You run k-means on customer data with age, income and number of purchases. What breaks?
easyAnswer
- The scales.
- Income in dollars ranges over tens of thousands while age spans a few decades, so squared Euclidean distance is essentially income distance and the other two variables contribute nothing.
- Standardize or use robust scaling first, and understand that scaling is a modelling decision, because it declares each feature equally important.
- Skew is the second problem: income is heavy-tailed, so a handful of high earners dominate the centroids, and a log transform usually helps.
- If some variables are categorical, k-means is the wrong algorithm entirely, since a mean of a category is meaningless; use k-prototypes or a Gower distance with a method that accepts arbitrary distances.
Check yourself — multiple choice
- Nothing, k-means is scale invariant
- Unscaled Euclidean distance is dominated by income, skew lets outliers drive centroids, and categorical variables have no meaningful mean
- Only k matters
- It fails because of too few features
K-means needs comparable, roughly symmetric, numeric scales; scaling is a modelling choice.
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