Applies alternating direction methods of multipliers algorithm to the optimal scoring formulation of sparse discriminant analysis proposed by Clemmensen et al. 2011.
SDAD(Xt, ...)# S3 method for default
SDAD(
Xt,
Yt,
Om,
gam,
lam,
mu,
q,
PGsteps,
PGtol,
maxits,
tol,
selector = rep(1, dim(Xt)[2]),
initTheta,
...
)
SDAD returns an object of class "SDAD" including a list
with the following named components: (More will be added later to handle the predict function)
callThe matched call.
Bp by q matrix of discriminant vectors.
QK by q matrix of scoring vectors.
subitsTotal number of iterations in proximal gradient subroutine.
totalitsNumber coordinate descent iterations for all discriminant vectors
NULL
n by p data matrix, (not a data frame, but a matrix)
n by K matrix of indicator variables (Yij = 1 if i in class j). This will later be changed to handle factor variables as well. Each observation belongs in a single class, so for a given row/observation, only one element is 1 and the rest is 0.
p by p parameter matrix Omega in generalized elastic net penalty.
Regularization parameter for elastic net penalty.
Regularization parameter for l1 penalty, must be greater than zero.
Penalty parameter for augmented Lagrangian term, must be greater than zero.
Desired number of discriminant vectors.
Maximum number if inner proximal gradient algorithm for finding beta.
Two stopping tolerances for inner ADMM method, first is absolute tolerance, second is relative.
Number of iterations to run
Stopping tolerance for proximal gradient algorithm.
Vector to choose which parameters in the discriminant vector will be used to calculate the regularization terms. The size of the vector must be *p* the number of predictors. The default value is a vector of all ones. This is currently only used for ordinal classification.
Initial first theta, default value is a vector of ones.
SDADcv, SDAAP and SDAP