In a k-Nearest Neighbors algorithm, similarity of records is based on the .

Question

In a k-Nearest Neighbors algorithm, similarity of records is based on the                .

BlackTom AI · Accepted Answer

k-Nearest Neighbors measures similarity by computing how close records are in the predictor (feature) space using a distance metric.

1) Relevant knowledge points and concepts
- k-NN is a nonparametric, instance-based learning algorithm that classifies or predicts a record based on the labels of its nearest neighbors in feature space.
- Similarity is quantified by distance metrics (Euclidean, Manhattan, Minkowski, cosine similarity for normalized data).
- Features should often be scaled (standardized or normalized) because distance depends on units and ranges.

2) Step-by-step reasoning with a numeric example
- Represent each record as a vector of numerical predictors. Example: Record A = (2, 3); Record B = (5, 7); Record C = (4, 2).
- Compute Euclidean distance between A and B:
  * difference in first feature = 5 − 2 = 3
  * difference in second feature = 7 − 3 = 4
  * squared differences = 3^2 = 9 and 4^2 = 16
  * sum of squared differences = 9 + 16 = 25
  * Euclidean distance = sqrt(25) = 5
- Compute Euclidean distance between A and C:
  * differences: 4 − 2 = 2 and 2 − 3 = −1
  * squared differences = 4 and 1; sum = 5
  * Euclidean distance = sqrt(5) ≈ 2.236
- Because A is closer to C (2.236 < 5), C would be considered a nearer neighbor and more influential in k-NN classification/prediction.

3) Why the correct answer is correct
- The provided correct option, "closeness of a record to numerical predictors in the other records," concisely describes that k-NN uses closeness in the numerical predictor space to determine similarity. That is exactly how neighbors are chosen.

4) Why the other options are incorrect
- "Nearness of a record to its own observations" is meaningless: a record compared to itself yields zero distance and does not describe similarity to other records.
- "Set of linear functions of predictors called discriminant functions" describes discriminant analysis (LDA/QDA), not k-NN.
- "Sum of the squares of the distance between the numerical predictors" misstates the general idea; while Euclidean distance involves squared differences, k-NN uses a distance (or similarity) measure rather than an aggregate “sum of squares” phrased that way, and k-NN is not defined by a single sum-of-squares criterion.

Conclusion: The correct interpretation is that k-NN bases similarity on the closeness of a record to the numerical predictors of other records, confirming the provided answer.

In a k-Nearest Neighbors algorithm, similarity of records is based on the .单项选择题

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