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 = {p₁, p₂,…,p_n} in Euclidian space, the problem of k-means clustering is to find a set of centre points (means) P = {c₁, c₂,…,c_k}, |P| = k in the space, such that S can be partitioned into k corresponding clusters C₁, C₂,…,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 = {p₁, p₂, …, p_n} in Euclidian space, the problem of k-medoids clustering is to find a set of objects as medoids P = {o₁, o₂,…,o_k}, |P| = k in the space, such that S can be partitioned into k corresponding clusters C₁, C₂,…,C_k, by assigning each object in Sto the...