SDAD: Sparse Discriminant Analysis solved via ADMM

In gumeo/accSDA: Accelerated Sparse Discriminant Analysis

Sparse Discriminant Analysis solved via ADMM

Description

Applies alternating direction methods of multipliers algorithm to the optimal scoring formulation of sparse discriminant analysis proposed by Clemmensen et al. 2011.

Usage

SDAD(x, ...)

## Default S3 method:
SDAD(
  Xt,
  Yt,
  Om,
  gam,
  lam,
  mu,
  q,
  PGsteps,
  PGtol,
  maxits,
  tol,
  selector = rep(1, dim(Xt)[2]),
  initTheta,
  ...
)

Arguments

Xt	n by p data matrix, (not a data frame, but a matrix)
Yt	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.
Om	p by p parameter matrix Omega in generalized elastic net penalty.
gam	Regularization parameter for elastic net penalty.
lam	Regularization parameter for l1 penalty, must be greater than zero.
mu	Penalty parameter for augmented Lagrangian term, must be greater than zero.
q	Desired number of discriminant vectors.
PGsteps	Maximum number if inner proximal gradient algorithm for finding beta.
PGtol	Two stopping tolerances for inner ADMM method, first is absolute tolerance, second is relative.
maxits	Number of iterations to run
tol	Stopping tolerance for proximal gradient algorithm.
selector	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.
initTheta	Initial first theta, default value is a vector of ones.

Value

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)

call

The matched call.

B

p by q matrix of discriminant vectors.

Q

K by q matrix of scoring vectors.

subits

Total number of iterations in proximal gradient subroutine.

totalits

Number coordinate descent iterations for all discriminant vectors

NULL

See Also

SDADcv, SDAAP and SDAP

gumeo/accSDA documentation built on Nov. 16, 2023, 11:47 p.m.