K-Nearest Neighbours

Distance from a new sample to labelled samples:

Sample Distance
A 0.90
B 0.22
C 0.45
D 0.73
E 0.51
F 0.52
G 0.11
H 0.47

If k = 3, which neighbours are selected?

Question

K-Nearest Neighbours

Distance from a new sample to labelled samples:

Sample	Distance
A	0.90
B	0.22
C	0.45
D	0.73
E	0.51
F	0.52
G	0.11
H	0.47

If k = 3, which neighbours are selected?

BlackTom AI · Accepted Answer

K-nearest neighbours classification chooses the k labelled samples with the smallest distances to the new sample. Therefore we must rank the provided distances from smallest to largest and take the first k = 3 items.

Relevant knowledge points:
- KNN decision rule: pick the k points with minimum distance to the query.
- Distances are compared numerically; ties would require tie-breaking, but none occur here.

Step-by-step reasoning and calculation:
List each sample with its distance:
- A: 0.90
- B: 0.22
- C: 0.45
- D: 0.73
- E: 0.51
- F: 0.52
- G: 0.11
- H: 0.47

Sort distances in ascending order (showing intermediate ordering):
1. G = 0.11 (smallest)
2. B = 0.22
3. C = 0.45
4. H = 0.47
5. E = 0.51
6. F = 0.52
7. D = 0.73
8. A = 0.90

Select the first k = 3 samples from this sorted list:
- 1st: G (0.11)
- 2nd: B (0.22)
- 3rd: C (0.45)

Why the correct answer is correct:
These three samples have the three smallest numerical distances to the new sample, so they are the nearest neighbours required by KNN with k = 3.

Why the other options are incorrect:
- "A, D and F": their distances (0.90, 0.73, 0.52) are much larger; they are not the three smallest.
- "B, and G": only lists two neighbours; k = 3 requires three neighbours.
- "All except B, and G": would exclude the true nearest neighbours and include many farther points; this contradicts the KNN rule.

Conclusion: The selected neighbours are B, C and G, which matches the provided correct answer.

K-Nearest Neighbours Distance from a new sample to labelled samples: Sample Distance A 0.90 B 0.22 C 0.45 D 0.73 E 0.51 F 0.52 G 0.11 H 0.47 If k = 3, which neighbours are selected?单项选择题

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