K-Means Clustering

Updated 04 Oct 2026

•
What it is
- •
  partitions observations into $K$ groups by minimizing within-cluster squared euclidean distances
•
Formula
- •
  $J=\sum_{k=1}^{K}\sum_{x_i\in C_k}|x_i-\mu_k|_2^2$ .
- •
  a nonempty cluster’s centroid is its componentwise mean.
•
Procedure
- •
  choose $K$ and initial centroids.
- •
  assign each point to its nearest centroid.
- •
  recompute centroids and repeat until assignments or centroids stabilize, a tolerance is met, or an iteration limit is reached.
•
Limitations
- •
  sensitive to initialization, feature scale, outlires, and cluster geometry
- •
  convergence does not guarantee the globally best partition
•
Source correction
- •
  Using the eleven observations listed on slide 11 and the initial centroids on slide 13, the converged centroids are approximately:
- •
  $A=(4.7333,48.4)$ , $B=(1.5,342.15)$ , $C=(16.95,2.0833)$ .
- •
  These differ from slide 13’s reported $(6.23,48.4)$ , $(1.53,343.1)$ , and $(18.13,1.9)$ . The slide-14 plots also appear to contain a different set of points, so the table and visualization should not be treated as a verified computation from slide 11.
- •
  Slide 15 swaps the earlier A/B color labels; cluster naming should stay consistent.
•
Reference
- •
  https://scikit-learn.org/stable/modules/clustering.html#k-means

Linked references 2