https://github.com/cran/clusterGeneration
Tip revision: dcaf06c7d40c7560f1330e963c190af194bb4a66 authored by Weiliang Qiu on 30 October 2007, 00:00:00 UTC
version 1.2.4
version 1.2.4
Tip revision: dcaf06c
plot2DProjection.Rd
\name{plot2DProjection}
\alias{plot2DProjection}
\title{PLOT A PAIR OF CLUSTERS ALONG A 2-D PROJECTION SPACE}
\description{
Plot a pair of clusters along a 2-D projection space.
}
\usage{
plot2DProjection(y1, y2, projDir,
sepValMethod=c("normal", "quantile"),
iniProjDirMethod=c("SL", "naive"),
projDirMethod=c("newton", "fixedpoint"),
xlim=NULL, ylim=NULL,
xlab="1st projection direction",
ylab="2nd projection direction",
title="Scatter plot of 2-D Projected Clusters",
font=2, font.lab=2, cex=1.2, cex.lab=1, cex.main=1.5,
lwd=4, lty1=1, lty2=2, pch1=18, pch2=19, col1=2, col2=4,
alpha=0.05, ITMAX=20, eps=1.0e-10, quiet=TRUE)
}
\arguments{
\item{y1}{
Data matrix of cluster 1. Rows correspond to observations. Columns correspond to variables.
}
\item{y2}{
Data matrix of cluster 2. Rows correspond to observations. Columns correspond to variables.
}
\item{projDir}{
1-D projection direction along which two clusters will be projected.
}
\item{sepValMethod}{
Method to calculate separation index for a pair of clusters projected onto a
1-D space. \code{sepValMethod="quantile"} indicates the quantile version of
separation index will be used: $sepVal=(L_2-U_1)/(U_2-L_1)$ where $L_i$ and
$U_i$, $i=1, 2$, are the lower and upper \code{alpha/2} sample percentiles
of projected cluster $i$. \code{sepValMethod="normal"} indicates the
normal version of separation index will be used:
$sepVal=[(\bar{x}_2-\bar{x}_1)-z_{\alpha/2}(s_1+s_2)]/
[(\bar{x}_2-\bar{x}_1)+z_{\alpha/2}(s_1+s_2)]$,
where $\bar{x}_i$ and $s_i$ are the sample mean and standard deviation
of projected cluster $i$.
}
\item{iniProjDirMethod}{
Indicating the method to get initial projection direction when calculating
the separation index between a pair of clusters (c.f. Qiu and Joe,
2006a, 2006b). \cr
\code{iniProjDirMethod}$=$\dQuote{SL} indicates the initial projection
direction is the sample version of the SL's projection direction
(Su and Liu, 1993)
\eqn{\left(\boldsymbol{\Sigma}_1+\boldsymbol{\Sigma}_2\right)^{-1}\left(\boldsymbol{\mu}_2-\boldsymbol{\mu}_1\right)}\cr
\code{iniProjDirMethod}$=$\dQuote{naive} indicates the initial projection
direction is \eqn{\boldsymbol{\mu}_2-\boldsymbol{\mu}_1}
}
\item{projDirMethod}{
Indicating the method to get the optimal projection direction when calculating
the separation index between a pair of clusters (c.f. Qiu and Joe,
2006a, 2006b). \cr
\code{projDirMethod}$=$\dQuote{newton} indicates we use the Newton-Raphson
method to search the optimal projection direction (c.f. Qiu and Joe, 2006a).
This requires the assumptions that both covariance matrices of the pair of
clusters are positive-definite. If this assumption is violated, the
\dQuote{fixedpoint} method could be used. The \dQuote{fixedpoint} method
iteratively searches the optimal projection direction based on the first
derivative of the separation index to the project direction
(c.f. Qiu and Joe, 2006b).
}
\item{xlim}{
Range of X axis.
}
\item{ylim}{
Range of Y axis.
}
\item{xlab}{
X axis label.
}
\item{ylab}{
Y axis label.
}
\item{title}{
Title of the plot.
}
\item{font}{
An integer which specifies which font to use for text (see \code{par}).
}
\item{font.lab}{
The font to be used for x and y labels (see \code{par}).
}
\item{cex}{
A numerical value giving the amount by which plotting text
and symbols should be scaled relative to the default (see \code{par}).
}
\item{cex.lab}{
The magnification to be used for x and y labels relative
to the current setting of 'cex' (see \code{par}).
