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FRM Part I · FRM Exam Part I · Machine Learning and Prediction

A K-means model is fitted to stocks for K = 1 to 5, producing total within-cluster sum of squares of 500, 220, 100, 90 and 85 respectively. Which conclusion is best supported by the elbow method?

The elbow method supports K = 3. Within-cluster sum of squares drops by 120 from K = 2 to K = 3, but only by 10 and 5 afterwards, so the curve flattens at three clusters. Choosing the lowest value (K = 5) would overfit, since it always falls as K rises.

  1. AK = 5, because it gives the lowest within-cluster sum of squares
  2. BK = 3, because the reduction from K = 2 to K = 3 is large (120) while further gains are small (10 or less)Correct
  3. CK = 2, because it gives the largest single drop from the previous value
  4. DK = 1, because within-cluster sum of squares is always minimized by a single cluster

Explanation

Within-cluster sum of squares always falls as K rises, so the minimum alone is uninformative. Drops are 280 (1 to 2), 120 (2 to 3), 10 (3 to 4), 5 (4 to 5). The bend where gains become marginal is at K = 3. Choosing K = 1 is wrong because WCSS is highest there.

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