CANDPARA                package:PTAk                R Documentation

_C_A_N_o_n_i_c_a_l _D_E_C_O_M_P_o_s_i_t_i_o_n _a_n_a_l_y_s_i_s _a_n_d _P_A_R_A_l_l_e_l _F_A_C_t_o_r _a_n_a_l_y_s_i_s

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

     Performs the identical models known as PARAFAC or CANDECOMP model.

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

     CANDPARA(X,dim=3,test=1E-8,Maxiter=1000,
                          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 number specifying the number of rank-one tensors 

    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 ranks of all (simple) bilinear forms , 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 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 checked at the www site quoted
     below.

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

     a `solutions.CANDPARA' (inherits from `solutions.PTAk') object

_N_o_t_e:

     The use of metrics (diagonal or not) and smoothing extends
     flexibility of analysis. This program runs slow! A PARAFAC
     orthogonal can be done with PTAk looking only for k-modes
     Principal Tensors i.e. with the options `nbPT=c(rep(0,k-2),dim),
     nbPT2=0'. It is identical to look in any `PTAk' decomposition only
     for the kmodes solution but obviously with unecessary
     computations.

_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.

