kgroups: K-Groups Clustering

In mariarizzo/energy: E-Statistics: Multivariate Inference via the Energy of Data

K-Groups Clustering

Description

Perform k-groups clustering by energy distance.

Usage

kgroups(x, k, iter.max = 10, nstart = 1, cluster = NULL)

Arguments

x	Data frame or data matrix or distance object
k	number of clusters
iter.max	maximum number of iterations
nstart	number of restarts
cluster	initial clustering vector

Details

K-groups is based on the multisample energy distance for comparing distributions. Based on the disco decomposition of total dispersion (a Gini type mean distance) the objective function should either maximize the total between cluster energy distance, or equivalently, minimize the total within cluster energy distance. It is more computationally efficient to minimize within distances, and that makes it possible to use a modified version of the Hartigan-Wong algorithm (1979) to implement K-groups clustering.

The within cluster Gini mean distance is

G(C_j) = \frac{1}{n_j^2} ∑_{i,m=1}^{n_j} |x_{i,j} - x_{m,j}|

and the K-groups within cluster distance is

W_j = \frac{n_j}{2}G(C_j) = \frac{1}{2 n_j} ∑_{i,m=1}^{n_j} |x_{i,j} - x_{m,j}.

If z is the data matrix for cluster C_j, then W_j could be computed as sum(dist(z)) / nrow(z).

If cluster is not NULL, the clusters are initialized by this vector (can be a factor or integer vector). Otherwise clusters are initialized with random labels in k approximately equal size clusters.

If x is not a distance object (class(x) == "dist") then x is converted to a data matrix for analysis.

Run up to iter.max complete passes through the data set until a local min is reached. If nstart > 1, on second and later starts, clusters are initialized at random, and the best result is returned.

Value

An object of class kgroups containing the components

call	the function call
cluster	vector of cluster indices
sizes	cluster sizes
within	vector of Gini within cluster distances
W	sum of within cluster distances
count	number of moves
iterations	number of iterations
k	number of clusters

cluster is a vector containing the group labels, 1 to k. print.kgroups prints some of the components of the kgroups object.

Expect that count is 0 if the algorithm converged to a local min (that is, 0 moves happened on the last iteration). If iterations equals iter.max and count is positive, then the algorithm did not converge to a local min.

Author(s)

Maria Rizzo and Songzi Li

References

Li, Songzi (2015). "K-groups: A Generalization of K-means by Energy Distance." Ph.D. thesis, Bowling Green State University.

Li, S. and Rizzo, M. L. (2017). "K-groups: A Generalization of K-means Clustering". ArXiv e-print 1711.04359. https://arxiv.org/abs/1711.04359

Szekely, G. J., and M. L. Rizzo. "Testing for equal distributions in high dimension." InterStat 5, no. 16.10 (2004).

Rizzo, M. L., and G. J. Szekely. "Disco analysis: A nonparametric extension of analysis of variance." The Annals of Applied Statistics (2010): 1034-1055.

Hartigan, J. A. and Wong, M. A. (1979). "Algorithm AS 136: A K-means clustering algorithm." Applied Statistics, 28, 100-108. doi: 10.2307/2346830.

Examples

  x <- as.matrix(iris[ ,1:4])
  set.seed(123)
  kg <- kgroups(x, k = 3, iter.max = 5, nstart = 2)
  kg
  fitted(kg)
  
  
    d <- dist(x)
    set.seed(123)
    kg <- kgroups(d, k = 3, iter.max = 5, nstart = 2)
    kg
    
    kg$cluster
  
    fitted(kg)
    fitted(kg, method = "groups")
    

mariarizzo/energy documentation built on Jan. 1, 2023, 9:43 a.m.