Predicting the class of a group of individuals with discriminant analysis of probability densities.
Description
Allocates several groups of individuals, one group after another, to one class of groups (among K classes of groups) using the L^2 distances between the density function associated to the group to allocate and the density functions associated to the K classes.
Usage
1 2  fdiscd.predict(x, classe, crit = 1, gaussiand = TRUE, kern = NULL, windowh = NULL,
misclass.ratio = FALSE)

Arguments
x 
data frame with (p+1) columns. The first p columns are numeric. The last column is a factor with T levels defining T groups. Each group, say t, consists of n_t individuals. 
classe 
data frame with two columns. The first column contains the names of the T groups (all the names must be different). The second column is a factor with K levels partitionning the T groups into K classes. 
crit 
1, 2 or 3. In order to select the densities associated to the classes. See Details. 
gaussiand 
logical. If 
kern 
string. If 
windowh 
strictly positive number. If 
misclass.ratio 
logical (default 
Details
To the group t is associated the density denoted f_t. To the class k consisting of T_k groups is associated the density denoted g_k. The crit
argument selects the estimation method of the K densities g_k.

The density g_k is estimated using the whole data of this class, that is the rows of
x
corresponding to the T_k groups of the class k. 
The T_k densities f_t are estimated using the corresponding data from
x
. Then they are averaged to obtain an estimation of the density g_k, that is g_k = (1/T_k)∑{f_t}. 
Each previous density f_t is weighted by n_t (the number of rows of x corresponding to f_t). Then they are averaged, that is g_k = (1/∑ n_t) ∑ n_t f_t.
Value
Returns an object of class fdiscd.predict
, that is a list including:
prediction 
data frame with 3 columns:

distances 
matrix with T rows and K columns, of the distances (d_{tk}): d_{tk} is the distance between the group t and the class k, 
proximities 
matrix of the proximities (in percents). The proximity of a group t to the class k is computed as so: (1/d_{tk})/∑_{l=1}^{l=K}(1/d_{tl}). 
confusion.mat 
the confusion matrix (if 
misclassed 
the misclassification ratio (if 
Author(s)
Rachid Boumaza, Pierre Santagostini, Smail Yousfi, Sabine DemotesMainard.
References
Boumaza, R. (2004). Discriminant analysis with independently repeated multivariate measurements: an L^2 approach. Computational Statistics & Data Analysis, 47, 823843.
Rudrauf, J.M., Boumaza, R. (2001). Contribution <e0> l'<e9>tude de l'architecture m<e9>di<e9>vale: les caract<e9>ristiques des pierres <e0> bossage des ch<e2>teaux forts alsaciens. Centre de Recherches Arch<e9>ologiques M<e9>di<e9>vales de Saverne, 5, 538.
Examples
1 2 3 4 5 6 7 8 9 10  data(castles.dated)
data(castles.nondated)
castles.stones < rbind(castles.dated$stones, castles.nondated$stones)
castles.periods < rbind(castles.dated$periods, castles.nondated$periods)
# The densities are supposed Gaussian and parametrically estimated
result1 < fdiscd.predict(castles.stones, castles.periods)
print(result1)
