Which of the following is true of the value of k in the k-Nearest Neighbors algorithm?

Question

BlackTom AI · Accepted Answer

In k-NN, k controls the bias–variance tradeoff: small k leads to low bias and high variance, while very large k produces high bias and low variance.

1) Relevant concepts
- k-nearest neighbors classifies a query by majority vote among the k closest training points.
- Bias is systematic error (model too simple), variance is sensitivity to training data (model too flexible).
- Edge cases: k = 1 uses only the single nearest neighbor; k = N (size of training set) uses every training point.

2) Step-by-step reasoning
- With k = 1, classification follows the single nearest training point. This can change dramatically if that neighbor changes (high variance) but can capture fine local structure (low bias).
- As k increases, the decision for a query averages over more neighbors. Local fluctuations are smoothed out, so predictions change less when you perturb the training set (variance decreases).
- When k becomes very large (approaching the training set size), the classifier effectively predicts the global majority class for almost every query—local structure is ignored, producing systematic error (high bias).

3) Intermediate illustration
- Suppose 100 training points, 60 of class A and 40 of class B. If k = 100, every query is classified as A (majority), regardless of query location. That is an extreme bias: the classifier cannot distinguish local regions where B should be predicted.
- If k = 3, a query near a small B-cluster may have two B neighbors and be correctly classified; with k = 99 it would be misclassified as A.

4) Why the correct answer is correct
- “If the value k is very large, it introduces biases into the classification decisions.” This matches the theoretical and practical behavior: very large k averages out local distinctions and forces predictions toward global class proportions, creating bias.

5) Why the other options are incorrect
- “k is always 1” is false; k is chosen (cross-validation) and can be >1.
- “If k is large, it drastically increases variability” is reversed: large k decreases variance.
- “If k is large, classification is very sensitive to the single closest record” describes k = 1, not large k.

6) Conclusion
Therefore the correct choice is: “If the value k is very large, it introduces biases into the classification decisions.” This matches the provided answer.

Which of the following is true of the value of k in the k-Nearest Neighbors algorithm?单项选择题

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