Description Usage Arguments Details Value Author(s) References See Also Examples

Performs functional principal component analysis of probability densities in order to describe a data folder, consisting of *T* groups of individuals on which are observed *p* variables. It returns an object of class `fpcad`

.

1 2 3 4 5 |

`xf` |
object of class Notice that for the versions earlier than 2.0, fpcad applied to a data frame. |

`gaussiand` |
logical. If |

`kern` |
string. If |

`windowh` |
either a list of |

`normed` |
logical. If |

`centered` |
logical. If |

`data.centered` |
logical. If |

`data.scaled` |
logical. If |

`common.variance` |
logical. If |

`nb.factors` |
numeric. Number of returned principal scores (default Warning: The |

`nb.values` |
numerical. Number of returned eigenvalues (default |

`sub.title` |
string. If provided, the subtitle for the graphs. |

`plot.eigen` |
logical. If |

`plot.score` |
logical. If |

`nscore` |
numeric vector. If |

`group.name` |
string. Name of the grouping variable. Default: |

`filename` |
string. Name of the file in which the results are saved. By default ( |

The *T* probability densities *f_t* corresponding to the *T* groups of individuals are either parametrically estimated (`gaussiand = TRUE`

) or estimated using the Gaussian kernel method (`gaussiand = FALSE`

). In the latter case, the `windowh`

argument provides the list of the bandwidths to use. Notice that in the multivariate case (*p*>1) the bandwidths are positive-definite matrices.

If `windowh`

is a numerical value, the matrix bandwidth is of the form *h S*, where *S* is either the square root of the covariance matrix (*p*>1) or the standard deviation of the estimated density.

If `windowh = NULL`

(default), *h* in the above formula is computed using the `bandwidth.parameter`

function.

Returns an object of class `fpcad`

, that is a list including:

`inertia ` |
data frame of the eigenvalues and percentages of inertia. |

`contributions ` |
data frame of the contributions to the first |

`qualities ` |
data frame of the qualities on the first |

`scores ` |
data frame of the first |

`norm ` |
vector of the |

`means ` |
list of the means. |

`variances ` |
list of the covariance matrices. |

`correlations ` |
list of the correlation matrices. |

`skewness ` |
list of the skewness coefficients. |

`kurtosis ` |
list of the kurtosis coefficients. |

Rachid Boumaza, Pierre Santagostini, Smail Yousfi, Gilles Hunault, Sabine Demotes-Mainard

Boumaza, R. (1998). Analyse en composantes principales de distributions gaussiennes multidimensionnelles. Revue de Statistique Appliqu<e9>e, XLVI (2), 5-20.

Boumaza, R., Yousfi, S., Demotes-Mainard, S. (2015). Interpreting the principal component analysis of multivariate density functions. Communications in Statistics - Theory and Methods, 44 (16), 3321-3339.

Delicado, P. (2011). Dimensionality reduction when data are density functions. Computational Statistics & Data Analysis, 55, 401-420.

Yousfi, S., Boumaza, R., Aissani, D., Adjabi, S. (2014). Optimal bandwith matrices in functional principal component analysis of density functions. Journal of Statistical Computation and Simulation, 85 (11), 2315-2330.

print.fpcad, plot.fpcad, interpret.fpcad, bandwidth.parameter

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
data(roses)
# Case of a normed non-centred PCA of Gaussian densities (on 3 architectural
# characteristics of roses: shape (Sha), foliage density (Den) and symmetry (Sym))
rosesf <- as.folder(roses[,c("Sha","Den","Sym","rose")])
result3 <- fpcad(rosesf, group.name = "rose")
print(result3)
plot(result3)
# Flower colors of the roses
scores <- result3$scores
scores <- data.frame(scores, color = scores$rose)
levels(scores$color) <- c(A = "yellow", B = "yellow", C = "pink", D = "yellow", E = "red",
F = "yellow", G = "pink", H = "pink", I = "yellow", J = "yellow")
# Scores according to the first two principal components, per color
plot(scores$PC.1, scores$PC.2, pch = 19, col = as.character(scores$color), cex = 1.5)
``` |

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