meE                  package:mclust                  R Documentation

_E_M _a_l_g_o_r_i_t_h_m _s_t_a_r_t_i_n_g _w_i_t_h _M-_s_t_e_p _f_o_r _a _p_a_r_a_m_e_t_e_r_i_z_e_d _M_V_N _m_i_x_t_u_r_e _m_o_d_e_l.

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

     Implements the EM algorithm for a parameterized MVN mixture model,
     starting with the maximization step.

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

     meE(data, z, eps, tol, itmax, equalPro, warnSingular, 
         noise = FALSE, Vinv)
     meV(data, z, eps, tol, itmax, equalPro, warnSingular, 
         noise = FALSE, Vinv)
     meEII(data, z, eps, tol, itmax, equalPro, warnSingular, 
           noise = FALSE, Vinv)
     meVII(data, z, eps, tol, itmax, equalPro, warnSingular, 
           noise = FALSE, Vinv)
     meEEI(data, z, eps, tol, itmax, equalPro, warnSingular, 
           noise = FALSE, Vinv)
     meVEI(data, z, eps, tol, itmax, equalPro, warnSingular, 
           noise = FALSE, Vinv)
     meEVI(data, z, eps, tol, itmax, equalPro, warnSingular, 
           noise = FALSE, Vinv)
     meVVI(data, z, eps, tol, itmax, equalPro, warnSingular, 
           noise = FALSE, Vinv)
     meEEE(data, z, eps, tol, itmax, equalPro, warnSingular, 
           noise = FALSE, Vinv)
     meEEV(data, z, eps, tol, itmax, equalPro, warnSingular, 
           noise = FALSE, Vinv)
     meVEV(data, z, eps, tol, itmax, equalPro, warnSingular, 
           noise = FALSE, Vinv)
     meVVV(data, z, eps, tol, itmax, equalPro, warnSingular, 
           noise = FALSE, Vinv)

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

    data: A numeric vector, matrix, or data frame of observations.
          Categorical variables are not allowed. If a matrix or data
          frame, rows correspond to observations and columns correspond
          to variables.  

       z: A matrix whose '[i,k]'th entry is the conditional probability
          of the ith observation belonging to the _k_th component of
          the mixture.   

     eps: A scalar tolerance for deciding when to terminate
          computations due to computational singularity in covariances.
            Smaller values of 'eps' allows computations to proceed
          nearer to singularity.  The default is '.Mclust\$eps'. 

     tol: A scalar tolerance for relative convergence of the
          loglikelihood values.  The default is '.Mclust\$tol'. 

   itmax: An integer limit on the number of EM iterations.  The default
          is '.Mclust\$itmax'. 

equalPro: Logical variable indicating whether or not the mixing
          proportions are equal in the model. The default is
          '.Mclust\$equalPro'. 

warnSingular: A logical value indicating whether or not a warning
          should be issued whenever a singularity is encountered. The
          default is '.Mclust\$warnSingular'. 

   noise: A logical value indicating whether or not the model includes
          a Poisson noise component. The default assumes there is no
          noise component. 

    Vinv: An estimate of the reciprocal hypervolume of the data region.
          The default is determined by applying function  'hypvol' to
          the data. Used only when 'noise = TRUE'. 

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

     A list including the following components:  

      mu: A matrix whose kth column is the mean of the _k_th component
          of the mixture model. 

   sigma: For multidimensional models, a three dimensional array  in
          which the '[,,k]'th entry gives the the covariance for the
          _k_th group in the best model. <br> For one-dimensional
          models, either a scalar giving a common variance for the
          groups or a vector whose entries are the variances for each
          group in the best model. 

     pro: A vector whose _k_th component is the mixing proportion for
          the _k_th component of the mixture model. 

       z: A matrix whose '[i,k]'th entry is the conditional probability
          of the _i_th observation belonging to the _k_th component of
          the mixture.   

modelName: Character string identifying the model. 

  loglik: The logliklihood for the data in the mixture model.  

Attributes:: The return value also has the following attributes:

          *  '"info"': Information on the iteration.

          *  '"warn"': An appropriate warning if problems are
             encountered in the computations. 

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

     C. Fraley and A. E. Raftery (2002a). Model-based clustering,
     discriminant analysis, and density estimation. _Journal of the
     American Statistical Association 97:611-631_.  See <URL:
     http://www.stat.washington.edu/mclust>. 

     C. Fraley and A. E. Raftery (2002b). MCLUST:Software for
     model-based clustering, density estimation and  discriminant
     analysis.  Technical Report, Department of Statistics, University
     of Washington.  See <URL: http://www.stat.washington.edu/mclust>.

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

     'em', 'me', 'estep', 'mclustOptions'

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

     data(iris)
     irisMatrix <- as.matrix(iris[,1:4])
     irisClass <- iris[,5]

     meVVV(data = irisMatrix, z = unmap(irisClass))

