kmedoids: K-Medoids Clustering

Description Usage Arguments Details Value References

Description

Compute a k-medoids partition of a dissimilarity object.

Usage

1
kmedoids(x, k)

Arguments

x

a dissimilarity object inheriting from class "dist", or a square matrix of pairwise object-to-object dissimilarity values.

k

an integer giving the number of classes to be used in the partition.

Details

Let d denote the pairwise object-to-object dissimilarity matrix corresponding to x. A k-medoids partition of x is defined as a partition of the numbers from 1 to n, the number of objects in x, into k classes C_1, …, C_k such that the criterion function L = ∑_l \min_{j \in C_l} ∑_{i \in C_l} d_{ij} is minimized.

This is an NP-hard optimization problem. PAM (Partitioning Around Medoids, see Kaufman & Rousseeuw (1990), Chapter 2) is a very popular heuristic for obtaining optimal k-medoids partitions, and provided by pam in package cluster.

kmedoids is an exact algorithm based on a binary linear programming formulation of the optimization problem (e.g., Gordon & Vichi (1998), [P4']), using lp from package lpSolve as solver. Depending on available hardware resources (the number of constraints of the program is of the order n^2), it may not be possible to obtain a solution.

Value

An object of class "kmedoids" representing the obtained partition, which is a list with the following components.

cluster

the class ids of the partition.

medoid_ids

the indices of the medoids.

criterion

the value of the criterion function of the partition.

References

L. Kaufman and P. J. Rousseeuw (1990). Finding Groups in Data: An Introduction to Cluster Analysis. Wiley, New York.

A. D. Gordon and M. Vichi (1998). Partitions of partitions. Journal of Classification, 15, 265–285. doi: 10.1007/s003579900034.



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