给定一下列表：You are given the following table:

如果应用 kNN 算法， k=1，对数据项 8 的决策是什么？If apply kNN algorithm, what is the decision for data item 8?

Question

给定一下列表：You are given the following table:

如果应用 kNN 算法， k=1，对数据项 8 的决策是什么？If apply kNN algorithm, what is the decision for data item 8?

BlackTom AI · Accepted Answer

kNN with k = 1 assigns the label of the single nearest neighbor (the instance with the smallest distance to the query). For categorical features, distance can be measured by simple mismatch count (Hamming distance): count how many attributes differ.

1) Relevant knowledge points and concepts
- k-Nearest Neighbors: predict the class of a query instance by the majority class among its k nearest neighbors.
- For k = 1, the predicted class is the class of the single nearest neighbor.
- For categorical attributes, use Hamming distance (number of differing attributes) to find nearest neighbor.

2) Complete reasoning process step by step
- Represent data item 8 as (Weather = Rain, Temperature = Warm, Humidity = High).
- Compare item 8 to each existing instance (rows 1–7) and count attribute mismatches (Weather, Temperature, Humidity).

3) Calculations with intermediate steps
- Row 1: (Sunny, Hot, High)
  - Weather: Rain vs Sunny → mismatch (1)
  - Temperature: Warm vs Hot → mismatch (1)
  - Humidity: High vs High → match (0)
  - Total distance = 1 + 1 + 0 = 2
- Row 2: (Sunny, Warm, High)
  - Weather: mismatch (1)
  - Temperature: Warm vs Warm → match (0)
  - Humidity: High vs High → match (0)
  - Total distance = 1 + 0 + 0 = 1
- Row 3: (Overcast, Hot, High)
  - Mismatches: Weather (1), Temp (1), Humidity (0) → distance = 2
- Row 4: (Rain, Warm, High)
  - Weather: Rain vs Rain → match (0)
  - Temperature: Warm vs Warm → match (0)
  - Humidity: High vs High → match (0)
  - Total distance = 0 (exact match)
- Row 5: (Sunny, Cold, Normal) → distance = 3
- Row 6: (Rain, Cold, Normal) → distance = 2
- Row 7: (Overcast, Cold, Normal) → distance = 3

4) Why the correct answer is correct
- The nearest neighbor (minimum distance) is row 4 with distance 0, and its class is "Yes". With k = 1, we therefore predict "Yes" for item 8.

5) Why the other options are incorrect
- "No." is incorrect because the closest instance is labeled "Yes", not "No".
- "The data is insufficient for making a decision." is incorrect because k = 1 yields a clear single nearest neighbor (row 4), so a decision is available.

6) Conclusion
- The kNN (k = 1) prediction for data item 8 is "Yes", which matches the provided correct answer.

给定一下列表：You are given the following table: 如果应用 kNN 算法， k=1，对数据项 8 的决策是什么？If apply kNN algorithm, what is the decision for data item 8? Single choice

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