mstep                 package:mclust                 R Documentation

_M-_s_t_e_p _i_n _t_h_e _E_M _a_l_g_o_r_i_t_h_m _f_o_r _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_s.

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

     Maximization step in the EM algorithm for parameterized MVN
     mixture models.

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

     mstep(modelName, data, z, ...)

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

modelName: A character string indicating the model: 

           "E": equal variance  (one-dimensional) 
           "V": variable variance (one-dimensional) 
           "EII": spherical, equal volume 
           "VII": spherical, unequal volume 
           "EEI": diagonal, equal volume and shape 
           "VEI": diagonal, varying volume, equal shape 
           "EVI": diagonal, equal volume, varying shape 
           "VVI": diagonal, varying volume and shape 
           "EEE": ellipsoidal, equal volume, shape, and orientation 
           "EEV": ellipsoidal, equal volume and equal shape
           "VEV": ellipsoidal, equal shape 
           "VVV": ellipsoidal, varying volume, shape, and orientation 

    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.   

     ...: Any number of the following:

          _e_q_u_a_l_P_r_o A logical value indicating whether or not the
               components in the model are present in equal
               proportions. The default is '.Mclust\$equalPro'.  

          _n_o_i_s_e A logical value indicating whether or not the model
               includes a Poisson noise component. The default assumes
               there is no noise component.

          _e_p_s 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'.  

               Not used for models "EII", "VII", "EEE", "VVV".

          _t_o_l For models with iterative M-step ("VEI", "VEE", "VVE",
               "VEV"),  a scalar tolerance for relative convergence of
               the parameters.  The default is '.Mclust\$tol'. 

          _i_t_m_a_x For models with iterative M-step ("VEI", "VEE", "VVE",
               "VEV"),  an integer limit on the number of EM
               iterations.  The default is '.Mclust\$itmax'. 

          _w_a_r_n_S_i_n_g_u_l_a_r A logical value indicating whether or not a
               warning should be issued whenever a singularity is
               encountered. The default is '.Mclust\$warnSingular'.

               Not used for models "EII", "VII", "EEE", "VVV".

_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: A character string identifying the model (same as the input
          argument). 

          *  '"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:

     'mstepE', ..., 'mstepVVV', 'me', 'estep', 'mclustOptions'.

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

     data(iris)
     irisMatrix <- as.matrix(iris[,1:4])
     irisClass <- iris[,5]
      
     mstep(modelName = "VII", data = irisMatrix, z = unmap(irisClass))

