Description Usage Arguments Details Value Author(s) References See Also Examples
HDMDA implements mixture discriminant analysis (MDA, Hastie & Tibshirani, 1996) with HD Gaussians instead of full Gaussians. Each class is assumed to be made of several classspecific groups in which the data live in lowdimensional subspaces. From a technical point of view, a clustering is done using hddc
in each class.
1 
X 
A matrix or a data frame of observations, assuming the rows are the observations and the columns the variables. Note that NAs are not allowed. 
cls 
The vector of the class of each observations, its type can be numeric or string. 
K 
A vector of integers specifying the number of clusters for which the BIC and the parameters are to be calculated; the function keeps the parameters which maximises the BIC. Note that the length of the vector K can't be larger than 20. Default is 1:10. 
model 
A character string vector, or an integer vector indicating the models to be used. The available models are: "AkjBkQkDk" (default), "AkBkQkDk", "ABkQkDk", "AkjBQkDk", "AkBQkDk", "ABQkDk", "AkjBkQkD", "AkBkQkD", "ABkQkD", "AkjBQkD", "AkBQkD", "ABQkD", "AjBQD", "ABQD". It is not case sensitive and integers can be used instead of names, see details for more information. Several models can be used, if it is, only the results of the one which maximizes the BIC criterion is kept. To run all models, use model="ALL". 
show 
Use show = TRUE to display some information related to the clustering. 
... 
Any argument that can be used by the function 
Some information on the signification of the model names:
if Akj: each class has its parameters and there is one parameter for each dimension
if Ak: the classes have different parameters but there is only one per class
if Aj: all the classes have the same parameters for each dimension (it's a particular case with a common orientation matrix)
if A: all classes have the same one parameter
If Bk: each class has its proper noise
if B: all classes have the same noise
if Qk: all classes have its proper orientation matrix
if Q: all classes have the same orientation matrix
if Dk: the dimensions are free and proper to each class
if D: the dimension is common to all classes
The model “all” will compute all the models, give their BIC and keep the model with the highest BIC value. Instead of writing the model names, they can also be specified using an integer. 1 represents the most general model (“AkjBkQkDk”) while 14 is the most constrained (“ABQD”), the others number/name matching are given below:
AkjBkQkDk  1  AkjBkQkD  7  
AkBkQkDk  2  AkBkQkD  8  
ABkQkDk  3  ABkQkD  9  
AkjBQkDk  4  AkjBQkD  10  
AkBQkDk  5  AkBQkD  11  
ABQkDk  6  ABQkD  12  
AjBQD  13  ABQD  14 
hdmda
returns an 'hdmda' object which is a list containing:
alpha 
Estimated prior probabilities for the classes. 
prms 
Estimated mixture parameters for each class. 
kname 
The name (level) of each class. 
Laurent Berge, Charles Bouveyron and Stephane Girard
C. Bouveyron and C. Brunet (2014), “Modelbased clustering of highdimensional data: A review”, Computational Statistics and Data Analysis, vol. 71, pp. 5278.
Bouveyron, C. Girard, S. and Schmid, C. (2007), “High Dimensional Discriminant Analysis”, Communications in Statistics: Theory and Methods, vol. 36 (14), pp. 26072623.
Bouveyron, C. Celeux, G. and Girard, S. (2011), “Intrinsic dimension estimation by maximum likelihood in probabilistic PCA”, Pattern Recognition Letters, vol. 32 (14), pp. 17061713.
Berge, L. Bouveyron, C. and Girard, S. (2012), “HDclassif: An R Package for ModelBased Clustering and Discriminant Analysis of HighDimensional Data”, Journal of Statistical Software, 46(6), pp. 129, url: http://www.jstatsoft.org/v46/i06/.
Hastie, T., & Tibshirani, R. (1996), “Discriminant analysis by Gaussian mixtures”, Journal of the Royal Statistical Society, Series B (Methodological), pp. 155176.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23  # Load the Wine data set
data(wine)
cls = wine[,1]; X = scale(wine[,1])
# A simple use...
out = hdmda(X[1:100,],cls[1:100])
res = predict(out,X[101:nrow(X),])
# Comparison between hdmda and hdda in a CV setup
set.seed(123); nb = 10; Err = matrix(NA,2,nb)
for (i in 1:nb){
cat('.')
test = sample(nrow(X),50)
out0 = lda(X[test,],cls[test])
res0 = predict(out0,X[test,])
Err[1,i] = sum(res0$class != cls[test]) / length(test)
out = hdmda(X[test,],cls[test],K=1:3,model="AKJBQKDK")
res = predict(out,X[test,])
Err[2,i] = sum(res$class != cls[test]) / length(test)
}
cat('\n')
boxplot(t(Err),names=c('LDA','HDMDA'),col=2:3,ylab="CV classifciation error",
main='CV classifciation error on Wine data')

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