plot1DProjection function

PLOT A PAIR OF CLUSTERS AND THEIR DENSITY ESTIMATES, WHICH ARE PROJECTED ALONG A SPECIFIED 1-D PROJECTION DIRECTION

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)

Arguments

• y1: Data matrix of cluster 1. Rows correspond to observations. Columns correspond to variables.
• y2: Data matrix of cluster 2. Rows correspond to observations. Columns correspond to variables.
• projDir: 1-D projection direction along which two clusters will be projected.
• sepValMethod: 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: c("$sepVal=[(xbar_2-xbar_1)-z_{\\alpha/2}(s_1+s_2)]/\n$", "$[(xbar_2-xbar_1)+z_{\\alpha/2}(s_1+s_2)]$"), where $xbar_i$ and $s_i$ are the sample mean and standard deviation of projected cluster $i$.
• bw: The smoothing bandwidth to be used by the function density.
• xlim: Range of X axis.
• ylim: Range of Y axis.
• xlab: X axis label.
• ylab: Y axis label.
• title: Title of the plot.
• font: An integer which specifies which font to use for text (see par).
• font.lab: The font to be used for x and y labels (see par).
• cex: A numerical value giving the amount by which plotting text and symbols should be scaled relative to the default (see par).
• cex.lab: The magnification to be used for x and y labels relative to the current setting of 'cex' (see par).
• cex.main: The magnification to be used for main titles relative to the current setting of 'cex' (see par).
• lwd: The line width, a positive number, defaulting to '1' (see par).
• lty1: Line type for cluster 1 (see par).
• lty2: Line type for cluster 2 (see par).
• pch1: Either an integer specifying a symbol or a single character to be used as the default in plotting points for cluster 1 (see points).
• pch2: Either an integer specifying a symbol or a single character to be used as the default in plotting points for cluster 2 (see points).
• col1: Color to indicates cluster 1.
• col2: Color to indicates cluster 2.
• type: What type of plot should be drawn (see plot).
• alpha: Tuning parameter reflecting the percentage in the two tails of a projected cluster that might be outlying.
• eps: 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 $1.0e-10$.
• quiet: A flag to switch on/off the outputs of intermediate results and/or possible warning messages. The default value is TRUE.

Details

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.

Returns

• sepVal: value of the separation index for the projected two clusters along the projection direction projDir.

• 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.

References

Qiu, W.-L. and Joe, H. (2006) Separation Index and Partial Membership for Clustering. Computational Statistics and Data Analysis, 50 , 585--603.

Author(s)

Weiliang Qiu weiliang.qiu@gmail.com

Harry Joe harry@stat.ubc.ca

See Also

plot2DProjection

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 = 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)