Description Usage Arguments Details Value Author(s) References See Also Examples

Plot a pair of clusters along a 2-D projection space.

1 2 3 4 5 6 7 8 9 10 11 | ```
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)
``` |

`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. |

`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). |

`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). |

`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 |

`font.lab` |
The font to be used for x and y labels (see |

`cex` |
A numerical value giving the amount by which plotting text
and symbols should be scaled relative to the default (see |

`cex.lab` |
The magnification to be used for x and y labels relative
to the current setting of 'cex' (see |

`cex.main` |
The magnification to be used for main titles relative
to the current setting of 'cex' (see |

`lwd` |
The line width, a \_positive\_ number, defaulting to '1' (see |

`lty1` |
Line type for cluster 1 (see |

`lty2` |
Line type for cluster 2 (see |

`pch1` |
Either an integer specifying a symbol or a single character
to be used as the default in plotting points for cluster 1 (see |

`pch2` |
Either an integer specifying a symbol or a single character
to be used as the default in plotting points for cluster 2 (see |

`col1` |
Color to indicates cluster 1. |

`col2` |
Color to indicates cluster 2. |

`alpha` |
Tuning parameter reflecting the percentage in the two tails of a projected cluster that might be outlying. |

`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. |

`eps` |
A small positive number to check if a quantitiy |

`quiet` |
A flag to switch on/off the outputs of intermediate results and/or possible warning messages. The default value is |

To get the second projection direction, we first construct an orthogonal
matrix with first column `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 *α/2* sample
percentiles of cluster *i* if `sepValMethod="quantile"`

.
If `sepValMethod="normal"`

,
*L_i=xbar_i-z_{α/2}s_i*, where *xbar_i* and *s_i* are the
sample mean and standard deviation of cluster *i*, and *z_{α/2}*
is the upper *α/2* percentile of standard normal distribution.

`sepValx` |
value of the separation index for the projected two clusters along the 1st projection direction. |

`sepValy` |
value of the separation index for the projected two clusters along the 2nd projection direction. |

`Q2` |
1st column is the 1st projection direction. 2nd column is the 2nd projection direction. |

Weiliang Qiu [email protected]

Harry Joe [email protected]

Qiu, W.-L. and Joe, H. (2006a)
Generation of Random Clusters with Specified Degree of Separaion.
*Journal of Classification*, **23**(2), 315-334.

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ```
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)
``` |

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