plot1DProjection      package:clusterGeneration      R Documentation

_P_L_O_T _A _P_A_I_R _O_F _C_L_U_S_T_E_R_S _A_N_D _T_H_E_I_R _D_E_N_S_I_T_Y _E_S_T_I_M_A_T_E_S, _W_H_I_C_H _A_R_E _P_R_O_J_E_C_T_E_D  _A_L_O_N_G _A _S_P_E_C_I_F_I_E_D _1-_D _P_R_O_J_E_C_T_I_O_N _D_I_R_E_C_T_I_O_N

_D_e_s_c_r_i_p_t_i_o_n:

     Plot a pair of clusters and their density estimates, which are
     projected along a specified 1-D projection direction.

_U_s_a_g_e:

     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)

_A_r_g_u_m_e_n_t_s:

      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: 
          $sepVal=[(\bar{x}_2-\bar{x}_1)-z_{alpha/2}(s_1+s_2)]/
          [(\bar{x}_2-\bar{x}_1)+z_{alpha/2}(s_1+s_2)]$,  where
          $\bar{x}_i$ 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'. 

_D_e_t_a_i_l_s:

     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"',
     $L_i=\bar{x}_i-z_{alpha/2}s_i$, where $\bar{x}_i$ 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.

_V_a_l_u_e:

  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'. 

_A_u_t_h_o_r(_s):

     Weiliang Qiu stwxq@channing.harvard.edu
      Harry Joe harry@stat.ubc.ca

_R_e_f_e_r_e_n_c_e_s:

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

_S_e_e _A_l_s_o:

     'plot2DProjection' 'viewClusters'

_E_x_a_m_p_l_e_s:

     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,]

     plot1DProjection(y1, y2, projDir)

