sepIndex          package:clusterGeneration          R Documentation

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

     Measure the magnitude of the gap or sparse area between a pair of
     clusters (or cluster distributions) along the specified projection
     direction.

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

     sepIndexTheory(projDir, mu1, Sigma1, mu2, Sigma2, 
                              alpha=0.05, eps=1.0e-10, quiet=TRUE)

     sepIndexData(projDir, y1, y2, alpha=0.05, eps=1.0e-10, quiet=TRUE)

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

 projDir: Projection direction. 

     mu1: Mean vector of cluster 1. 

  Sigma1: Covariance matrix of cluster 1. 

     mu2: Mean vector of cluster 2. 

  Sigma2: Covariance matrix of cluster 2. 

      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. 

   alpha: Tuning parameter reflecting the percentage in the two tails
          of a projected cluster that might be outlying. We set
          'alpha'=0.05 like we set the significance level in hypothesis
          testing as 0.05. 

     eps: Convergence threshold. A small positive number to check if a
          quantitiy q  is equal to zero.  If |q|<'eps', then we regard
          q is equal  to zero.  'eps' is used to check if an algorithm
          converges. The default value 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'. 

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

     The value of the separation index defined in Qiu and Joe (2006).

_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.

_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)
     sepIndexTheory(projDir, mu1, Sigma1, mu2, Sigma2)

     library(MASS)
     y1<-mvrnorm(n1, mu1, Sigma1)
     y2<-mvrnorm(n2, mu2, Sigma2)
     sepIndexData(projDir, y1, y2)

