sigma2decomp             package:mclust             R Documentation

_C_o_n_v_e_r_t _m_i_x_t_u_r_e _c_o_m_p_o_n_e_n_t _c_o_v_a_r_i_a_n_c_e_s _t_o _d_e_c_o_m_p_o_s_i_t_i_o_n _f_o_r_m.

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

     Converts a set of covariance matrices from representation as a 3-D
     array  to a parameterization by eigenvalue decomposition.

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

     sigma2decomp(sigma, G, tol, ...)

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

   sigma: Either a 3-D array whose [,,k]th component is the covariance
          matrix for the kth component in an MVN mixture model, or a
          single covariance matrix in the case that all components have
          the same covariance. 

       G: The number of components in the mixture. When  'sigma' is a
          3-D array, the number of components can be inferred from its
          dimensions. 

     tol: Tolerance for determining whether or not the covariances have
          equal volume, shape, and or orientation. The default is the
          square root of the relative machine precision,
          'sqrt(.Machine\$double.eps)',  which is about '1.e-8'. 

     ...: Catch unused arguments from a 'do.call' call. 

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

     The covariance matrices for the mixture components in
     decomposition form, including the following components:  

       d: The dimension of the data.  

       G: The number of components in the mixture model.  

   scale: Either a _G_-vector giving the scale of the covariance (the
          _d_th root of its determinant) for each component in the
          mixture model, or a single numeric value if the scale is the
          same for each component. 

   shape: Either a _G_ by _d_ matrix in which the _k_th column is the
          shape of the covariance matrix (normalized to have
          determinant 1) for the _k_th component, or a _d_-vector
          giving a common shape for all components.  

orientation: Either a _d_ by _d_ by _G_ array whose '[,,k]'th entry is
          the orthonomal matrix of eigenvectors of the covariance
          matrix of the _k_th component, or a _d_ by _d_ orthonormal
          matrix if the mixture components have a common orientation.
          The 'orientation' component of 'decomp' can be omitted in
          spherical and diagonal models, for which the principal
          components are parallel to the coordinate axes so that the
          orientation matrix is the identity.   

_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:

     'decomp2sigma'

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

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

     meEst <- meEEE(irisMatrix, unmap(irisClass)) 
     names(meEst)
     meEst$sigma

     sigma2decomp(meEst$sigma)
     ## Not run: 
     do.call("sigma2decomp", meEst)  ## alternative call
     ## End(Not run)

