viewClusters function

PLOT ALL CLUSTERS IN A 2-D PROJECTION SPACE

Plot all clusters in a 2-D projection space.

viewClusters(
             y, 
             cl, 
             outlierLabel = 0,
             projMethod = "Eigen", 
             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 = 1.2)

Arguments

• y: Data matrix. Rows correspond to observations. Columns correspond to variables.
• cl: Cluster membership vector.
• outlierLabel: Label for outliers. Outliers are not involved in calculating the projection directions. Outliers will be represented by red triangles in the plot. By default, outlierLabel=0.
• projMethod: Method to construct 2-D projection directions. projMethod="Eigen" indicates that we project data to the 2-dimensional space spanned by the first two eigenvectors of the between cluster distance matrix c("B={2\\over k_0}\\sum_{i=1}^{k_0}\\Sigma_i+{2\\over\n", "k_0(k_0-1)}\\sum_{i<j}(\\theta_i-\\theta_j) (\\theta_i-\\theta_j)^T"). projMethod="DMS" indicates that we project data to the 2-dimensional space spanned by the first two eigenvectors of the between cluster distance matrix c("$B=\\sum_{i=2}^{k_0}\\sum_{j=1}^{i-1}\n$", "$n_i n_j(\\theta_i-\\theta_j)(\\theta_i-\\theta_j)^T$"). DMS method is proposed by Dhillon et al. (2002).
• 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).

Returns

• B: Between cluster distance matrix measuring the between cluster variation.

• Q: Columns of Q are eigenvectors of the matrix B.

• proj: Projected clusters in the 2-D space spanned by the first 2 columns of the matrix Q.

References

Dhillon I. S., Modha, D. S. and Spangler, W. S. (2002) Class visualization of high-dimensional data with applications. computational Statistics and Data Analysis, 41 , 59--90.

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

plot1DProjection

plot2DProjection

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)
n3 <- 30
mu3 <- c(10, 10)
Sigma3 <- matrix(c(3, 1.5, 1.5, 1), 2, 2)
n4 <- 10
mu4 <- c(0, 0)
Sigma4 <- 50*diag(2)

library(MASS)
set.seed(1234)
y1 <- mvrnorm(n1, mu1, Sigma1)
y2 <- mvrnorm(n2, mu2, Sigma2)
y3 <- mvrnorm(n3, mu3, Sigma3)
y4 <- mvrnorm(n4, mu4, Sigma4)
y <- rbind(y1, y2, y3, y4)
cl <- rep(c(1:3, 0), c(n1, n2, n3, n4))

par(mfrow=c(2,1))
viewClusters(y = y, cl = cl)
viewClusters(y = y, cl = cl, projMethod = "DMS")