▶K-means loss
The objective sums squared distances from every point to its assigned centroid.
Determining the Number of Clusters
Using loss reduction without over-partitioning
Increasing k always lowers k-means loss, so the smallest loss alone cannot choose the model. The elbow method looks for the point where extra clusters yield diminishing returns.
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The essential idea: choose k near the bend in the loss curve, not at its absolute minimum.
One Concept · One Example
What to notice
- Within-cluster loss decreases as k grows.
- The elbow marks diminishing improvement.
- The visual choice remains empirical and subjective.
Trade fit against complexity
Elbow criterion
Look for a sharp change in the rate at which loss decreases.
Where is the elbow?
Move across candidate values of k and compare the selected partition with its loss curve.
The elbow method chooses a parsimonious number of clusters where additional complexity buys little improvement.