Description Usage Arguments Value Author(s) References

CDpca performs a clustering and disjoint principal components analysis (CDPCA) on the given numeric data matrix and returns a list of results Given a (IxJ) real data matrix X = [xij], the CDPCA methodology is allowed to cluster the I objects into P nonempty and nonoverlapping clusters Cp, p = 1,...,P, which are identified by theirs centroids, and, simultaneously, to partitioning the J attributes into Q disjoint components, PCq, q = 1,...,Q. The CDpca function models X estimating the parameter of the model using an Alternating Least Square (ALS) procedure originally proposed by Vichi and Saport (2009) and described in two steps by Macedo and Freitas (2015).

1 |

`data` |
A numeric matrix or data frame which provides the data for the CDPCA |

`class` |
A numeric vector containing the real classification of the objects in the data, or NULL if the class of objects is unknown |

`P` |
An integer value indicating the number of clusters of objects |

`Q` |
An integer value indicating the number of clusters of variables |

`SDPinitial` |
A logical value indicating whether the initial assignment matrices U and V are randomly generated (by default) or an algorithmic framework based on a semidefinite programming approach is preferred (TRUE) |

`tol` |
A positive (low) value indicating the maximum term for the difference between two consecutives values of the objective function. A tolerance value of 10^(-5) is indicated by default |

`maxit` |
The maximum number of iterations of one run of the ALS algorithm |

`r` |
Number of runs of the ALS algorithm for the final solution |

`cdpcaplot` |
A logical value indicating whether an additional graphic is created (showing the data projected on the first two CDPCA principal components) |

Cdpca returns a list of results containing the following components:

`Iter` |
The total number of iterations used in the best loop for computing the best solution |

`loop` |
The best loop number |

`timebestloop` |
The computation time on the best loop |

`timeallloops` |
The computation time for all loops |

`Y` |
The component score matrix |

`Ybar` |
The object centroids matrix in the reduced space |

`A` |
The component loading matrix |

`U` |
The partition of objects |

`V` |
The partition of variables |

`F` |
The value of the objective function to maximize |

`bcdev` |
The between cluster deviance |

`bcdevTotal` |
The between cluster deviance over the total variability |

`tableclass` |
The cdpca classification |

`pseudocm` |
The pseudo confusion matrix concerning the true (given by class) and cdpca classifications |

`Enorm` |
The error norm for the obtained cdpca model |

Eloisa Macedo macedo@ua.pt, Adelaide Freitas adelaide@ua.pt, Maurizio Vichi maurizio.vichi@uniroma1.it

Vichi, M and Saporta, G. (2009). Clustering and disjoint principal component analysis.

*Computational Statistics and Data Analysis*, 53, 3194-3208.Macedo, E. and Freitas, A. (2015). The alternating least-squares algorithm for CDPCA.

*Communications in Computer and Information Science (CCIS), Springer Verlag pp. 173-191*.

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