Description Usage Arguments Details Value Note Author(s) References

Performs the identical models known as PARAFAC or CANDECOMP model.

1 2 3 4 |

`X` |
a tensor (as an array) of order |

`dim` |
a number specifying the number of rank-one tensors |

`test` |
control of convergence |

`Maxiter` |
maximum number of iterations allowed for convergence |

`smoothing` |
see |

`smoo` |
see |

`verbose` |
control printing |

`file` |
output printed at the prompt if |

`modesnam` |
character vector of the names of the modes, if |

`addedcomment` |
character string printed after the title of the analysis |

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-*k*modes will look for best approximation according to the
*orthogonal rank* (*i.e.* the rank-one tensors are
orthogonal), PCA-*k*modes 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-*n*modes 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.

a `CANDPARA`

(inherits from `PTAk`

) object

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
*k*modes solution but obviously with unecessary computations.

Didier G. Leibovici

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
http://three-mode.leidenuniv.nl)

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.

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