# 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. ```r 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 ```r 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) ```

plot1DProjection function