kGmedian

Description

Fast k-medians clustering based on recursive averaged stochastic gradient algorithms. The procedure is similar to the kmeans clustering technique performed recursively with the MacQueen algorithm. The advantage of the kGmedian algorithm compared to MacQueen strategy is that it deals with sum of norms instead of sum of squared norms, ensuring a more robust behaviour against outlying values.

Usage

kGmedian(X, ncenters=2, gamma=1, alpha=0.75, nstart = 10, nstartkmeans = 10)

Arguments

Details

See Cardot, Cenac and Monnez (2012).

Value

References

Cardot, H., Cenac, P. and Monnez, J-M. (2012). A fast and recursive algorithm for clustering large datasets with k-medians. Computational Statistics and Data Analysis, 56, 1434-1449.

Cardot, H., Cenac, P. and Zitt, P-A. (2013). Efficient and fast estimation of the geometric median in Hilbert spaces with an averaged stochastic gradient algorithm. Bernoulli, 19, 18-43.

MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations. In Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, eds L. M. Le Cam and J. Neyman, 1, pp. 281-297. Berkeley, CA: University of California Press.

See Also

See also Gmedian and kmeans.

Examples

# a 2-dimensional example 
x <- rbind(matrix(rnorm(100, sd = 0.3), ncol = 2),
           matrix(rnorm(100, mean = 1, sd = 0.3), ncol = 2))
colnames(x) <- c("x", "y")

cl.kmeans <- kmeans(x, 2)
cl.kmedian <- kGmedian(x)

par(mfrow=c(1,2))
plot(x, col = cl.kmeans$cluster, main="kmeans")
points(cl.kmeans$centers, col = 1:2, pch = 8, cex = 2)

plot(x, col = cl.kmedian$cluster, main="kmedian")
points(cl.kmedian$centers, col = 1:2, pch = 8, cex = 2)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(Gmedian)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/Gmedian/kGmedian.Rd_%03d_medium.png", width=480, height=480)
> ### Name: kGmedian
> ### Title: kGmedian
> ### Aliases: kGmedian
> ### Keywords: Gmedian
> 
> ### ** Examples
> 
> # a 2-dimensional example 
> x <- rbind(matrix(rnorm(100, sd = 0.3), ncol = 2),
+            matrix(rnorm(100, mean = 1, sd = 0.3), ncol = 2))
> colnames(x) <- c("x", "y")
> 
> cl.kmeans <- kmeans(x, 2)
> cl.kmedian <- kGmedian(x)
> 
> par(mfrow=c(1,2))
> plot(x, col = cl.kmeans$cluster, main="kmeans")
> points(cl.kmeans$centers, col = 1:2, pch = 8, cex = 2)
> 
> plot(x, col = cl.kmedian$cluster, main="kmedian")
> points(cl.kmedian$centers, col = 1:2, pch = 8, cex = 2)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>