Cheatsheet: Grouping without labels: k-means clustering

The setup

Term	Meaning
Clustering	unsupervised: find natural groups in unlabeled data
k	the number of clusters (you choose it)
Centroid	a cluster’s center: the mean position of its points

The loop

Step	Action
0	choose k, place k centroids (often random)
1. Assign	each point joins its nearest centroid’s cluster
2. Update	move each centroid to the mean of its assigned points
Repeat	steps 1-2 until assignments stop changing

Worked trace (points 1,2,3,10,11,12; k=2; init centroids 2,3)

Iter	Assign	New centroids
1	A={1,2}, B={3,10,11,12}	1.5, 9
2	A={1,2,3}, B={10,11,12}	2, 11
3	no change	converged

Choosing k and the big caution

Idea	Note
Elbow method	run several k, plot cluster tightness, pick the bend
Always returns k clusters	even on noise; finding k groups is NOT proof they are real
Your job	judge whether the clusters are meaningful

Limitations

Limitation	Note
Must choose k	strongly shapes the result
Init-sensitive	run several times; k-means++ seeds smartly
Assumes round clusters	struggles with elongated or unequal groups
Distance-based	scale features first