PCAn                  package:PTAk                  R Documentation

_P_r_i_n_c_i_p_a_l _C_o_m_p_o_n_e_n_t _A_n_a_l_y_s_i_s _o_n _n _m_o_d_e_s

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

     Performs the Tuckern model using a space version of RPVSCC
     (`SINGVA').

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

      PCAn(X,dim=c(2,2,2,3),test=1E-12,Maxiter=400,
                   smoothing=FALSE,smoo=list(NA),
                     verbose=getOption("verbose"),file=NULL,
                       modesnam=NULL,addedcomment="")

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

       X: a tensor (as an array) of order k, if non-identity metrics
          are used `X' is a list with `data'  as the array and `met' a
          list of metrics

     dim: a vector of  numbers specifying the dimensions in each space 

    test: control of convergence

 Maxiter: maximum number of iterations allowed for convergence

smoothing: see `SVDgen'

    smoo: see `PTA3'

 verbose: control printing

    file: output printed at the prompt if `NULL', or printed in the
          given  `file'

modesnam: character vector of the names of the modes, if `NULL' "`mo
          1'" ..."`mo k'"

addedcomment: character string printed after the title of the analysis

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

     Looking for the best rank-one tensor approximation (LS) the three
     methods described in the package are equivalent. If the number of
     tensors looked for is greater then one the  methods differs:
     PTA-kmodes will look for best approximation according to the
     orthogonal rank (i.e. the rank-one tensors are orthogonal),
     PCA-kmodes will look for best approximation according to the space
     ranks (i.e. the rank of every bilinear form, that is the number of
     components in each space), PARAFAC/CANDECOMP will look for best
     approximation according to the rank (i.e. the rank-one tensors are
     not necessarily orthogonal). For the sake of comparisons the
     PARAFAC/CANDECOMP method and the PCA-nmodes are also in the 
     package but complete functionnality  of the use these methods  and
     more complete packages may be fetched at the www site quoted
     below.

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

     a `solutions.PCAn' (inherits `solutions.PTAk') object

_N_o_t_e:

     The use of metrics (diagonal or not) and smoothing extend
     flexibility of analysis.

_A_u_t_h_o_r(_s):

     Didier Leibovici didier@fmrib.ox.ac.uk

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

     Caroll J.D  and Chang J.J (1970) Analysis of individual
     differences in multidimensional   scaling via n-way generalization
     of "Eckart-Young" decomposition. Psychometrika 35,283-319.

     Harshman R.A (1970) Foundations of the PARAFAC procedure: models
     and conditions for "an explanatory" multi-mode factor analysis.
     UCLA Working Papers in Phonetics, 16,1-84.

     Kroonenberg P (1983) Three-mode Principal Component Analysis:
     Theory and Applications. DSWO press. Leiden.(related references in
     <URL: http://www.fsw.leidenuniv.nl/~kroonenb/>)

     Leibovici D and Sabatier R (1998) A Singular Value Decomposition
     of a k-ways array for a Principal Component Analysis of multi-way
     data, the PTA-k. Linear Algebra and its Applications, 269:307-329.

