 是基于什么来指定标签？

Nearest Neighbor Classifier k-NN assigns a label to a node based on

BlackTom AI · Accepted Answer

k-NN assigns a label by the majority label among the k closest training points.

1. Relevant knowledge points and concepts
- k-Nearest Neighbors (k-NN) is a nonparametric instance-based classifier. It uses a distance metric (e.g., Euclidean, Manhattan) on feature vectors to find the k nearest training samples to a query point. Classification is typically by majority vote of those neighbors’ labels. Variants include distance-weighted votes or using k to control bias–variance tradeoff.

2. Step-by-step reasoning process
- Given a query instance x, compute distances d(x, x_i) to all training instances x_i.
- Sort training instances by increasing distance and select the k nearest.
- Collect the labels y_j of these k neighbors.
- Count how many neighbors belong to each class and choose the class with the highest count (majority vote).
- If there is a tie, apply a tie-breaking rule (e.g., choose the class of the nearest neighbor or use distance-weighted votes).

3. Intermediate steps / small example
- Suppose k = 3 and the 3 nearest neighbors have labels {A, A, B}.
- Count: A → 2, B → 1.
- Majority label = A, so assign label A to the query.
- Formally: predicted label = argmax_c sum_{j=1}^k I(y_j = c), where I is the indicator function.

4. Why the correct answer is correct
- The canonical definition of k-NN classification is majority voting among the k nearest neighbors’ labels. That directly matches “majority label of its k neighbors.”

5. Why the other options are incorrect
- “Conditional probability of each possible label values”: k-NN implicitly estimates class proportions among neighbors but does not directly compute model-based conditional probabilities; standard k-NN uses majority vote rather than explicit conditional probability models.
- “Frequency of each attribute value”: k-NN uses distances on feature vectors, not frequencies of attribute values as the decision rule.
- “Eigenvector of each node”: eigenvectors are unrelated to the k-NN labeling rule.

6. Conclusion
- Therefore the correct answer is: its k neighbors’ labels’ majority value, matching the provided answer.

最近邻分类器 k-NN 是基于什么来指定标签？ Nearest Neighbor Classifier k-NN assigns a label to a node based on单项选择题

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