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

group.name 
string.

gaussiand 
logical. If 
windowh 
either a list of T bandwidths (one per density associated to a group), or a strictly positive number. If 
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 
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 positivedefinite 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 L^2 norms of the densities. 
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 DemotesMainard
Boumaza, R. (1998). Analyse en composantes principales de distributions gaussiennes multidimensionnelles. Revue de Statistique Appliqu?e, XLVI (2), 520.
Boumaza, R., Yousfi, S., DemotesMainard, S. (2015). Interpreting the principal component analysis of multivariate density functions. Communications in Statistics  Theory and Methods, 44 (16), 33213339.
Delicado, P. (2011). Dimensionality reduction when data are density functions. Computational Statistics & Data Analysis, 55, 401420.
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), 23152330.
print.fpcad, plot.fpcad, interpret.fpcad, bandwidth.parameter
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23  data(roses)
# Case of a normed noncentred 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)
# Applied to a data frame:
result3df < fpcad(roses[,c("Sha","Den","Sym","rose")], group.name = "rose")
print(result3df)
plot(result3df)
# Flower colors of the roses
scores < result3$scores
scores < data.frame(scores, color = scores$rose, stringsAsFactors = TRUE)
colours < scores$rose
colours < factor(c(A = "yellow", B = "yellow", C = "pink", D = "yellow", E = "red",
F = "yellow", G = "pink", H = "pink", I = "yellow", J = "yellow"))
levels(scores$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(result3, nscore = 1:2, color = colours)

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