The function implements a Principal components analysis of histogram variable based on Wasserstein distance. It performs a centered (not standardized) PCA on a set of quantiles of a variable. Being a distribution a multivalued description, the analysis performs a dimensional reduction and a visualization of distributions. It is a 1d (one dimension) becuse it is considered just one histogram variable.

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`data` |
A MatH object (a matrix of distributionH). |

`var` |
An integer, the variable number. |

`quantiles` |
An integer, it is the number of quantiles used in the analysis. |

`plots` |
a logical value. Default=TRUE plots are drawn. |

`listaxes` |
A vector of integers listing the axis for the 2d factorial reperesntations. |

`axisequal` |
A logical value. Default TRUE, the plot have the same scale for the x and the y axes. |

`qcut` |
a number between 0.5 and 1, it is used for the representation of densities for avoiding very peaked densities in the plot. Default=1, all the densities are considered. |

In the framework of symbolic data analysis (SDA), distribution-valued data are defined as multivalued data, where each unit is described by a distribution (e.g., a histogram, a density, or a quantile function) of a quantitative variable. SDA provides different methods for analyzing multivalued data. Among them, the most relevant techniques proposed for a dimensional reduction of multivalued quantitative variables is principal component analysis (PCA). This paper gives a contribution in this context of analysis. Starting from new association measures for distributional variables based on a peculiar metric for distributions, the squared Wasserstein distance, a PCA approach is proposed for distribution-valued data, represented by quantile-variables.

a list with the results of the PCA in the MFA format of package FactoMineR for function MFA

Verde, R.; Irpino, A.; Balzanella, A., "Dimension Reduction Techniques for Distributional Symbolic Data," Cybernetics, IEEE Transactions on , vol.PP, no.99, pp.1,1 doi: 10.1109/TCYB.2015.2389653 keywords: Correlation;Covariance matrices;Distribution functions;Histograms;Measurement;Principal component analysis;Shape;Distributional data;Wasserstein distance;principal components analysis;quantiles, http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=7024099&isnumber=6352949

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