Principal component analysis using the alpha-transformation | R Documentation |

Principal component analysis using the *α*-transformation.

alfa.pca(x, a, center = TRUE, scale = TRUE, k = NULL, vectors = FALSE)

`x` |
A matrix with the compositional data. Zero values are allowed. In that case "a" should be positive. |

`a` |
The value of |

`center` |
Do you want your data centered? TRUE or FALSE. |

`scale` |
Do you want each of your variables scaled, i.e. to have unit variance? TRUE or FALSE. |

`k` |
If you want a specific number of eigenvalues and eigenvectors set it here, otherwise all eigenvalues (and eigenvectors if requested) will be returned. |

`vectors` |
Do you want the eigenvectors be returned? By dafault this is FALSE. |

The *α*-transformation is applied to the compositional data and then
PCA is performed. Note however, that the right multiplication by the Helmert
sub-matrix is not applied in order to be in accordance with Aitchison (1983).
When *α=0*, this results to the PCA proposed by Aitchison (1983).

A list including:

`values` |
The eigenvalues. |

`vectors` |
The eigenvectors. |

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

Aitchison J. (1986). The statistical analysis of compositional data. Chapman & Hall.

Aitchison, J. (1983). Principal component analysis of compositional data. Biometrika, 70(1), 57-65.

Tsagris M.T., Preston S. and Wood A.T.A. (2011). A data-based power transformation for compositional data. In Proceedings of the 4th Compositional Data Analysis Workshop, Girona, Spain. http://arxiv.org/pdf/1106.1451.pdf

```
logpca, alfa.pcr, kl.alfapcr
```

x <- as.matrix(iris[, 1:4]) x <- x/ rowSums(x) a <- alfa.pca(x, 0.5)

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