rqda: Robust (quadratic) discriminant analysis

In MBCbook: Companion Package for the Book "Model-Based Clustering and Classification for Data Science" by Bouveyron et al. (2019, ISBN:9781108644181).

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)

Example output

Loading required package: mclust
Package 'mclust' version 5.4.7
Type 'citation("mclust")' for citing this R package in publications.
Loading required package: Rmixmod
Loading required package: Rcpp
Rmixmod v. 2.1.5 / URI: www.mixmod.org
Loading required package: MASS
Loading required package: mvtnorm

Attaching package: ‘mvtnorm’

The following object is masked from ‘package:mclust’:

    dmvnorm

..................................................   
cls   1   2
  1  49   1
  2   0 100

MBCbook documentation built on July 2, 2019, 9:08 a.m.