为何多次运行K-Means聚类会得到完全相同的结果？技术咨询

Hey there! Great question—let's unpack why your K-Means runs are all giving the same output, even though you'd expect random initialization to create differences.

The main reason: Your dataset has highly distinct, well-separated clusters #

K-Means works by minimizing the inertia (sum of squared distances from each point to its cluster center). When your data has clusters that are clearly separated (like the don dataset you're using), there's only one global optimal clustering solution. No matter how the initial centroids are randomly chosen, the algorithm will converge to this same best possible partition every single time.

Think of it like this: if you have four tight, far-apart groups of points, any random starting centroids will quickly "gravitate" to the center of each distinct group. There's no ambiguity here—there's only one logical way to split the data into 4 clusters.

A quick check to confirm this #

To verify this is the case, try two things:

• Add noise to your dataset: Introduce some random noise to the V1 and V2 columns, then re-run your code. You'll likely start seeing different clustering results across runs, since the cluster boundaries are now blurred.
• Force different initializations: Explicitly set different random_state values for KMeans, like:

  kmeans = KMeans(n_clusters=4, random_state=42)
  

  and

  kmeans = KMeans(n_clusters=4, random_state=123)
  

  If the results are still identical, that's definitive proof your dataset's cluster structure is so strong that even different initializations lead to the same final solution.

A note on sklearn's K-Means defaults #

You mentioned you know K-Means uses random initialization—sklearn's KMeans defaults to init='k-means++', which is a smarter random initialization method that picks initial centroids to be far apart. But even with this, if your data's clusters are distinct enough, the end result won't change between runs.

内容的提问来源于stack exchange，提问作者Akira