rqda {MBCbook}

Robust (quadratic) discriminant analysis

Description

Robust (quadratic) discriminant analysis implements a discriminant analysis method which is robust to label noise. This function implements the method described in Lawrence and Scholkopf (2003, ISBN:1-55860-778-1).

Usage

rqda(X,lbl,Y,maxit=50,disp=FALSE,...)

Arguments

X

a data frame containing the learning observations.

lbl

the class labels of the learning observations.

Y

a data frame containing the new observations to classify.

maxit

the maximum number of iterations.

disp

logical, if TRUE, several plots are displayed.

...

additional arguments to provide to subfunctions.

Value

A list is returned with the following elements:

nu

the estimated class proportions.

mu

the estimated class means.

S

the estimated covariance matrices.

gamma

the estimated purity level of the labels.

Ti

the posterior probabilties of the labels knowing the observed labels for the learning observations.

Pi

the class posterior probabilities of the observations to classify.

cls

the class assignments of the observations to classify.

ll

the log-likelihood value.

Author(s)

C. Bouveyron

References

Lawrence, N., and Scholkopf, B., Estimating a kernel Fisher discriminant in the presence of label noise, Pages 306–313 of: Proceedings of the Eighteenth International Conference on Machine Learning. ICML’01. San Francisco, CA, USA, 2001 (ISBN:1-55860-778-1).

Examples

n = 50
m1 = c(0,0); m2 = 1.5*c(1,-1)
S1 = 0.1*diag(2); S2 = 0.25 * diag(2)
X = rbind(mvrnorm(n,m1,S1),mvrnorm(2*n,m2,S2))
cls = rep(1:2,c(n,2*n))

# Label perturbation
ind = rbinom(3*n,1,0.4); lb = cls
lb[ind==1 & cls==1] = 2
lb[ind==1 & cls==2] = 1

# Classification with RQDA
res = rqda(X,lb,X)
table(cls,res$cls)