Robust Linear Discriminant Analysis
Robust linear discriminant analysis based on MCD and returns
the results as an object of class Linda (aka constructor).
Linda(x, ...)
## Default S3 method:
Linda(x, grouping, prior = proportions, tol = 1.0e-4,
method = c("mcd", "mcdA", "mcdB", "mcdC", "fsa", "mrcd", "ogk"),
alpha=0.5, l1med=FALSE, cov.control, trace=FALSE, ...)x |
a matrix or data frame containing the explanatory variables (training set). |
grouping |
grouping variable: a factor specifying the class for each observation. |
prior |
prior probabilities, default to the class proportions for the training set. |
tol |
tolerance |
method |
method |
alpha |
this parameter measures the fraction of outliers the algorithm should resist. In MCD alpha controls the size of the subsets over which the determinant is minimized, i.e. alpha*n observations are used for computing the determinant. Allowed values are between 0.5 and 1 and the default is 0.5. |
l1med |
whether to use L1 median (space median) instead of MCD to compute
the group means locations in order to center the data in methods |
cov.control |
specifies which covariance estimator to use by providing
a |
.
trace |
whether to print intermediate results. Default is |
... |
arguments passed to or from other methods |
details
Returns an S4 object of class Linda
Valentin Todorov valentin.todorov@chello.at
Hawkins, D.M. and McLachlan, G.J. (1997) High-Breakdown Linear Discriminant Analysis, Journal of the American Statistical Association, 92, 136–143.
Todorov V. (2007) Robust selection of variables in linear discriminant analysis, Statistical Methods and Applications, 15, 395–407, doi:10.1007/s10260-006-0032-6.
Todorov, V. and Pires, A.M. (2007) Comparative Performance of Several Robust Linear Discriminant Analysis Methods. REVSTAT Statistical Journal, 5, p 63–83. URL http://www.ine.pt/revstat/pdf/rs070104.pdf.
Todorov V and Filzmoser P (2009), An Object Oriented Framework for Robust Multivariate Analysis. Journal of Statistical Software, 32(3), 1–47. URL http://www.jstatsoft.org/v32/i03/.
## Example anorexia library(MASS) data(anorexia) ## start with the classical estimates lda <- LdaClassic(Treat~., data=anorexia) predict(lda)@classification ## try now the robust LDA with the default method (MCD with pooled whitin cov matrix) rlda <- Linda(Treat~., data= anorexia) predict(rlda)@classification ## try the other methods Linda(Treat~., data= anorexia, method="mcdA") Linda(Treat~., data= anorexia, method="mcdB") Linda(Treat~., data= anorexia, method="mcdC") ## try the Hawkins&McLachlan method ## use the default method grp <- anorexia[,1] grp <- as.factor(grp) x <- anorexia[,2:3] Linda(x, grp, method="fsa") ## Do DA with Linda and method mcdB or mcdC, when some classes ## have very few observations. Use L1 median instead of MCD ## to compute the group means (l1med=TRUE). data(fish) # remove observation #14 containing missing value fish <- fish[-14,] # The height and width are calculated as percentages # of the third length variable fish[,5] <- fish[,5]*fish[,4]/100 fish[,6] <- fish[,6]*fish[,4]/100 table(fish$Species) Linda(Species~., data=fish, l1med=TRUE) Linda(Species~., data=fish, method="mcdC", l1med=TRUE)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.