estepE                package:mclust                R Documentation

_E-_s_t_e_p _i_n _t_h_e _E_M _a_l_g_o_r_i_t_h_m _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 expectation step in the EM algorithm for a 
     parameterized MVN mixture model.

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

     estepE(data, mu, sigmasq, pro, eps, warnSingular, Vinv, ...)
     estepV(data, mu, sigmasq, pro, eps, warnSingular, Vinv, ...)
     estepEII(data, mu, sigmasq, pro, eps, warnSingular, Vinv, ...)
     estepVII(data, mu, sigmasq, pro, eps, warnSingular, Vinv, ...)
     estepEEI(data, mu, decomp, pro, eps, warnSingular, Vinv, ...)
     estepVEI(data, mu, decomp, pro, eps, warnSingular, Vinv, ...)
     estepEVI(data, mu, decomp, pro, eps, warnSingular, Vinv, ...)
     estepVVI(data, mu, decomp, pro, eps, warnSingular, Vinv, ...)
     estepEEE(data, mu, Sigma, pro, eps, warnSingular, Vinv, ...)
     estepEEV(data, mu, decomp, pro, eps, warnSingular, Vinv, ...)
     estepVEV(data, mu, decomp, pro, eps, warnSingular, Vinv, ...)
     estepVVV(data, mu, sigma, pro, eps, warnSingular, 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. 

      mu: The mean for each component. If there is more than one
          component, 'mu' is a matrix whose columns are the means of
          the components. 

 sigmasq: for the one-dimensional models ("E", "V") and spherical
          models ("EII", "VII"). This is either a vector whose _k_th
          component is the variance for the _k_th component in the
          mixture model ("V" and "VII"), or a scalar giving the common
          variance for all components in the mixture model ("E" and
          "EII"). 

  decomp: for the diagonal models ("EEI", "VEI", "EVI", "VVI") and some
          ellipsoidal models ("EEV", "VEV"). This is a list described
          in more detail in 'cdens'. 

   sigma: for the unconstrained variance model "VVV" or the equal
          variance model "EEE". A _d_ by _d_ by _G_ matrix array whose
          '[,,k]'th entry is the covariance matrix for the _k_th
          component of the mixture model. 

   Sigma: for the equal variance model "EEE". A _d_ by _d_ matrix
          giving the common covariance for all components of the
          mixture model. 

     pro: Mixing proportions for the components of the mixture. There
          should one more mixing proportion than the number of MVN
          components if the mixture model includes a  Poisson noise
          term.  

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

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

    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 'pro' includes an additional mixing
          proportion for a noise component.  

     ...: Other arguments to describe the variance, in particular
          'decomp', 'sigma' or 'cholsigma' for model "VVV", 'decomp'
          for models "VII" and "EII", and 'Sigma' or 'cholSigma' for
          model "EEE".  'Sigma' is an _d_ by _d_ matrix giving the
          common covariance for all components of the mixture model.

          Also used to catch unused arguments from a 'do.call' call. 

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

     This function can be used with an indirect or list call using
     'do.call', allowing the output of e.g. 'mstep' to be passed
     without the need to specify individual parameters as arguments.

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

     A list including the following components: 

       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.   

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

modelName: Character string identifying the model. 

             *  '"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_.  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:

     'estep', 'em', 'mstep', 'do.call', 'mclustOptions'

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

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

     msEst <- mstepEII(data = irisMatrix, z = unmap(irisClass))
     names(msEst)

     estepEII(data = irisMatrix, mu = msEst$mu, pro = msEst$pro, 
              sigmasq = msEst$sigmasq)
     ## Not run: 
     do.call("estepEII", c(list(data=irisMatrix), msEst)) ## alternative call
     ## End(Not run)

