给定两个聚类中的四个节点与它们与整体质心的距离。

You are given the four nodes in two clusters and their distances to the overall centroid.

1. 整个数据集的内聚性是多少？ What is the cohesiveness of entire dataset?

[選擇]
0
6
12
26
117

2. 整个数据集的离散性是多少？ What is is the separateness of the entire dataset?

[選擇]
0
4
26
64
117
81

Question

给定两个聚类中的四个节点与它们与整体质心的距离。

You are given the four nodes in two clusters and their distances to the overall centroid.

1. 整个数据集的内聚性是多少？ What is the cohesiveness of entire dataset?

[選擇]
0
6
12
26
117

2. 整个数据集的离散性是多少？ What is is the separateness of the entire dataset?

[選擇]
0
4
26
64
117
81

BlackTom AI · Accepted Answer

Cohesiveness is the within-cluster sum of squared distances (WSS). Compute cluster centroids first:
- Cluster 1 points: -12 and -6 → centroid = (-12 + (-6))/2 = -9.
- Cluster 2 points: 4 and 8 → centroid = (4 + 8)/2 = 6.

Now compute squared distances of each point to its cluster centroid:
- Cluster 1: |-12 − (−9)| = 3 → 3^2 = 9; |-6 − (−9)| = 3 → 3^2 = 9. Sum for cluster 1 = 9 + 9 = 18.
- Cluster 2: |4 − 6| = 2 → 2^2 = 4; |8 − 6| = 2 → 2^2 = 4. Sum for cluster 2 = 4 + 4 = 8.

WSS (cohesiveness of entire dataset) = 18 + 8 = 26. This matches option 26.

Separateness here is defined as the sum of squared distances of the cluster centroids to the overall centroid (unweighted by cluster size). The overall centroid is given at -3. Compute distances:
- Centroid of cluster 1: −9 → distance to overall centroid = |−9 − (−3)| = 6 → 6^2 = 36.
- Centroid of cluster 2: 6 → distance to overall centroid = |6 − (−3)| = 9 → 9^2 = 81.

Separateness = 36 + 81 = 117. This matches option 117.

Why other options are incorrect (briefly):
- For cohesiveness: 117 is the separateness (centroid-to-overall sum) not within-cluster SSE; 12, 6, 0 would come from incorrect or partial calculations (e.g., summing absolute distances or halving sums).
- For separateness: 26 is the WSS (cohesiveness), 81 is just 9^2 (only one centroid contribution), 64 or 4 or 0 do not reflect the correct squared distances of both centroids to the overall centroid.

Final confirmation: Cohesiveness = 26; Separateness = 117.

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