Plot a pair of clusters and their density estimates, which are projected along a specified 1-D projection direction.
plot1DProjection(
y1,
y2,
projDir,
sepValMethod = c("normal", "quantile"),
bw = "nrd0",
xlim = NULL,
ylim = NULL,
xlab = "1-D projected clusters",
ylab = "density estimates",
title = "1-D Projected Clusters and their density estimates",
font = 2,
font.lab = 2,
cex = 1.2,
cex.lab = 1.2,
cex.main = 1.5,
lwd = 4,
lty1 = 1,
lty2 = 2,
pch1 = 18,
pch2 = 19,
col1 = 2,
col2 = 4,
type = "l",
alpha = 0.05,
eps = 1.0e-10,
quiet = TRUE)
value of the separation index for the projected two clusters along
the projection direction projDir.
projection direction. To make sure the projected cluster 1 is on the
left-hand side of the projected cluster 2, the input projDir
might be changed to -projDir.
Data matrix of cluster 1. Rows correspond to observations. Columns correspond to variables.
Data matrix of cluster 2. Rows correspond to observations. Columns correspond to variables.
1-D projection direction along which two clusters will be projected.
Method to calculate separation index for a pair of clusters projected onto a
1-D space. 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 alpha/2 sample percentiles
of projected cluster \(i\). sepValMethod="normal" indicates the
normal version of separation index will be used:
\(sepVal=[(xbar_2-xbar_1)-z_{\alpha/2}(s_1+s_2)]/
[(xbar_2-xbar_1)+z_{\alpha/2}(s_1+s_2)]\),
where \(xbar_i\) and \(s_i\) are the sample mean and standard deviation
of projected cluster \(i\).
The smoothing bandwidth to be used by the function density.
Range of X axis.
Range of Y axis.
X axis label.
Y axis label.
Title of the plot.
An integer which specifies which font to use for text (see par).
The font to be used for x and y labels (see par).
A numerical value giving the amount by which plotting text
and symbols should be scaled relative to the default (see par).
The magnification to be used for x and y labels relative
to the current setting of 'cex' (see par).
The magnification to be used for main titles relative
to the current setting of 'cex' (see par).
The line width, a positive number, defaulting to '1' (see par).
Line type for cluster 1 (see par).
Line type for cluster 2 (see par).
Either an integer specifying a symbol or a single character
to be used as the default in plotting points for cluster 1 (see points).
Either an integer specifying a symbol or a single character
to be used as the default in plotting points for cluster 2 (see points).
Color to indicates cluster 1.
Color to indicates cluster 2.
What type of plot should be drawn (see plot).
Tuning parameter reflecting the percentage in the two tails of a projected cluster that might be outlying.
A small positive number to check if a quantitiy \(q\) is equal to zero.
If \(|q|<\)eps, then we regard \(q\) as equal to zero.
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 eps is \(1.0e-10\).
A flag to switch on/off the outputs of intermediate results and/or possible warning messages. The default value is TRUE.
Weiliang Qiu weiliang.qiu@gmail.com
Harry Joe harry@stat.ubc.ca
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 sepValMethod="quantile".
If sepValMethod="normal",
\(L_i=xbar_i-z_{\alpha/2}s_i\), where \(xbar_i\) 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.
Qiu, W.-L. and Joe, H. (2006) Separation Index and Partial Membership for Clustering. Computational Statistics and Data Analysis, 50, 585--603.
plot2DProjection
viewClusters
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 = y,
cl = cl,
iniProjDirMethod = "SL",
projDirMethod = "newton")
# projection direction for clusters 1 and 2
projDir <- b$projDirArray[1, 2, ]
plot1DProjection(
y1 = y1,
y2 = y2,
projDir = projDir)
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