sparseLDA (version 0.1-7)

sda: Sparse discriminant analysis

Description

Performs sparse linear discriminant analysis. Using an alternating minimization algorithm to minimize the SDA criterion.

Usage

sda(x, ...)
"sda"(x, y, lambda = 1e-6, stop = -p, maxIte = 100, Q = K-1, trace = FALSE, tol = 1e-6, ...)

Arguments

x

A matrix of the training data with observations down the rows and variables in the columns.

y

A matrix initializing the dummy variables representing the groups.

lambda

The weight on the L2-norm for elastic net regression. Default: 1e-6.

stop

If STOP is negative, its absolute value corresponds to the desired number of variables. If STOP is positive, it corresponds to an upper bound on the L1-norm of the b coefficients. There is a one to one correspondence between stop and t. The default is -p (-the number of variables).

maxIte

Maximum number of iterations. Default: 100.

Q

Number of components. Maximum and default is K-1 (the number of classes less one).

trace

If TRUE, prints out its progress. Default: FALSE.

tol

Tolerance for the stopping criterion (change in RSS). Default is 1e-6.

...

additional arguments

Value

beta

The loadings of the sparse discriminative directions.

theta

The optimal scores.

rss

A vector of the Residual Sum of Squares at each iteration.

varNames

Names on included variables

.

Details

The function finds sparse directions for linear classification.

References

Clemmensen, L., Hastie, T. Witten, D. and Ersboell, K. (2011) "Sparse discriminant analysis", Technometrics, To appear.

See Also

normalize, normalizetest, smda

Examples

## load data
data(penicilliumYES)

X <- penicilliumYES$X
Y <- penicilliumYES$Y
colnames(Y) <- c("P. Melanoconidium",
                 "P. Polonicum",
                 "P. Venetum")

## test samples
Iout<-c(3,6,9,12)
Iout<-c(Iout,Iout+12,Iout+24)

## training data
Xtr<-X[-Iout,]
k<-3
n<-dim(Xtr)[1]

## Normalize data
Xc<-normalize(Xtr)
Xn<-Xc$Xc
p<-dim(Xn)[2]

## Perform SDA with one non-zero loading for each discriminative
## direction with Y as matrix input
out <- sda(Xn, Y,
           lambda = 1e-6,
           stop = -1,
           maxIte = 25,
           trace = TRUE)

## predict training samples
train <- predict(out, Xn)

## testing
Xtst<-X[Iout,]
Xtst<-normalizetest(Xtst,Xc)

test <- predict(out, Xtst)
print(test$class)

## Factor Y as input
Yvec <- factor(rep(colnames(Y), each = 8))
out2 <- sda(Xn, Yvec,
            lambda = 1e-6,
            stop = -1,
            maxIte = 25,
            trace = TRUE)