K-Means and K-Medoids

Synonyms

CLARA (Clustering LARge Applications); CLARANS (Clustering large applications based upon randomized search); K-means partition; PAM (Partitioning Around Medoids)

Definitions

K-Means

Given an integer k and a set of objects S = {p ₁ , p ₂ ,...,p _n } in Euclidian space, the problem of k-means clustering is to find a set of centre points (means) P = {c ₁ , c ₂ ,...,c _k }, |P| = k in the space, such that S can be partitioned into k corresponding clusters C ₁ , C ₂ ,...,C _k , by assigning each object in S to the closest centre c _i . The sum of square error criterion (SEC) measure, defined as ${\displaystyle {\sum}_{i=1}^k{\displaystyle \sum_{p\in {C}_i}\Big|p-{c}_i}}\Big|{}^2$, is minimized.

K-Medoids

Given an integer k and a set of objects S = {p ₁ , p ₂ , ..., p _n } in Euclidian space, the problem of k-medoids clustering is to find a set of objects as medoids P = {o ₁ , o ₂ ,...,o _k }, |P| = k in the space, such that S can be partitioned into k corresponding clusters C...