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Compare k-means, k-medoids, k-modes
Short answer
k-means uses mean (numeric, sensitive to outliers); k-medoids uses an actual object as medoid (robust to outliers, any dissimilarity, but slower O(k(n−k)²)); k-modes uses the mode for categorical data with matching dissimilarity. All three are partitioning methods that iteratively relocate objects.
Compare k-means, k-medoids, and k-modes algorithm.
All three are partitioning methods that form k clusters by iterative relocation, but they differ in the cluster representative and the type of data.
| Basis | k-means | k-medoids (PAM) | k-modes |
|---|---|---|---|
| Cluster centre | Mean of the objects (may not be an actual object) | Medoid: an actual, most central object | Mode: the most frequent value of each attribute |
| Data type | Numeric (continuous) | Numeric, and any type with a dissimilarity measure | Categorical |
| Dissimilarity | Euclidean distance | Any distance (e.g. Manhattan) | Number of mismatches between attribute values (simple matching) |
| Objective | Minimise sum of squared errors | Minimise sum of absolute dissimilarities to medoids | Minimise total mismatches to modes |
| Update step | Recompute mean | Swap a medoid with a non-medoid if cost falls | Recompute mode of each attribute |
| Outliers/noise | Very sensitive | Robust (medoid is not shifted by outliers) | Moderately robust |
| Complexity | O(nkt) | O(k(n − k)²) per iteration, costly for big data | O(nkt), efficient |
| Scalability | High | Low (CLARA/CLARANS for large data) | High |
| Example | Cluster customers by (age, income) | Cluster with outliers, e.g. house prices | Cluster by (colour, make, city) |
Summary: k-means is fast but sensitive to outliers; k-medoids is robust but slower; k-modes extends the k-means paradigm to categorical data by using modes and a matching dissimilarity (k-prototypes handles mixed data).
✓ Answer checked by Claude Opus 5.5 (high effort)
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