Euclidean distance is the default choice, but the right metric depends on what the features mean.
- Euclidean, the straight-line distance. Fine for continuous features that share comparable scales.
- Manhattan, the sum of absolute differences along each axis. It holds up better in high dimensions and with grid-like or count data.
- Minkowski, the general form with a parameter p. Setting p to 1 gives Manhattan and setting it to 2 gives Euclidean.
- Cosine, the angle between two vectors. It ignores magnitude, which suits text and sparse counts where document length varies.
- Hamming, the count of positions where two rows differ. Use it for binary or categorical features.
The metric is a real hyperparameter, not a detail. Change it and the neighbour set changes, so the prediction changes with it. Mixed numeric and categorical data usually needs a combined measure such as Gower distance, since no single formula fits both types.
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