Perform LGA/RLGA

Description

Linear Grouping Analysis

Usage

## Default S3 method:
lga(x, k, biter = NULL, niter = 10, showall = FALSE, scale = TRUE,
    nnode=NULL, silent=FALSE, ...)
## Default S3 method:
rlga(x, k, alpha=0.9, biter = NULL, niter = 10, showall = FALSE, scale = TRUE,
    nnode=NULL, silent=FALSE, ...)

Arguments

Details

This code tries to find k clusters using the lga algorithm described in Van Aelst et al (2006). For each attempt, it has up to niter steps to get to convergence, and it does this from biter different starting hyperplanes. It then selects the clustering with the smallest Residual Orthoganal Sum of Squareds.

If biter is left as NULL, then it is selected via the equation given in Van Aeslt et al (2006).

The function rlga is the robust equivalent to LGA, and is introduced in Garcia-Escudero et al (2008).

Both functions are parallel computing aware via the nnode argument, and works with the package snow. In order to use parallel computing, one of MPI (e.g. lamboot) or PVM is necessary. For further details, see the documentation for snow.

Associated with the lga and rlga functions are a print method and a plot method (see the examples). In the plot method, the fitted hyperplanes are also shown as dashed-lines when there are only two dimensions.

Value

An object of class ‘“lga”’. The list contains

and the attributes include

Author(s)

Justin Harrington harringt@stat.ubc.ca

References

Van Aelst, S. and Wang, X. and Zamar, R. and Zhu, R. (2006) ‘Linear Grouping Using Orthogonal Regression’, Computational Statistics & Data Analysis 50, 1287–1312.

Garcia-Escudero, L.A., Gordaliza, A., San Martin, R., Van Aelst, S. and Zamar, R.H. (2008) ‘Robust linear clustering’. To appear in Journal of the Royal Statistical Society, Series B (accepted June, 2008).

See Also

gap

Examples

## Synthetic Data
## Make a dataset with 2 clusters in 2 dimensions

library(MASS)
set.seed(1234)
X <- rbind(mvrnorm(n=100, mu=c(1,-1), Sigma=diag(0.1,2)+0.9),
            mvrnorm(n=100, mu=c(1,1), Sigma=diag(0.1,2)+0.9))

lgaout <- lga(X,2)
plot(lgaout)
print(lgaout)

## Robust equivalent

rlgaout <- rlga(X,2, alpha=0.75)
plot(rlgaout)
print(rlgaout)


## nhl94 data set

data(nhl94)
plot(lga(nhl94, k=3, niter=30))


## Allometry data set
data(brain)
plot(lga(log(brain, base=10), k=3))


## Second Allometry data set
data(ob)
plot(lga(log(ob[,2:3]), k=3), pch=as.character(ob[,1]))

## Corridor Walls data set
## To obtain the results reported in Garcia-Escudero et al. (2008):
data(corridorWalls)
rlgaout <- rlga(corridorWalls, k=3, biter = 100, niter = 30, alpha=0.85)
pairs(corridorWalls, col=rlgaout$cluster+1)
plot(rlgaout)

## Parallel processing case
## In this example, running using 4 nodes. 

## Not run: 
set.seed(1234)
X <- rbind(mvrnorm(n=1e6, mu=c(1,-1), Sigma=diag(0.1,2)+0.9),
            mvrnorm(n=1e6, mu=c(1,1), Sigma=diag(0.1,2)+0.9))
abc <- lga(X, k=2, nnode=4)

## End(Not run)

Results