}
\item{cex.main}{
The magnification to be used for main titles relative
to the current setting of 'cex' (see \code{par}).
}
\item{lwd}{
The line width, a \_positive\_ number, defaulting to '1' (see \code{par}).
}
\item{lty1}{
Line type for cluster 1 (see \code{par}).
}
\item{lty2}{
Line type for cluster 2 (see \code{par}).
}
\item{pch1}{
Either an integer specifying a symbol or a single character
to be used as the default in plotting points for cluster 1 (see \code{points}).
}
\item{pch2}{
Either an integer specifying a symbol or a single character
to be used as the default in plotting points for cluster 2 (see \code{points}).
}
\item{col1}{
Color to indicates cluster 1.
}
\item{col2}{
Color to indicates cluster 2.
}
\item{alpha}{
Tuning parameter reflecting the percentage in the two
tails of a projected cluster that might be outlying.
}
\item{ITMAX}{
Maximum iteration allowed when iteratively calculating the
optimal projection direction.
The actual number of iterations is usually much less than the default value 20.
}
\item{eps}{
A small positive number to check if a quantitiy \eqn{q} is equal to zero.
If \eqn{|q|<}\code{eps}, then we regard \eqn{q} as equal to zero.
\code{eps} is used to check the denominator in the formula of the separation
index is equal to zero. Zero-value denominator indicates two clusters are
totally overlapped. Hence the separation index is set to be $-1$.
The default value of \code{eps} is \eqn{1.0e-10}.
}
\item{quiet}{
A flag to switch on/off the outputs of intermediate results and/or possible warning messages. The default value is \code{TRUE}.
}
}
\details{
To get the second projection direction, we first construct an orthogonal
matrix with first column \code{projDir}. Then we rotate the data points
according to this orthogonal matrix. Next, we remove the first dimension
of the rotated data points, and obtain the optimal projection direction
$projDir2$ for the rotated data points in the remaining dimensions.
Finally, we rotate the vector
$projDir3=(0, projDir2)$ back to the original space.
The vector $projDir3$ is the second projection direction.
The ticks along X axis indicates the positions of points of the projected
two clusters. The positions of $L_i$ and $U_i$, $i=1, 2$, are also indicated
on X axis, where $L_i$ and $U_i$ are the lower and upper $\alpha/2$ sample
percentiles of cluster $i$ if \code{sepValMethod="quantile"}.
If \code{sepValMethod="normal"},
$L_i=\bar{x}_i-z_{\alpha/2}s_i$, where $\bar{x}_i$ and $s_i$ are the
sample mean and standard deviation of cluster $i$, and $z_{\alpha/2}$
is the upper $\alpha/2$ percentile of standard normal distribution.
}
\value{
\item{sepValx}{
value of the separation index for the projected two clusters along the
1st projection direction.
}
\item{sepValy}{
value of the separation index for the projected two clusters along the
2nd projection direction.
}
\item{Q2}{
1st column is the 1st projection direction. 2nd column is the 2nd
projection direction.
}
}
\references{
Qiu, W.-L. and Joe, H. (2006a)
Generation of Random Clusters with Specified Degree of Separaion.
\emph{Journal of Classification}, \bold{23}(2), 315-334.
Qiu, W.-L. and Joe, H. (2006b)
Separation Index and Partial Membership for Clustering.
\emph{Computational Statistics and Data Analysis}, \bold{50}, 585--603.
}
\author{
Weiliang Qiu \email{stwxq@channing.harvard.edu}\cr
Harry Joe \email{harry@stat.ubc.ca}
}
\seealso{
\code{\link{plot1DProjection}}
\code{\link{viewClusters}}
}
\examples{
n1<-50
mu1<-c(0,0)
Sigma1<-matrix(c(2,1,1,5),2,2)
n2<-100
mu2<-c(10,0)
Sigma2<-matrix(c(5,-1,-1,2),2,2)
projDir<-c(1, 0)
library(MASS)
set.seed(1234)
y1<-mvrnorm(n1, mu1, Sigma1)
y2<-mvrnorm(n2, mu2, Sigma2)
y<-rbind(y1, y2)
cl<-rep(1:2, c(n1, n2))
b<-getSepProjData(y, cl, iniProjDirMethod="SL", projDirMethod="newton")
# projection direction for clusters 1 and 2
projDir<-b$projDirArray[1,2,]
par(mfrow=c(2,1))
plot1DProjection(y1, y2, projDir)
plot2DProjection(y1, y2, projDir)
}
\keyword{cluster}