# inckmed: Increasing number of clusters in k-medoids algorithm In kmed: Distance-Based k-Medoids

## Description

This function runs the increasing number of clusters in the k-medoids algorithm proposed by Yu et. al. (2018).

## Usage

 1 inckmed(distdata, ncluster, iterate = 10, alpha = 1) 

## Arguments

 distdata A distance matrix (n x n) or dist object. ncluster A number of clusters. iterate A number of iterations for the clustering algorithm. alpha A stretch factor to determine the range of initial medoid selection (see Details).

## Details

This algorithm is claimed to manage with the weakness of the simple and fast-kmedoids (fastkmed). The origin of the algorithm is a centroid-based algorithm by applying the Euclidean distance. Then, Bbecause the function is a medoid-based algorithm, the object mean (centroid) and variance are redefined into medoid and deviation, respectively.

The alpha argument is a stretch factor, i.e. a constant defined by the user. It is applied to determine a set of medoid candidates. The medoid candidates are calculated by O_c = {X_i| σ_i ≤q α σ, i = 1, 2, …, n }, where σ_i is the average deviation of object i, and σ is the average deviation of the data set. They are computed by

σ = √{\frac{1}{n-1} ∑_{i=1}^n d(O_i, v_1)}

σ_i = √{\frac{1}{n-1} ∑_{i=1}^n d(O_i, O_j)}

where n is the number of objects, O_i is the object i, and v_1 is the most centrally located object.

## Value

Function returns a list of components:

cluster is the clustering memberships result.

medoid is the id medoids.

minimum_distance is the distance of all objects to their cluster medoid.

## Author(s)

Weksi Budiaji
Contact: budiaji@untirta.ac.id

## References

Yu, D., Liu, G., Guo, M., Liu, X., 2018. An improved K-medoids algorithm based on step increasing and optimizing medoids. Expert Systems with Applications 92, pp. 464-473.

## Examples

 1 2 3 4 num <- as.matrix(iris[,1:4]) mrwdist <- distNumeric(num, num, method = "mrw") result <- inckmed(mrwdist, ncluster = 3, iterate = 50, alpha = 1.5) table(result\$cluster, iris[,5]) 

kmed documentation built on Jan. 8, 2021, 2:40 a.m.