dLDA: Estimate the matrix of discriminant vectors using L_1 penalty...
In irinagain/MGSDApackage: Multi-Group Sparse Discriminant Analysis

Description Usage Arguments Details Value Author(s) References Examples

View source: R/dLDA.R

Solve Multi-Group Sparse Discriminant Anlalysis problem for the supplied value of the tuning parameter lambda.

1	dLDA(xtrain, ytrain, lambda, Vinit = NULL,eps=1e-6,maxiter=1000,rho=1)

`xtrain`	A Nxp data matrix; N observations on the rows and p features on the columns.
`ytrain`	A N-vector containing the group labels. Should be coded as 1,2,...,G, where G is the number of groups.
`lambda`	Tuning parameter.
`Vinit`	A px(G-1) optional initial value for the optimization algorithm; the default value is NULL.
`eps`	Tolerance level for the convergence of the optimization algorithm; the default value is 1e-6.
`maxiter`	Maximal number of iterations for the optimization algorithm; the default value is 1000.
`rho`	A scalar that ensures the objective function is bounded from below; the default value is 1.

Solves the following optimization problem:

min_V {1/2*Tr(V'WV+rho*V'DD'V-2D'V)+lambda*sum(||v_i||_2)}.

Here W is the within-group sample covariance matrix and D is the matrix of orthogonal contrasts between the group means, both are constructed based on the supplied values of xtrain and ytrain.

When G=2, the row penalty reduces to vector L_1 penalty.

Returns a px(G-1) matrix of canonical vectors V.

Irina Gaynanova

I.Gaynanova, J.Booth and M.Wells (2016) "Simultaneous Sparse Estimation of Canonical Vectors in the p>>N setting", JASA, 111(514), 696-706.

# Example 1
n=10
p=100
G=3
ytrain=rep(1:G,each=n)
set.seed(1)
xtrain=matrix(rnorm(p*n*G),n*G,p)
V=dLDA(xtrain,ytrain,lambda=0.1)
sum(rowSums(V)!=0) # number of non-zero rows