# corePCA

### Description

corePCA performs the core of principal components analysis (PCA), generalized PCA (GPCA), multidimensionsal scaling (MDS), and related techniques.

### Usage

1 |

### Arguments

`DATA` |
original data to decompose and analyze via the singular value decomposition. |

`M` |
a vector or diagonal matrix with masses for the rows (observations). If NULL, one is created or the plain SVD is used. |

`W` |
a vector or diagonal matrix with weights for the columns (measures). If NULL, one is created or the plain SVD is used. |

`decomp.approach` |
string. A switch for different decompositions (typically for speed). See |

`k` |
number of components to return (this is not a rotation, just an |

### Details

This function should not be used directly. Please use `epPCA`

or `epGPCA`

unless you plan on writing extensions to ExPosition.

### Value

Returns a large list of items which are also returned in `epPCA`

and `epGPCA`

(the help files for those functions will refer to this as well).

All items with a letter followed by an *i* are for the *I* rows of a DATA matrix. All items with a letter followed by an *j* are for the *J* rows of a DATA matrix.

`fi` |
factor scores for the row items. |

`di` |
square distances of the row items. |

`ci` |
contributions (to the variance) of the row items. |

`ri` |
cosines of the row items. |

`fj` |
factor scores for the column items. |

`dj` |
square distances of the column items. |

`cj` |
contributions (to the variance) of the column items. |

`rj` |
cosines of the column items. |

`t` |
the percent of explained variance per component (tau). |

`eigs` |
the eigenvalues from the decomposition. |

`pdq` |
the set of left singular vectors (pdq$p) for the rows, singular values (pdq$Dv and pdq$Dd), and the set of right singular vectors (pdq$q) for the columns. |

`X` |
the final matrix that was decomposed (includes scaling, centering, masses, etc...). |

### Author(s)

Derek Beaton and HervĂ© Abdi.

### References

Abdi, H., and Williams, L.J. (2010). Principal component analysis. *Wiley Interdisciplinary Reviews: Computational Statistics*, 2, 433-459.

Abdi, H. (2007). Singular Value Decomposition (SVD) and Generalized Singular Value Decomposition (GSVD). In N.J. Salkind (Ed.): *Encyclopedia of Measurement and Statistics*.Thousand Oaks (CA): Sage. pp. 907-912.

### See Also

`epPCA`

, `epGPCA`