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FRM Part I · FRM Exam Part I · Machine-Learning Methods

In k-means clustering, an analyst increases k from 3 to 4 on the same dataset and re-runs the algorithm to convergence. Which outcome is most accurate regarding the within-cluster sum of squares (inertia)?

Inertia typically falls or stays the same as k rises, since extra centroids allow tighter clusters. It reaches zero only when k equals the number of observations. Therefore inertia alone cannot choose k, and tools such as the elbow method or silhouette scores are used.

  1. AIt cannot decrease, because adding a cluster forces extra distance
  2. BIt will always be zero when k equals 4
  3. CIt typically falls or stays the same, so inertia alone cannot pick the best kCorrect
  4. DIt must rise because the centroids are further apart

Explanation

Adding a centroid generally allows a tighter fit, so the optimal inertia is non-increasing in k, although local optima may blur this slightly. Because inertia keeps falling, the elbow method or silhouette scores are needed to choose k. Zero inertia occurs only when k equals the number of observations.

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